9788:
8705:
1630:
9783:{\displaystyle {\begin{aligned}r(Y,{\hat {Y}})&={\frac {\sum _{i}(Y_{i}-{\bar {Y}})({\hat {Y}}_{i}-{\bar {Y}})}{\sqrt {\sum _{i}(Y_{i}-{\bar {Y}})^{2}\cdot \sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}}}\\&={\frac {\sum _{i}(Y_{i}-{\hat {Y}}_{i}+{\hat {Y}}_{i}-{\bar {Y}})({\hat {Y}}_{i}-{\bar {Y}})}{\sqrt {\sum _{i}(Y_{i}-{\bar {Y}})^{2}\cdot \sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}}}\\&={\frac {\sum _{i}}{\sqrt {\sum _{i}(Y_{i}-{\bar {Y}})^{2}\cdot \sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}}}\\&={\frac {\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}{\sqrt {\sum _{i}(Y_{i}-{\bar {Y}})^{2}\cdot \sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}}}\\&={\sqrt {\frac {\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}{\sum _{i}(Y_{i}-{\bar {Y}})^{2}}}}.\end{aligned}}}
950:
1625:{\displaystyle {\begin{aligned}\mu _{X}={}&\operatorname {\mathbb {E} } \\\mu _{Y}={}&\operatorname {\mathbb {E} } \\\sigma _{X}^{2}={}&\operatorname {\mathbb {E} } \left\right)^{2}\,\right]=\operatorname {\mathbb {E} } \left-\left(\operatorname {\mathbb {E} } \right)^{2}\\\sigma _{Y}^{2}={}&\operatorname {\mathbb {E} } \left\right)^{2}\,\right]=\operatorname {\mathbb {E} } \left-\left(\,\operatorname {\mathbb {E} } \right)^{2}\\&\operatorname {\mathbb {E} } =\operatorname {\mathbb {E} } \right)\left(Y-\operatorname {\mathbb {E} } \right)\,]=\operatorname {\mathbb {E} } -\operatorname {\mathbb {E} } \operatorname {\mathbb {E} } \,,\end{aligned}}}
5122:
5621:
18840:
14897:
6234:
6924:
52:
40:
18826:
6572:
1927:
5854:
18864:
18852:
4604:
1658:
6229:{\displaystyle f(r)={\frac {(n-2)\,\mathrm {\Gamma } (n-1)\left(1-\rho ^{2}\right)^{\frac {n-1}{2}}\left(1-r^{2}\right)^{\frac {n-4}{2}}}{{\sqrt {2\pi }}\,\operatorname {\Gamma } {\mathord {\left(n-{\tfrac {1}{2}}\right)}}(1-\rho r)^{n-{\frac {3}{2}}}}}{}_{2}\mathrm {F} _{1}{\mathord {\left({\tfrac {1}{2}},{\tfrac {1}{2}};{\tfrac {1}{2}}(2n-1);{\tfrac {1}{2}}(\rho r+1)\right)}}}
6919:{\displaystyle \pi (\rho \mid r)={\frac {\nu (\nu -1)\Gamma (\nu -1)}{{\sqrt {2\pi }}\Gamma \left(\nu +{\frac {1}{2}}\right)}}\left(1-r^{2}\right)^{\frac {\nu -1}{2}}\cdot \left(1-\rho ^{2}\right)^{\frac {\nu -2}{2}}\cdot \left(1-r\rho \right)^{\frac {1-2\nu }{2}}\operatorname {F} \left({\tfrac {3}{2}},-{\tfrac {1}{2}};\nu +{\tfrac {1}{2}};{\tfrac {1+r\rho }{2}}\right)}
13648:
5108:
4923:
8590:
3161:
2402:
12521:
1922:{\displaystyle \rho _{X,Y}={\frac {\operatorname {\mathbb {E} } -\operatorname {\mathbb {E} } \operatorname {\mathbb {E} } }{{\sqrt {\operatorname {\mathbb {E} } \left-\left(\operatorname {\mathbb {E} } \right)^{2}}}~{\sqrt {\operatorname {\mathbb {E} } \left-\left(\operatorname {\mathbb {E} } \right)^{2}}}}}.}
2828:
4279:
12340:
6516:
5216:
Several authors have offered guidelines for the interpretation of a correlation coefficient. However, all such criteria are in some ways arbitrary. The interpretation of a correlation coefficient depends on the context and purposes. A correlation of 0.8 may be very low if one is verifying a physical
4776:
Both the uncentered (non-Pearson-compliant) and centered correlation coefficients can be determined for a dataset. As an example, suppose five countries are found to have gross national products of 1, 2, 3, 5, and 8 billion dollars, respectively. Suppose these same five countries (in the same order)
71:
for each set. The correlation reflects the strength and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case the correlation coefficient is
13237:
The
Pearson "distance" defined this way assigns distance greater than 1 to negative correlations. In reality, both strong positive correlation and negative correlations are meaningful, so care must be taken when Pearson "distance" is used for nearest neighbor algorithm as such algorithm will only
12045:
14353:
It is always possible to remove the correlations between all pairs of an arbitrary number of random variables by using a data transformation, even if the relationship between the variables is nonlinear. A presentation of this result for population distributions is given by Cox & Hinkley.
112:
of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of children from a primary school to have a
Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an
12186:
3427:
13382:
13934:
11367:
8295:
4323:
The values of both the sample and population
Pearson correlation coefficients are on or between −1 and 1. Correlations equal to +1 or −1 correspond to data points lying exactly on a line (in the case of the sample correlation), or to a bivariate distribution entirely
2157:
11113:
9961:
10938:
4986:
5370:
values generated in step (2) that are larger than the
Pearson correlation coefficient that was calculated from the original data. Here "larger" can mean either that the value is larger in magnitude, or larger in signed value, depending on whether a
4820:
12809:
8342:
2948:
7146:
13143:, the range of values is reduced and the correlations on long time scale are filtered out, only the correlations on short time scales being revealed. Thus, the contributions of slow components are removed and those of fast components are retained.
12351:
11869:
10337:
2618:
12649:
4135:
737:
12052:
12202:
3833:
302:
11862:
6375:
10748:
will typically reveal a situation where lack of robustness might be an issue, and in such cases it may be advisable to use a robust measure of association. Note however that while most robust estimators of association measure
4028:
10432:
7689:
8710:
10140:
11709:
13068:
5734:
3262:
10513:
588:
7218:
12943:
7456:
4749:
For centered data (i.e., data which have been shifted by the sample means of their respective variables so as to have an average of zero for each variable), the correlation coefficient can also be viewed as the
13741:
coefficient measures the strength of dependence between a pair of variables that is not accounted for by the way in which they both change in response to variations in a selected subset of the other variables.
13643:{\displaystyle r_{\text{circular}}={\frac {\sum _{i=1}^{n}\sin(x_{i}-{\bar {x}})\sin(y_{i}-{\bar {y}})}{{\sqrt {\sum _{i=1}^{n}\sin(x_{i}-{\bar {x}})^{2}}}{\sqrt {\sum _{i=1}^{n}\sin(y_{i}-{\bar {y}})^{2}}}}}}
2100:
10248:
13796:
11256:
3617:
15391:
7917:
5563:
2547:
14779:
14598:
10646:, this is an important consideration. However, the existence of the correlation coefficient is usually not a concern; for instance, if the range of the distribution is bounded, ρ is always defined.
14333:
7273:
4406:, without changing the correlation coefficient. (This holds for both the population and sample Pearson correlation coefficients.) More general linear transformations do change the correlation: see
8699:
is zero. Thus, the sample correlation coefficient between the observed and fitted response values in the regression can be written (calculation is under expectation, assumes
Gaussian statistics)
7862:
8114:
8097:
7952:
3915:
3509:
2907:
955:
12825:
Scaled correlation is a variant of
Pearson's correlation in which the range of the data is restricted intentionally and in a controlled manner to reveal correlations between fast components in
108:; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear
10987:
5805:
6326:
9799:
11476:
11225:
5743:-distribution in the null case (zero correlation). This holds approximately in case of non-normal observed values if sample sizes are large enough. For determining the critical values for
5267:
provide a direct approach to performing hypothesis tests and constructing confidence intervals. A permutation test for
Pearson's correlation coefficient involves the following two steps:
5103:{\displaystyle \cos \theta ={\frac {\mathbf {x} \cdot \mathbf {y} }{\left\|\mathbf {x} \right\|\left\|\mathbf {y} \right\|}}={\frac {0.308}{{\sqrt {30.8}}{\sqrt {0.00308}}}}=1=\rho _{xy},}
918:
14711:
14530:
10843:
14467:
will be the identity matrix. This has to be further divided by the standard deviation to get unit variance. The transformed variables will be uncorrelated, even though they may not be
4918:{\displaystyle \cos \theta ={\frac {\mathbf {x} \cdot \mathbf {y} }{\left\|\mathbf {x} \right\|\left\|\mathbf {y} \right\|}}={\frac {2.93}{{\sqrt {103}}{\sqrt {0.0983}}}}=0.920814711.}
473:
13306:, can be applied, which will take both positive and negative correlations into consideration. The information on positive and negative association can be extracted separately, later.
10579:
10546:
13304:
5178:
13225:
8585:{\displaystyle 1={\frac {\sum _{i}(Y_{i}-{\hat {Y}}_{i})^{2}}{\sum _{i}(Y_{i}-{\bar {Y}})^{2}}}+{\frac {\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}{\sum _{i}(Y_{i}-{\bar {Y}})^{2}}}.}
15300:
3156:{\displaystyle r_{xy}={\frac {n\sum x_{i}y_{i}-\sum x_{i}\sum y_{i}}{{\sqrt {n\sum x_{i}^{2}-\left(\sum x_{i}\right)^{2}}}~{\sqrt {n\sum y_{i}^{2}-\left(\sum y_{i}\right)^{2}}}}},}
2397:{\displaystyle r_{xy}={\frac {\sum _{i=1}^{n}(x_{i}-{\bar {x}})(y_{i}-{\bar {y}})}{{\sqrt {\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}{\sqrt {\sum _{i=1}^{n}(y_{i}-{\bar {y}})^{2}}}}}}
14977:
12660:
8697:
327:
14261:
10015:
10779:
A stratified analysis is one way to either accommodate a lack of bivariate normality, or to isolate the correlation resulting from one factor while controlling for another. If
8033:
6946:
618:
7048:
7496:
18902:
12982:
8648:
8334:
222:
11765:
10791:, then calculate a correlation coefficient within each stratum. The stratum-level estimates can then be combined to estimate the overall correlation while controlling for
6984:
3210:
14195:
14142:
14083:
14024:
13971:
6541:
15168:"The British Association: Section II, Anthropology: Opening address by Francis Galton, F.R.S., etc., President of the Anthropological Institute, President of the Section"
3549:
2469:
796:
769:
411:
359:
14109:
13709:
13680:
12516:{\displaystyle \operatorname {corr} _{r}(X,Y)=\operatorname {corr} _{r}(Y,X)=\operatorname {corr} _{r}(X,bY)\neq \operatorname {corr} _{r}(X,a+bY),\quad a\neq 0,b>0.}
2576:
7347:
12196:
The reflective correlation is a variant of
Pearson's correlation in which the data are not centered around their mean values. The population reflective correlation is
873:
825:
14441:
14400:
10260:
7538:
6359:
6257:
4130:
2823:{\displaystyle r_{xy}={\frac {\sum _{i}x_{i}y_{i}-n{\bar {x}}{\bar {y}}}{{\sqrt {\sum _{i}x_{i}^{2}-n{\bar {x}}^{2}}}~{\sqrt {\sum _{i}y_{i}^{2}-n{\bar {y}}^{2}}}}},}
10965:
3701:
3671:
3250:
2940:
2610:
2150:
2006:
1968:
13098:
7574:
4274:{\displaystyle \Sigma ={\begin{bmatrix}\sigma _{X}^{2}&\rho _{X,Y}\sigma _{X}\sigma _{Y}\\\rho _{X,Y}\sigma _{X}\sigma _{Y}&\sigma _{Y}^{2}\\\end{bmatrix}}}
4100:
4059:
1653:
942:
611:
211:
10772:
approaches may give more meaningful results in some situations where bivariate normality does not hold. However the standard versions of these approaches rely on
12536:
11527:
11158:
5217:
law using high-quality instruments, but may be regarded as very high in the social sciences, where there may be a greater contribution from complicating factors.
19232:
15946:
Lai, Chun Sing; Tao, Yingshan; Xu, Fangyuan; Ng, Wing W.Y.; Jia, Youwei; Yuan, Haoliang; Huang, Chao; Lai, Loi Lei; Xu, Zhao; Locatelli, Giorgio (January 2019).
12335:{\displaystyle \operatorname {corr} _{r}(X,Y)={\frac {\operatorname {\mathbb {E} } }{\sqrt {\operatorname {\mathbb {E} } \cdot \operatorname {\mathbb {E} } }}}.}
14215:
14162:
14044:
13991:
13788:
13768:
13141:
13118:
12890:
12870:
12850:
7320:
7300:
7038:
5606:
5586:
5491:
5471:
3637:
2427:
2120:
893:
845:
431:
383:
16501:– A free web interface and R package for the statistical comparison of two dependent or independent correlations with overlapping or non-overlapping variables.
10677:
If the sample size is large and the population is not normal, then the sample correlation coefficient remains approximately unbiased, but may not be efficient.
6511:{\displaystyle f(r)={\frac {\left(1-r^{2}\right)^{\frac {n-4}{2}}}{\operatorname {\mathrm {B} } {\mathord {\left({\tfrac {1}{2}},{\tfrac {n-2}{2}}\right)}}}},}
149:
of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first
3709:
3215:
This formula suggests a convenient single-pass algorithm for calculating sample correlations, though depending on the numbers involved, it can sometimes be
10804:
12040:{\displaystyle \operatorname {cov} (x,y;w)={\frac {\sum _{i}w_{i}\cdot (x_{i}-\operatorname {m} (x;w))(y_{i}-\operatorname {m} (y;w))}{\sum _{i}w_{i}}}.}
16551:– A game where players guess how correlated two variables in a scatter plot are, in order to gain a better understanding of the concept of correlation.
10776:
of the data, meaning that there is no ordering or grouping of the data pairs being analyzed that might affect the behavior of the correlation estimate.
10348:
3922:
15778:
Davey, Catherine E.; Grayden, David B.; Egan, Gary F.; Johnston, Leigh A. (January 2013). "Filtering induces correlation in fMRI resting state data".
18895:
7583:
15747:"On the distribution of the correlation coefficient in small samples. Appendix II to the papers of "Student" and R.A. Fisher. A co-operative study"
12181:{\displaystyle \operatorname {corr} (x,y;w)={\frac {\operatorname {cov} (x,y;w)}{\sqrt {\operatorname {cov} (x,x;w)\operatorname {cov} (y,y;w)}}}.}
10756:
Statistical inference for
Pearson's correlation coefficient is sensitive to the data distribution. Exact tests, and asymptotic tests based on the
10034:
4420:
The correlation coefficient ranges from −1 to 1. An absolute value of exactly 1 implies that a linear equation describes the relationship between
3422:{\displaystyle r_{xy}={\frac {1}{n-1}}\sum _{i=1}^{n}\left({\frac {x_{i}-{\bar {x}}}{s_{x}}}\right)\left({\frac {y_{i}-{\bar {y}}}{s_{y}}}\right)}
15424:
Garren, Steven T. (15 June 1998). "Maximum likelihood estimation of the correlation coefficient in a bivariate normal model, with missing data".
11611:
12990:
5658:
17961:
5125:
This figure gives a sense of how the usefulness of a
Pearson correlation for predicting values varies with its magnitude. Given jointly normal
10684:
of the population correlation coefficient as long as the sample means, variances, and covariance are consistent (which is guaranteed when the
10438:
5820:
In the case where the underlying variables are not normal, the sampling distribution of Pearson's correlation coefficient follows a Student's
5421:
is calculated based on the resampled data. This process is repeated a large number of times, and the empirical distribution of the resampled
489:
18466:
15543:
Schmid, John Jr. (December 1947). "The relationship between the coefficient of correlation and the angle included between regression lines".
10598:
18888:
7168:
19031:
13230:
Considering that the Pearson correlation coefficient falls between , the Pearson distance lies in . The Pearson distance has been used in
12898:
7362:
18616:
13238:
include neighbors with positive correlation and exclude neighbors with negative correlation. Alternatively, an absolute valued distance,
2011:
18240:
16881:
15007:
15389:
Moriya, N. (2008). "Noise-related multivariate optimal joint-analysis in longitudinal stochastic processes". In Yang, Fengshan (ed.).
10173:
7963:
4525:
tend to be simultaneously greater than, or simultaneously less than, their respective means. The correlation coefficient is negative (
13929:{\displaystyle \mathbb {Cor} (X,Y)={\frac {\mathbb {E} -\mathbb {E} \cdot \mathbb {E} }{\sqrt {\mathbb {V} \cdot \mathbb {V} }}}\,,}
11362:{\displaystyle r=\operatorname {\mathbb {E} } \approx r_{\text{adj}}-{\frac {r_{\text{adj}}\left(1-r_{\text{adj}}^{2}\right)}{2n}}.}
17:
18938:
18014:
5624:
Critical values of Pearson's correlation coefficient that must be exceeded to be considered significantly nonzero at the 0.05 level
14879:
14867:
19046:
18453:
7499:
5493:
are random variables, with a simple linear relationship between them with an additive normal noise (i.e., y= a + bx + e), then a
5503:
3556:
7882:
4297:
reports degraded correlation values due to the heavy noise contributions. A generalization of the approach is given elsewhere.
2479:
15094:
14717:
14536:
16368:
16102:
16078:
15408:
14266:
10760:
can be applied if the data are approximately normally distributed, but may be misleading otherwise. In some situations, the
8290:{\displaystyle \sum _{i}(Y_{i}-{\bar {Y}})^{2}=\sum _{i}(Y_{i}-{\hat {Y}}_{i})^{2}+\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2},}
7229:
16876:
16576:
7700:
16232:
11108:{\displaystyle r_{\text{adj}}=r\,\mathbf {_{2}F_{1}} \left({\frac {1}{2}},{\frac {1}{2}};{\frac {n-1}{2}};1-r^{2}\right),}
10674:, which roughly means that it is impossible to construct a more accurate estimate than the sample correlation coefficient.
8038:
7922:
17480:
16628:
15476:
14942:
14937:
7013:
5391:
can be used to construct confidence intervals for Pearson's correlation coefficient. In the "non-parametric" bootstrap,
3844:
3438:
2836:
16358:
16217:
14834:
9956:{\displaystyle r(Y,{\hat {Y}})^{2}={\frac {\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}{\sum _{i}(Y_{i}-{\bar {Y}})^{2}}}}
5753:
2008:
by substituting estimates of the covariances and variances based on a sample into the formula above. Given paired data
15882:
11738:
Suppose observations to be correlated have differing degrees of importance that can be expressed with a weight vector
4547:
tend to lie on opposite sides of their respective means. Moreover, the stronger either tendency is, the larger is the
19036:
18263:
18155:
16472:
16289:
16110:
16009:; Gnanadesikan, R.; Kettenring J.R. (1975). "Robust estimation and outlier detection with correlation coefficients".
15729:
15602:
6266:
18868:
18441:
18315:
14459:
is the data transformed so all variables have zero mean and zero correlation with all other variables – the sample
13364:, it is possible to define a circular analog of Pearson's coefficient. This is done by transforming data points in
11399:
11165:
10933:{\displaystyle \operatorname {\mathbb {E} } \left=\rho -{\frac {\rho \left(1-\rho ^{2}\right)}{2n}}+\cdots ,\quad }
7545:
899:
19292:
19119:
18499:
18160:
17905:
17276:
14967:
14821:
14655:
5225:
Statistical inference based on Pearson's correlation coefficient often focuses on one of the following two aims:
14477:
10642:
follows such a distribution. In some practical applications, such as those involving data suspected to follow a
19297:
18943:
18550:
17762:
17569:
17458:
17416:
4294:
4103:
440:
17490:
10699:. The adjusted correlation coefficient must be used instead: see elsewhere in this article for the definition.
10555:
10522:
5652: − 2. Specifically, if the underlying variables have a bivariate normal distribution, the variable
4328:
on a line (in the case of the population correlation). The Pearson correlation coefficient is symmetric: corr(
18953:
18793:
17752:
16655:
15396:
14817:
14785:
13241:
12804:{\displaystyle rr_{xy,w}={\frac {\sum w_{i}x_{i}y_{i}}{\sqrt {(\sum w_{i}x_{i}^{2})(\sum w_{i}y_{i}^{2})}}}.}
10826:
10773:
7503:
5833:
5629:
5140:
19209:
13169:
10809:
Variations of the correlation coefficient can be calculated for different purposes. Here are some examples.
10753:
in some way, they are generally not interpretable on the same scale as the Pearson correlation coefficient.
18968:
18344:
18293:
18278:
18268:
18137:
18009:
17976:
17802:
17757:
17587:
14833:
Python library implements Pearson correlation coefficient calculation as the default option for the method
7974:
31:
16199:
14805:
13723:. This measure can be useful in fields like meteorology where the angular direction of data is important.
8653:
7141:{\displaystyle F(r)\equiv {\tfrac {1}{2}}\,\ln \left({\frac {1+r}{1-r}}\right)=\operatorname {artanh} (r)}
312:
19302:
19175:
19104:
19041:
18856:
18688:
18489:
18413:
17714:
17468:
17137:
16601:
15350:
14223:
13712:
10660:
10655:
If the sample size is moderate or large and the population is normal, then, in the case of the bivariate
9969:
5641:
7992:
6931:
18988:
18963:
18948:
18573:
18545:
18540:
18288:
18047:
17953:
17933:
17841:
17552:
17370:
16853:
16725:
16423:
14947:
14920:
10761:
5388:
5336:
4714:
is measured counterclockwise within the first quadrant formed around the lines' intersection point if
4554:
Rodgers and Nicewander cataloged thirteen ways of interpreting correlation or simple functions of it:
18978:
18973:
18305:
18073:
17794:
17719:
17648:
17577:
17497:
17485:
17355:
17343:
17336:
17044:
16765:
10769:
10643:
7468:
4031:
16319:
15932:
12951:
8617:
8303:
19074:
18788:
18555:
18418:
18103:
18068:
18032:
17817:
17259:
17168:
17127:
17039:
16730:
16569:
16393:"Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification"
14915:
14797:
14468:
10730:
are present. Specifically, the PMCC is neither distributionally robust, nor outlier resistant (see
10613:
10549:
7986:
7954:, or (0.5814, 1.1532). Converting back to the correlation scale yields (0.5237, 0.8188).
6951:
4325:
3169:
14851:
14169:
14116:
14051:
13998:
13945:
6524:
4942:. The Pearson correlation coefficient must therefore be exactly one. Centering the data (shifting
19165:
19069:
19064:
18697:
18310:
18250:
18187:
17825:
17809:
17547:
17409:
17399:
17249:
17163:
14860:
11228:
10671:
10664:
10146:
7514: = 2.2 is observed and a two-sided p-value is desired to test the null hypothesis that
6560:
6329:
4743:
3514:
2434:
774:
747:
389:
337:
93:
16392:
14357:
A corresponding result exists for reducing the sample correlations to zero. Suppose a vector of
14088:
13685:
13656:
10732:
10332:{\displaystyle r(Y,{\hat {Y}})^{2}={\frac {{\text{SS}}_{\text{reg}}}{{\text{SS}}_{\text{tot}}}}}
4507:
lie on the same side of their respective means. Thus the correlation coefficient is positive if
2552:
19006:
18735:
18665:
18458:
18395:
18150:
18037:
17034:
16931:
16838:
16717:
16616:
16314:
16303:"Minimum Pearson distance detection for multilevel channels with gain and / or offset mismatch"
14992:
10750:
10617:
7325:
5121:
166:
16530:
15948:"A robust correlation analysis framework for imbalanced and dichotomous data with uncertainty"
15400:
15229:
15190:
15167:
15113:
14845:
851:
803:
18760:
18702:
18645:
18471:
18364:
18273:
17999:
17883:
17742:
17734:
17624:
17616:
17431:
17327:
17305:
17264:
17229:
17196:
17142:
17117:
17072:
17011:
16971:
16773:
16596:
15919:
14910:
14413:
14372:
10757:
10624:
7517:
7017:
6995:
6338:
6242:
5633:
5426:
5362:
To perform the permutation test, repeat steps (1) and (2) a large number of times. The
4351:
under separate changes in location and scale in the two variables. That is, we may transform
4115:
4106:
16505:
15364:
12644:{\displaystyle rr_{xy}={\frac {\sum x_{i}y_{i}}{\sqrt {(\sum x_{i}^{2})(\sum y_{i}^{2})}}}.}
10947:
3676:
3646:
3225:
2915:
2585:
2125:
1981:
1943:
19227:
19127:
19016:
19011:
18683:
18258:
18207:
18183:
18145:
18063:
18042:
17994:
17873:
17851:
17820:
17729:
17606:
17557:
17475:
17448:
17404:
17360:
17122:
16898:
16778:
16514:– an interactive Flash simulation on the correlation of two normally distributed variables.
15241:
15125:
14997:
14972:
14962:
13076:
10703:
10685:
10681:
10667:
10609:
10582:
7559:
7001:
4650:
For uncentered data, there is a relation between the correlation coefficient and the angle
4073:
4037:
1638:
927:
732:{\displaystyle \rho _{X,Y}={\frac {\operatorname {\mathbb {E} } }{\sigma _{X}\sigma _{Y}}}}
596:
184:
153:
about the origin) of the product of the mean-adjusted random variables; hence the modifier
150:
16518:
4452:
decreases. A value of 0 implies that there is no linear dependency between the variables.
8:
18933:
18920:
18830:
18755:
18678:
18359:
18123:
18116:
18078:
17986:
17966:
17938:
17671:
17537:
17532:
17522:
17514:
17332:
17293:
17183:
17173:
17082:
16861:
16817:
16735:
16660:
16562:
15831:
Hotelling, Harold (1953). "New Light on the Correlation Coefficient and its Transforms".
14987:
14841:
13738:
13732:
13315:
11506:
11137:
10784:
10656:
10631:
10627:
7159:
5430:
5245:
5185:
4348:
4312:
4308:
4289:
Under heavy noise conditions, extracting the correlation coefficient between two sets of
3216:
1937:
15502:
15245:
15129:
10783:
represents cluster membership or another factor that it is desirable to control, we can
19253:
19219:
19099:
18928:
18844:
18655:
18509:
18405:
18354:
18230:
18127:
18111:
18088:
17865:
17599:
17582:
17542:
17453:
17348:
17310:
17281:
17241:
17201:
17147:
17064:
16750:
16745:
16435:
16332:
16263:
16180:
16139:
16135:
16026:
15970:
15947:
15848:
15844:
15813:
15665:
15560:
15525:
15282:
15210:
15143:
14902:
14618:
14460:
14200:
14147:
14029:
13976:
13773:
13753:
13126:
13103:
12875:
12855:
12835:
12820:
7305:
7285:
7023:
5620:
5591:
5571:
5476:
5456:
4429:
4301:
3828:{\displaystyle r_{xy}={\frac {\sum x_{i}y_{i}-n{\bar {x}}{\bar {y}}}{(n-1)s_{x}s_{y}}}}
3622:
2412:
2105:
878:
830:
416:
368:
362:
297:{\displaystyle \rho _{X,Y}={\frac {\operatorname {cov} (X,Y)}{\sigma _{X}\sigma _{Y}}}}
105:
18880:
15437:
12829:. Scaled correlation is defined as average correlation across short segments of data.
11857:{\displaystyle \operatorname {m} (x;w)={\frac {\sum _{i}w_{i}x_{i}}{\sum _{i}w_{i}}}.}
19248:
19137:
19084:
18839:
18750:
18720:
18712:
18532:
18523:
18448:
18379:
18235:
18220:
18195:
18083:
18024:
17890:
17878:
17504:
17421:
17365:
17288:
17132:
17054:
16833:
16707:
16468:
16364:
16302:
16285:
16255:
16251:
16122:
Hotelling, H. (1953). "New Light on the Correlation Coefficient and its Transforms".
16106:
16098:
16074:
15817:
15805:
15791:
15725:
15657:
15598:
15404:
15080:
14952:
14896:
14830:
12527:
10805:
Correlation and dependence § Other measures of dependence among random variables
10723:
7694:
The inverse Fisher transformation brings the interval back to the correlation scale.
4929:
4762:
15974:
12345:
The reflective correlation is symmetric, but it is not invariant under translation:
8336:
are the fitted values from the regression analysis. This can be rearranged to give
19271:
19056:
19021:
18958:
18911:
18775:
18730:
18494:
18481:
18374:
18349:
18283:
18215:
18093:
17701:
17594:
17527:
17440:
17387:
17206:
17077:
16871:
16755:
16670:
16637:
16449:
16445:
16404:
16336:
16324:
16267:
16247:
16170:
16131:
16066:
16018:
15962:
15905:
15840:
15795:
15787:
15760:
15649:
15556:
15552:
15517:
15433:
15272:
15202:
15147:
15133:
13231:
10765:
5264:
4526:
4433:
4290:
134:
7551:
To obtain a confidence interval for ρ, we first compute a confidence interval for
4023:{\textstyle s_{x}={\sqrt {{\frac {1}{n-1}}\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}}
129:
in the 1880s, and for which the mathematical formula was derived and published by
19204:
19147:
19026:
18692:
18436:
18298:
18225:
17900:
17774:
17747:
17724:
17693:
17320:
17315:
17269:
16999:
16650:
16006:
10427:{\displaystyle {\text{SS}}_{\text{reg}}=\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}
7462:
7005:
5372:
5230:
4347:
A key mathematical property of the Pearson correlation coefficient is that it is
130:
18182:
15910:
15901:
13234:
and data detection for communications and storage with unknown gain and offset.
18641:
18636:
17099:
17029:
16675:
16005:
15451:
15301:"Analyse mathematique sur les probabilités des erreurs de situation d'un point"
15152:
In the "Appendix" on page 532, Galton uses the term "reversion" and the symbol
15002:
14957:
14622:
13790:, in a bipartite quantum system Pearson correlation coefficient is defined as
7353:
7224:
6260:
5494:
5376:
4548:
3253:
480:
126:
43:
Examples of scatter diagrams with different values of correlation coefficient (
16175:
16158:
16060:
16022:
15966:
15764:
7684:{\displaystyle 100(1-\alpha )\%{\text{CI}}:\operatorname {artanh} (\rho )\in }
7282:
is the sample size. The approximation error is lowest for a large sample size
6547:, which is one way of writing the density of a Student's t-distribution for a
19286:
19089:
18798:
18765:
18628:
18589:
18400:
18369:
17833:
17787:
17392:
17094:
16921:
16685:
16680:
16328:
16070:
15661:
14348:
8611:
6544:
16408:
15277:
15260:
10135:{\displaystyle \sum _{i}(Y_{i}-{\hat {Y}}_{i})({\hat {Y}}_{i}-{\bar {Y}})=0}
18740:
18673:
18650:
18565:
17895:
17191:
17089:
17024:
16966:
16951:
16888:
16843:
16259:
15809:
15683:
13737:
If a population or data-set is characterized by more than two variables, a
12852:
be the number of segments that can fit into the total length of the signal
11704:{\displaystyle r_{\text{adj}}={\sqrt {1-{\frac {(1-r^{2})(n-1)}{(n-2)}}}}.}
122:
16233:"Scaled correlation analysis: a better way to compute a cross-correlogram"
15579:
13063:{\displaystyle {\bar {r}}_{s}={\frac {1}{K}}\sum \limits _{k=1}^{K}r_{k},}
10680:
If the sample size is large, then the sample correlation coefficient is a
10630:
are defined and are non-zero. Some probability distributions, such as the
5729:{\displaystyle t={\frac {r}{\sigma _{r}}}=r{\sqrt {\frac {n-2}{1-r^{2}}}}}
39:
18783:
18745:
18428:
18329:
18191:
18004:
17971:
17463:
17380:
17375:
17019:
16976:
16956:
16936:
16926:
16695:
15742:
14930:
14925:
12826:
10737:
6548:
5637:
5312:
4807:
109:
15684:"Derivation of the standard error for Pearson's correlation coefficient"
15564:
15056:
As early as 1877, Galton was using the term "reversion" and the symbol "
10508:{\displaystyle {\text{SS}}_{\text{tot}}=\sum _{i}(Y_{i}-{\bar {Y}})^{2}}
5237:
is equal to 0, based on the value of the sample correlation coefficient
583:{\displaystyle \operatorname {cov} (X,Y)=\operatorname {\mathbb {E} } ,}
51:
19183:
19094:
19079:
17629:
17109:
16809:
16740:
16690:
16665:
16585:
16184:
16143:
16030:
15852:
15800:
15751:
15722:
The Advanced Theory of Statistics, Volume 2: Inference and Relationship
15669:
15637:
15529:
15286:
15214:
14982:
14800:'s statistics base-package implements the correlation coefficient with
10620:
5438:
3673:
are also available. For example, one can use the following formula for
330:
146:
101:
81:
10608:
The population Pearson correlation coefficient is defined in terms of
10599:
Correlation and dependence § Sensitivity to the data distribution
7969:
The square of the sample correlation coefficient is typically denoted
4932:. The above data were deliberately chosen to be perfectly correlated:
19001:
17782:
17634:
17254:
17049:
16961:
16946:
16941:
16906:
16421:
15195:
Journal of the Anthropological Institute of Great Britain and Ireland
15138:
13745:
10716:
10691:
If the sample size is small, then the sample correlation coefficient
7213:{\displaystyle {\text{mean}}=F(\rho )=\operatorname {artanh} (\rho )}
5813:
Another early paper provides graphs and tables for general values of
5437:
can be defined as the interval spanning from the 2.5th to the 97.5th
4436:: a value of +1 implies that all data points lie on a line for which
15746:
15653:
15521:
15206:
14455:
is the data transformed so every random variable has zero mean, and
14335:, and its absolute value is invariant under affine transformations.
12938:{\displaystyle K=\operatorname {round} \left({\frac {T}{s}}\right).}
7451:{\displaystyle z={\frac {x-{\text{mean}}}{\text{SE}}}={\sqrt {n-3}}}
5256:
Methods of achieving one or both of these aims are discussed below.
17298:
16916:
16793:
16788:
16783:
16492:
16124:
Journal of the Royal Statistical Society. Series B (Methodological)
10586:
4603:
4110:
16440:
15582:. ch. 5 (as illustrated for a special case in the next paragraph).
7510:
can be obtained from a normal probability table. For example, if
5817:, for small sample sizes, and discusses computational approaches.
5248:
that, on repeated sampling, has a given probability of containing
2095:{\displaystyle \left\{(x_{1},y_{1}),\ldots ,(x_{n},y_{n})\right\}}
100:
correlation between two sets of data. It is the ratio between the
19109:
18996:
18803:
18504:
16546:
15477:"Introductory Business Statistics: The Correlation Coefficient r"
15095:"Correlation Coefficient: Simple Definition, Formula, Easy Steps"
10727:
7507:
5363:
3619:
is the standard score (and analogously for the standard score of
15230:"Notes on regression and inheritance in the case of two parents"
14978:
Normally distributed and uncorrelated does not imply independent
10243:{\displaystyle {\text{RSS}}=\sum _{i}(Y_{i}-{\hat {Y}}_{i})^{2}}
5810:
Alternatively, large sample, asymptotic approaches can be used.
4777:
are found to have 11%, 12%, 13%, 15%, and 18% poverty. Then let
4728:.) One can show that if the standard deviations are equal, then
4721:, or counterclockwise from the fourth to the second quadrant if
18725:
17706:
17680:
17660:
16911:
16702:
16282:
Bioinformatics: Applications in Life and Environmental Sciences
15870:. Vol. Part 2 (2nd ed.). Princeton, NJ: Van Nostrand.
14884:
function for calculating the pearson's correlation coefficient.
4751:
4582:
Rescaled variance of the difference between standardized scores
4576:
Function of the angle between two standardized regression lines
97:
16300:
16218:"Weighted Correlation Matrix – File Exchange – MATLAB Central"
10145:
can be proved by noticing that the partial derivatives of the
7964:
Coefficient of determination § In a multiple linear model
7875:=50, and we wish to obtain a 95% confidence interval for
5208:
will be about 13% smaller than the 95% prediction interval of
5116:
4928:
This uncentered correlation coefficient is identical with the
16554:
14875:
14863:
14814:
12654:
The weighted version of the sample reflective correlation is
7977:. In this case, it estimates the fraction of the variance in
5323:
is selected randomly, with equal probabilities placed on all
4755:
133:
in 1844. The naming of the coefficient is thus an example of
13376:
function such that the correlation coefficient is given as:
5413:) are resampled "with replacement" from the observed set of
5327:! possible permutations. This is equivalent to drawing the
19188:
19160:
19155:
19132:
16645:
13373:
3612:{\textstyle \left({\frac {x_{i}-{\bar {x}}}{s_{x}}}\right)}
476:
16422:
Maccone, L.; Dagmar, B.; Macchiavello, C. (1 April 2015).
15261:"Francis Galton's account of the invention of correlation"
7912:{\textstyle \operatorname {arctanh} \left(r\right)=0.8673}
6554:
6361:(zero population correlation), the exact density function
5558:{\displaystyle \sigma _{r}={\sqrt {\frac {1-r^{2}}{n-2}}}}
2542:{\textstyle {\bar {x}}={\frac {1}{n}}\sum _{i=1}^{n}x_{i}}
16159:"Unbiased Estimation of Certain Correlation Coefficients"
16095:
Multivariable Analysis – A Practical Guide for Clinicians
15865:
10548:
is called the regression sum of squares, also called the
7919:, so the confidence interval on the transformed scale is
5611:
5289:), randomly redefine the pairs to create a new data set (
16230:
15993:
Introduction to robust estimation and hypothesis testing
15777:
15745:; Young, A.W.; Cave, B.M.; Lee, A.; Pearson, K. (1917).
14774:{\displaystyle t=d(D^{\mathsf {T}}D)^{-{\frac {1}{2}}}.}
14629:
will be the identity matrix. If a new data observation
14593:{\displaystyle T=D(D^{\mathsf {T}}D)^{-{\frac {1}{2}}},}
10634:, have undefined variance and hence ρ is not defined if
8108:
around their average value can be decomposed as follows
6559:
Confidence intervals and tests can be calculated from a
4785:
be ordered 5-element vectors containing the above data:
4408:
944:
can be expressed in terms of uncentered moments. Since
18910:
16531:"Critical values for Pearson's correlation coefficient"
15883:"Correlation Coefficient—Bivariate Normal Distribution"
15638:"The Standard Deviation of the Correlation Coefficient"
14328:{\displaystyle \mathbb {Cor} (X,Y)=\mathbb {Cor} (Y,X)}
10592:
8595:
The two summands above are the fraction of variance in
7957:
5824:-distribution, but the degrees of freedom are reduced.
16462:
15623:
Statistical Power Analysis for the Behavioral Sciences
15503:"Thirteen ways to look at the correlation coefficient"
14338:
10764:
can be applied to construct confidence intervals, and
8614:
regression models, that the sample covariance between
7885:
7268:{\displaystyle ={\text{SE}}={\frac {1}{\sqrt {n-3}}},}
7068:
6889:
6874:
6853:
6835:
6476:
6461:
6190:
6157:
6142:
6127:
6039:
4444:
increases, whereas a value of -1 implies a line where
4150:
3925:
3559:
2482:
16356:
15191:"Regression towards mediocrity in hereditary stature"
14720:
14658:
14539:
14480:
14416:
14375:
14269:
14226:
14203:
14172:
14150:
14119:
14091:
14054:
14032:
14001:
13979:
13948:
13799:
13776:
13756:
13688:
13659:
13385:
13244:
13172:
13163:
can be defined from their correlation coefficient as
13129:
13106:
13079:
12993:
12954:
12901:
12878:
12858:
12838:
12663:
12539:
12354:
12205:
12191:
12055:
11872:
11768:
11614:
11605:
Another proposed adjusted correlation coefficient is
11509:
11402:
11259:
11168:
11140:
10990:
10950:
10846:
10768:
can be applied to carry out hypothesis tests. These
10558:
10525:
10441:
10351:
10263:
10176:
10037:
9972:
9802:
8708:
8656:
8620:
8345:
8306:
8117:
8041:
7995:
7925:
7857:{\displaystyle 100(1-\alpha )\%{\text{CI}}:\rho \in }
7703:
7586:
7562:
7520:
7471:
7365:
7328:
7308:
7288:
7232:
7171:
7051:
7026:
6954:
6934:
6575:
6527:
6378:
6341:
6269:
6245:
5857:
5756:
5661:
5594:
5574:
5506:
5479:
5459:
5143:
4989:
4823:
4591:
Function of test statistics from designed experiments
4588:
Related to the bivariate ellipses of isoconcentration
4138:
4118:
4076:
4065:
4040:
3847:
3712:
3679:
3649:
3625:
3517:
3441:
3265:
3228:
3172:
2951:
2918:
2839:
2621:
2588:
2555:
2437:
2415:
2160:
2128:
2108:
2014:
1984:
1946:
1936:
Pearson's correlation coefficient, when applied to a
1661:
1641:
953:
930:
902:
881:
854:
833:
806:
777:
750:
621:
599:
492:
443:
419:
392:
371:
340:
315:
225:
187:
165:
Pearson's correlation coefficient, when applied to a
18467:
Autoregressive conditional heteroskedasticity (ARCH)
16231:
Nikolić, D; Muresan, RC; Feng, W; Singer, W (2012).
15593:
Buda, Andrzej; Jarynowski, Andrzej (December 2010).
14892:
14637:
elements, then the same transform can be applied to
13100:
is Pearson's coefficient of correlation for segment
8099:
then as a starting point the total variation in the
8092:{\displaystyle {\hat {Y}}_{1},\dots ,{\hat {Y}}_{n}}
7947:{\displaystyle 0.8673\pm {\frac {1.96}{\sqrt {47}}}}
16156:
13309:
12526:The sample reflective correlation is equivalent to
11733:
10812:
5347:are equal and drawn with replacement from {1, ...,
5331:randomly without replacement from the set {1, ...,
3910:{\displaystyle n,x_{i},y_{i},{\bar {x}},{\bar {y}}}
3504:{\displaystyle n,x_{i},y_{i},{\bar {x}},{\bar {y}}}
2902:{\displaystyle n,x_{i},y_{i},{\bar {x}},{\bar {y}}}
17929:
14773:
14705:
14592:
14524:
14435:
14394:
14327:
14255:
14209:
14189:
14156:
14136:
14103:
14077:
14038:
14018:
13985:
13965:
13928:
13782:
13762:
13746:Pearson correlation coefficient in quantum systems
13703:
13674:
13642:
13298:
13219:
13135:
13112:
13092:
13062:
12976:
12937:
12884:
12864:
12844:
12803:
12643:
12515:
12334:
12180:
12039:
11856:
11703:
11521:
11470:
11361:
11219:
11152:
11107:
10959:
10932:
10663:of the population correlation coefficient, and is
10573:
10540:
10507:
10426:
10331:
10242:
10134:
10009:
9955:
9782:
8691:
8642:
8584:
8328:
8289:
8091:
8027:
7946:
7911:
7856:
7683:
7568:
7532:
7490:
7450:
7341:
7314:
7294:
7267:
7212:
7140:
7032:
6989:
6978:
6940:
6918:
6535:
6510:
6353:
6320:
6251:
6228:
5799:
5728:
5600:
5580:
5557:
5485:
5465:
5366:for the permutation test is the proportion of the
5172:
5102:
4917:
4579:Function of the angle between two variable vectors
4273:
4124:
4094:
4053:
4022:
3909:
3827:
3695:
3665:
3631:
3611:
3543:
3503:
3421:
3244:
3204:
3155:
2934:
2901:
2822:
2604:
2570:
2541:
2463:
2421:
2396:
2144:
2114:
2094:
2000:
1962:
1921:
1647:
1624:
936:
912:
887:
867:
839:
819:
790:
763:
731:
605:
582:
467:
425:
405:
377:
353:
321:
296:
213:(for example, Height and Weight), the formula for
205:
16301:Immink, K. Schouhamer; Weber, J. (October 2010).
15741:
15500:
12948:The scaled correlation across the entire signals
12814:
10167:are equal to 0 in the least squares model, where
7498:, given the assumption that the sample pairs are
5800:{\displaystyle r={\frac {t}{\sqrt {n-2+t^{2}}}}.}
19284:
15322:Wright, S. (1921). "Correlation and causation".
5192:may be reduced given the corresponding value of
18015:Multivariate adaptive regression splines (MARS)
15642:Journal of the American Statistical Association
15345:
15343:
15341:
15339:
15337:
11742:. To calculate the correlation between vectors
10970:The unique minimum variance unbiased estimator
10715:Like many commonly used statistics, the sample
6321:{\displaystyle {}_{2}\mathrm {F} _{1}(a,b;c;z)}
5827:
3222:An equivalent expression gives the formula for
15595:Life Time of Correlations and its Applications
15592:
15034:Pearson product-moment correlation coefficient
2471:are the individual sample points indexed with
169:, is commonly represented by the Greek letter
63:) points, with the correlation coefficient of
18896:
16570:
16363:. New Jersey: World Scientific. p. 176.
11471:{\displaystyle r_{\text{adj}}\approx r\left,}
11220:{\displaystyle \mathbf {_{2}F_{1}} (a,b;c;z)}
10702:Correlations can be different for imbalanced
7962:For more general, non-linear dependency, see
4802:By the usual procedure for finding the angle
913:{\displaystyle \operatorname {\mathbb {E} } }
16357:Jammalamadaka, S. Rao; SenGupta, A. (2001).
16157:Olkin, Ingram; Pratt, John W. (March 1958).
16097:. 2nd Edition. Cambridge University Press.
15334:
15124:(388, 389, 390): 492–495, 512–514, 532–533.
10706:data when there is variance error in sample.
10659:, the sample correlation coefficient is the
6948:is the Gaussian hypergeometric function and
4573:Mean cross-product of standardized variables
4432:. The correlation sign is determined by the
4300:In case of missing data, Garren derived the
2912:Rearranging again gives us this formula for
16224:
15452:"2.6 - (Pearson) Correlation Coefficient r"
14791:
14706:{\displaystyle d=x-{\frac {1}{m}}Z_{1,m}X,}
14085:is the expectation value of the observable
14026:is the expectation value of the observable
13973:is the expectation value of the observable
10254:In the end, the equation can be written as
5259:
5200:= 0.5, then the 95% prediction interval of
5117:Interpretation of the size of a correlation
4598:
4567:Geometric mean of the two regression slopes
4428:perfectly, with all data points lying on a
18903:
18889:
16615:
16577:
16563:
15945:
15616:
15614:
15234:Proceedings of the Royal Society of London
14525:{\displaystyle D=X-{\frac {1}{m}}Z_{m,m}X}
6551:sample correlation coefficient, as above.
5844:) for the sample correlation coefficient
5640:Pearson's correlation coefficient follows
4409:§ Decorrelation of n random variables
4318:
179:population Pearson correlation coefficient
104:of two variables and the product of their
17228:
16439:
16318:
16174:
16121:
15986:
15984:
15909:
15899:
15830:
15799:
15597:. Wydawnictwo Niezależne. pp. 5–21.
15392:Progress in Applied Mathematical Modeling
15311:: 255–332. 1844 – via Google Books.
15276:
15137:
14451:square matrix with every element 1. Then
14306:
14303:
14300:
14277:
14274:
14271:
14234:
14231:
14228:
14174:
14121:
14056:
14003:
13950:
13922:
13906:
13889:
13873:
13856:
13833:
13807:
13804:
13801:
12322:
12311:
12300:
12291:
12280:
12269:
12261:
12257:
12253:
12242:
11570:has minimum variance for large values of
11268:
11007:
10849:
10612:, and therefore exists for any bivariate
7079:
6016:
5891:
4570:Square root of the ratio of two variances
4564:Standardized slope of the regression line
1896:
1892:
1881:
1864:
1853:
1840:
1816:
1812:
1801:
1784:
1773:
1760:
1750:
1746:
1735:
1729:
1725:
1714:
1705:
1701:
1697:
1686:
1614:
1610:
1606:
1595:
1589:
1585:
1574:
1565:
1561:
1557:
1546:
1537:
1528:
1524:
1513:
1491:
1487:
1476:
1462:
1451:
1442:
1389:
1378:
1356:
1352:
1341:
1338:
1323:
1312:
1299:
1288:
1260:
1245:
1232:
1189:
1185:
1174:
1157:
1146:
1133:
1122:
1094:
1079:
1066:
1034:
1030:
1019:
992:
988:
977:
905:
646:
519:
468:{\displaystyle \operatorname {cov} (X,Y)}
145:Pearson's correlation coefficient is the
16059:Vaart, A. W. van der (13 October 1998).
15833:Journal of the Royal Statistical Society
15444:
14625:of a matrix. The correlation matrix of
10833:for the sample correlation coefficient
10574:{\displaystyle {\text{SS}}_{\text{tot}}}
10541:{\displaystyle {\text{SS}}_{\text{reg}}}
5619:
5120:
4978:= (−0.028, −0.018, −0.008, 0.012, 0.042)
4602:
50:
38:
16307:IEEE Transactions on Information Theory
15611:
15258:
15227:
15008:Spearman's rank correlation coefficient
13299:{\displaystyle d_{X,Y}=1-|\rho _{X,Y}|}
11551:can also be obtained by maximizing log(
10028:In the derivation above, the fact that
7871: = 0.7 with a sample size of
7500:independent and identically distributed
6555:Using the exact confidence distribution
5417:pairs, and the correlation coefficient
5173:{\displaystyle 1-{\sqrt {1-\rho ^{2}}}}
2549:(the sample mean); and analogously for
14:
19285:
18541:Kaplan–Meier estimator (product limit)
15990:
15981:
15635:
15577:
15542:
15423:
15388:
15321:
15188:
15165:
15111:
14739:
14558:
13726:
13360:} that are defined on the unit circle
13220:{\displaystyle d_{X,Y}=1-\rho _{X,Y}.}
5233:that the true correlation coefficient
2582:Rearranging gives us this formula for
1976:sample Pearson correlation coefficient
113:unrealistically perfect correlation).
18884:
18614:
18181:
17928:
17227:
16997:
16614:
16558:
16163:The Annals of Mathematical Statistics
16058:
16043:
15880:
15620:
15362:
15081:"SPSS Tutorials: Pearson Correlation"
15060:" for what would become "regression".
14850:function, or (with the P value) with
13146:
11385:An approximate solution to equation (
11248:and solving this truncated equation:
7989:. So if we have the observed dataset
116:
18851:
18551:Accelerated failure time (AFT) model
16519:"Correlation coefficient calculator"
16390:
16200:"Re: Compute a weighted correlation"
15866:Kenney, J.F.; Keeping, E.S. (1951).
15586:
15426:Statistics & Probability Letters
13151:A distance metric for two variables
11393:
11250:
11235:An approximately unbiased estimator
10981:
10726:, so its value can be misleading if
10593:Sensitivity to the data distribution
8692:{\displaystyle Y_{i}-{\hat {Y}}_{i}}
7958:In least squares regression analysis
5382:
5354:Construct a correlation coefficient
322:{\displaystyle \operatorname {cov} }
173:(rho) and may be referred to as the
18863:
18146:Analysis of variance (ANOVA, anova)
16998:
16350:
15711:, Charles Griffin and Company, 1968
15545:The Journal of Educational Research
15307:. Sci. Math, et Phys. (in French).
14943:Concordance correlation coefficient
14938:Coefficient of multiple correlation
14256:{\displaystyle \mathbb {Cor} (X,Y)}
13027:
10817:The sample correlation coefficient
10733:Robust statistics § Definition
10010:{\displaystyle r(Y,{\hat {Y}})^{2}}
8603:(right) and that is unexplained by
7014:Variance-stabilizing transformation
7012:are usually carried out using the,
5425:values are used to approximate the
4293:is nontrivial, in particular where
4284:
3252:as the mean of the products of the
181:. Given a pair of random variables
160:
24:
18241:Cochran–Mantel–Haenszel statistics
16867:Pearson product-moment correlation
16467:. Chapman & Hall. Appendix 3.
16424:"Complementarity and Correlations"
16136:10.1111/j.2517-6161.1953.tb00135.x
15845:10.1111/j.2517-6161.1953.tb00135.x
15720:Kendall, M. G., Stuart, A. (1973)
15709:A Course in Theoretical Statistics
14804:, or (with the P value also) with
14197:is the variance of the observable
14144:is the variance of the observable
12192:Reflective correlation coefficient
11985:
11945:
11769:
10021:explained by a linear function of
8028:{\displaystyle Y_{1},\dots ,Y_{n}}
7722:
7605:
6941:{\displaystyle \operatorname {F} }
6935:
6823:
6648:
6618:
6563:. An exact confidence density for
6529:
6445:
6281:
6246:
6109:
6018:
5893:
5339:, a closely related approach, the
4654:between the two regression lines,
4315:) do not have a defined variance.
4139:
4119:
4066:For jointly gaussian distributions
175:population correlation coefficient
125:from a related idea introduced by
72:undefined because the variance of
25:
19314:
16485:
16463:Cox, D.R.; Hinkley, D.V. (1974).
15305:Mem. Acad. Roy. Sci. Inst. France
14784:This decorrelation is related to
10017:is the proportion of variance in
7544:, where Φ is the standard normal
5497:associated to the correlation is
5448:
5184:) is the factor by which a given
4415:
18862:
18850:
18838:
18825:
18824:
18615:
16252:10.1111/j.1460-9568.2011.07987.x
16240:European Journal of Neuroscience
15792:10.1016/j.neuroimage.2012.08.022
15324:Journal of Agricultural Research
15166:Galton, F. (24 September 1885).
14895:
13310:Circular correlation coefficient
11734:Weighted correlation coefficient
11229:Gaussian hypergeometric function
11184:
11180:
11174:
11023:
11019:
11013:
10813:Adjusted correlation coefficient
7867:For example, suppose we observe
7546:cumulative distribution function
6330:Gaussian hypergeometric function
5747:the inverse function is needed:
5271:Using the original paired data (
5038:
5025:
5014:
5006:
4872:
4859:
4848:
4840:
4797:= (0.11, 0.12, 0.13, 0.15, 0.18)
4773:observations of each variable).
4558:Function of raw scores and means
4551:of the correlation coefficient.
19259:Pearson correlation coefficient
18500:Least-squares spectral analysis
16456:
16415:
16384:
16294:
16274:
16210:
16192:
16150:
16115:
16087:
16052:
16037:
15999:
15939:
15893:
15874:
15859:
15824:
15771:
15735:
15714:
15701:
15676:
15629:
15571:
15536:
15494:
15469:
15417:
15382:
15356:
15315:
15293:
14968:Maximal information coefficient
14641:to get the transformed vectors
12491:
10929:
10821:is not an unbiased estimate of
10787:the data based on the value of
10695:is not an unbiased estimate of
7491:{\displaystyle \rho =\rho _{0}}
6990:Using the Fisher transformation
5628:For pairs from an uncorrelated
5180:(plotted here as a function of
4585:Estimated from the balloon rule
1931:
86:Pearson correlation coefficient
17481:Mean-unbiased minimum-variance
16584:
16450:10.1103/PhysRevLett.114.130401
16065:. Cambridge University Press.
15557:10.1080/00220671.1947.10881608
15353:", retrieved 22 February 2015.
15349:Real Statistics Using Excel, "
15252:
15228:Pearson, Karl (20 June 1895).
15221:
15182:
15159:
15112:Galton, F. (5–19 April 1877).
15105:
15087:
15073:
15050:
15019:
14749:
14730:
14568:
14549:
14322:
14310:
14293:
14281:
14250:
14238:
14184:
14178:
14131:
14125:
14072:
14060:
14013:
14007:
13960:
13954:
13916:
13910:
13899:
13893:
13883:
13877:
13866:
13860:
13849:
13837:
13823:
13811:
13695:
13666:
13626:
13619:
13597:
13557:
13550:
13528:
13494:
13488:
13466:
13457:
13451:
13429:
13292:
13271:
13001:
12977:{\displaystyle {\bar {r}}_{s}}
12962:
12815:Scaled correlation coefficient
12792:
12761:
12758:
12727:
12632:
12611:
12608:
12587:
12485:
12464:
12445:
12430:
12411:
12399:
12380:
12368:
12323:
12308:
12292:
12277:
12262:
12250:
12231:
12219:
12169:
12151:
12142:
12124:
12113:
12095:
12080:
12062:
12006:
12003:
11991:
11969:
11966:
11963:
11951:
11929:
11897:
11879:
11787:
11775:
11690:
11678:
11673:
11661:
11658:
11639:
11282:
11276:
11244:can be obtained by truncating
11214:
11190:
10649:
10496:
10489:
10467:
10415:
10408:
10387:
10377:
10289:
10282:
10267:
10231:
10218:
10195:
10123:
10117:
10096:
10086:
10083:
10071:
10048:
9998:
9991:
9976:
9941:
9934:
9912:
9891:
9884:
9863:
9853:
9828:
9821:
9806:
9760:
9753:
9731:
9710:
9703:
9682:
9672:
9636:
9629:
9608:
9598:
9576:
9569:
9547:
9526:
9519:
9498:
9488:
9453:
9446:
9425:
9415:
9393:
9386:
9364:
9349:
9340:
9333:
9312:
9302:
9296:
9290:
9269:
9259:
9256:
9244:
9221:
9218:
9183:
9176:
9155:
9145:
9123:
9116:
9094:
9079:
9073:
9052:
9042:
9039:
9033:
9012:
8990:
8967:
8932:
8925:
8904:
8894:
8872:
8865:
8843:
8828:
8822:
8801:
8791:
8788:
8782:
8760:
8737:
8731:
8716:
8677:
8643:{\displaystyle {\hat {Y}}_{i}}
8628:
8567:
8560:
8538:
8517:
8510:
8489:
8479:
8451:
8444:
8422:
8401:
8388:
8365:
8329:{\displaystyle {\hat {Y}}_{i}}
8314:
8275:
8268:
8247:
8237:
8215:
8202:
8179:
8157:
8150:
8128:
8077:
8049:
7851:
7848:
7819:
7813:
7804:
7792:
7763:
7757:
7748:
7739:
7719:
7707:
7678:
7649:
7643:
7634:
7628:
7622:
7602:
7590:
7432:
7429:
7416:
7407:
7401:
7395:
7207:
7201:
7189:
7183:
7135:
7129:
7061:
7055:
6633:
6621:
6615:
6603:
6591:
6579:
6388:
6382:
6315:
6291:
6216:
6201:
6183:
6168:
6073:
6057:
5909:
5897:
5888:
5876:
5867:
5861:
5042:
5034:
5029:
5021:
4971:= (−2.8, −1.8, −0.8, 1.2, 4.2)
4876:
4868:
4863:
4855:
4295:Canonical Correlation Analysis
4089:
4077:
4009:
4002:
3980:
3901:
3886:
3799:
3787:
3779:
3767:
3586:
3495:
3480:
3396:
3347:
2893:
2878:
2800:
2743:
2695:
2683:
2562:
2489:
2380:
2373:
2351:
2317:
2310:
2288:
2260:
2254:
2232:
2229:
2223:
2201:
2084:
2058:
2046:
2020:
1978:. We can obtain a formula for
1972:sample correlation coefficient
1970:and may be referred to as the
1897:
1889:
1817:
1809:
1751:
1743:
1730:
1722:
1706:
1694:
1611:
1603:
1590:
1582:
1566:
1554:
1538:
1529:
1521:
1492:
1484:
1459:
1443:
1386:
1357:
1349:
1274:
1268:
1190:
1182:
1108:
1102:
1035:
1027:
993:
985:
701:
698:
679:
676:
657:
654:
574:
571:
552:
549:
530:
527:
511:
499:
462:
450:
413:is the standard deviation of
266:
254:
200:
188:
13:
1:
19198:Deep Learning Related Metrics
18794:Geographic information system
18010:Simultaneous equations models
16360:Topics in circular statistics
15835:. Series B (Methodological).
15438:10.1016/S0167-7152(98)00035-2
15397:Nova Science Publishers, Inc.
15351:Basic Concepts of Correlation
15066:
14786:principal components analysis
14361:random variables is observed
10827:bivariate normal distribution
10710:
8610:Next, we apply a property of
7973:and is a special case of the
7504:bivariate normal distribution
6979:{\displaystyle \nu =n-1>1}
5836:, the exact density function
5834:bivariate normal distribution
5630:bivariate normal distribution
5244:The other aim is to derive a
3205:{\displaystyle n,x_{i},y_{i}}
1940:, is commonly represented by
475:can be expressed in terms of
140:
27:Measure of linear correlation
17977:Coefficient of determination
17588:Uniformly most powerful test
15501:Rodgers; Nicewander (1988).
15259:Stigler, Stephen M. (1989).
15044:, or simply the unqualified
15013:
14190:{\displaystyle \mathbb {V} }
14137:{\displaystyle \mathbb {V} }
14078:{\displaystyle \mathbb {E} }
14019:{\displaystyle \mathbb {E} }
13966:{\displaystyle \mathbb {E} }
10603:
7975:coefficient of determination
6536:{\displaystyle \mathrm {B} }
5828:Using the exact distribution
5220:
4412:for an application of this.
32:Coefficient of determination
7:
19042:Sensitivity and specificity
18546:Proportional hazards models
18490:Spectral density estimation
18472:Vector autoregression (VAR)
17906:Maximum posterior estimator
17138:Randomized controlled trial
16391:Reid, M. D. (1 July 1989).
16280:Fulekar (Ed.), M.H. (2009)
15911:10.13140/RG.2.2.23673.49769
15902:"Confidence in Correlation"
15580:"Understanding Correlation"
14888:
14406:th variable of observation
11496:
11484:
11387:
11375:
11121:
10798:
10661:maximum likelihood estimate
7879:. The transformed value is
7352:Using the approximation, a
4814:correlation coefficient is
4489:is positive if and only if
3544:{\displaystyle s_{x},s_{y}}
2464:{\displaystyle x_{i},y_{i}}
791:{\displaystyle \sigma _{X}}
764:{\displaystyle \sigma _{Y}}
406:{\displaystyle \sigma _{Y}}
354:{\displaystyle \sigma _{X}}
10:
19319:
18306:Multivariate distributions
16726:Average absolute deviation
16093:Katz., Mitchell H. (2006)
15900:Taraldsen, Gunnar (2020).
15114:"Typical laws of heredity"
14948:Correlation and dependence
14921:Coefficient of colligation
14346:
14104:{\displaystyle X\otimes Y}
13730:
13704:{\displaystyle {\bar {y}}}
13675:{\displaystyle {\bar {x}}}
13313:
13123:By choosing the parameter
12818:
11540:is a suboptimal estimator,
10825:. For data that follows a
10802:
10596:
7961:
7158:) approximately follows a
6993:
4307:Some distributions (e.g.,
3511:are defined as above, and
2571:{\displaystyle {\bar {y}}}
29:
18:Pearson's correlation
19267:
19241:
19218:
19197:
19174:
19146:
19118:
19055:
18987:
18919:
18820:
18774:
18711:
18664:
18627:
18623:
18610:
18582:
18564:
18531:
18522:
18480:
18427:
18388:
18337:
18328:
18294:Structural equation model
18249:
18206:
18202:
18177:
18136:
18102:
18056:
18023:
17985:
17952:
17948:
17924:
17864:
17773:
17692:
17656:
17647:
17630:Score/Lagrange multiplier
17615:
17568:
17513:
17439:
17430:
17240:
17236:
17223:
17182:
17156:
17108:
17063:
17045:Sample size determination
17010:
17006:
16993:
16897:
16852:
16826:
16808:
16764:
16716:
16636:
16627:
16623:
16610:
16592:
16497:comparingcorrelations.org
16044:Huber, Peter. J. (2004).
15967:10.1016/j.ins.2018.08.017
15868:Mathematics of Statistics
15510:The American Statistician
15365:"Statistical Correlation"
11726:for large values of
10944:is a biased estimator of
10837:of a normal bivariate is
10644:heavy-tailed distribution
7349:and increases otherwise.
7342:{\displaystyle \rho _{0}}
6335:In the special case when
5848:of a normal bivariate is
5429:of the statistic. A 95%
5358:from the randomized data.
4806:between two vectors (see
4761:between the two observed
4694:, obtained by regressing
4032:sample standard deviation
3917:are defined as above and:
3643:Alternative formulae for
18789:Environmental statistics
18311:Elliptical distributions
18104:Generalized linear model
18033:Simple linear regression
17803:Hodges–Lehmann estimator
17260:Probability distribution
17169:Stochastic approximation
16731:Coefficient of variation
16538:frank.mtsu.edu/~dkfuller
16329:10.1109/tit.2014.2342744
16071:10.1017/cbo9780511802256
15991:Wilcox, Rand R. (2005).
14916:Association (statistics)
14792:Software implementations
10614:probability distribution
10550:explained sum of squares
7987:simple linear regression
7221:
5648:with degrees of freedom
5612:Testing using Student's
5260:Using a permutation test
4769:-dimensional space (for
4742:, where sec and tan are
4599:Geometric interpretation
868:{\displaystyle \mu _{Y}}
820:{\displaystyle \mu _{X}}
30:Not to be confused with
19070:Calinski-Harabasz index
18449:Cross-correlation (XCF)
18057:Non-standard predictors
17491:Lehmann–Scheffé theorem
17164:Adaptive clinical trial
16547:"Guess the Correlation"
16428:Physical Review Letters
16409:10.1103/PhysRevA.40.913
16176:10.1214/aoms/1177706717
16023:10.1093/biomet/62.3.531
15765:10.1093/biomet/11.4.328
15046:correlation coefficient
14869:correlation_coefficient
14788:for multivariate data.
14436:{\displaystyle Z_{m,m}}
14395:{\displaystyle X_{i,j}}
11750:with the weight vector
10147:residual sum of squares
8035:and the fitted dataset
7542:2 Φ(−2.2) = 0.028
7533:{\displaystyle \rho =0}
7506:. Thus an approximate
6561:confidence distribution
6354:{\displaystyle \rho =0}
6252:{\displaystyle \Gamma }
5832:For data that follow a
5588:is the correlation and
5229:One aim is to test the
4744:trigonometric functions
4561:Standardized covariance
4319:Mathematical properties
4125:{\displaystyle \Sigma }
4034:); and analogously for
1655:can also be written as
613:can also be written as
94:correlation coefficient
19293:Correlation indicators
18845:Mathematics portal
18666:Engineering statistics
18574:Nelson–Aalen estimator
18151:Analysis of covariance
18038:Ordinary least squares
17962:Pearson product-moment
17366:Statistical functional
17277:Empirical distribution
17110:Controlled experiments
16839:Frequency distribution
16617:Descriptive statistics
16465:Theoretical Statistics
15927:Cite journal requires
15636:Bowley, A. L. (1928).
14993:Polychoric correlation
14881:correl(array1, array2)
14775:
14707:
14594:
14526:
14437:
14396:
14329:
14257:
14211:
14191:
14158:
14138:
14105:
14079:
14040:
14020:
13987:
13967:
13930:
13784:
13764:
13705:
13676:
13644:
13590:
13521:
13422:
13300:
13221:
13137:
13114:
13094:
13064:
13046:
12978:
12939:
12886:
12866:
12846:
12805:
12645:
12517:
12336:
12182:
12041:
11858:
11705:
11523:
11472:
11363:
11221:
11154:
11109:
10961:
10960:{\displaystyle \rho .}
10934:
10751:statistical dependence
10575:
10542:
10509:
10428:
10333:
10244:
10136:
10011:
9957:
9784:
8693:
8644:
8586:
8330:
8291:
8093:
8029:
7948:
7913:
7858:
7685:
7570:
7534:
7492:
7452:
7343:
7316:
7296:
7269:
7214:
7142:
7034:
6980:
6942:
6920:
6537:
6512:
6355:
6322:
6253:
6230:
5801:
5730:
5625:
5602:
5582:
5559:
5487:
5467:
5213:
5174:
5104:
4919:
4647:
4275:
4126:
4096:
4055:
4024:
3979:
3911:
3829:
3697:
3696:{\displaystyle r_{xy}}
3667:
3666:{\displaystyle r_{xy}}
3633:
3613:
3545:
3505:
3423:
3320:
3246:
3245:{\displaystyle r_{xy}}
3212:are defined as above.
3206:
3157:
2936:
2935:{\displaystyle r_{xy}}
2909:are defined as above.
2903:
2824:
2606:
2605:{\displaystyle r_{xy}}
2572:
2543:
2528:
2465:
2423:
2398:
2350:
2287:
2200:
2146:
2145:{\displaystyle r_{xy}}
2116:
2096:
2002:
2001:{\displaystyle r_{xy}}
1964:
1963:{\displaystyle r_{xy}}
1923:
1649:
1626:
938:
914:
889:
869:
841:
821:
792:
765:
733:
607:
584:
469:
427:
407:
379:
355:
323:
298:
207:
77:
48:
19298:Parametric statistics
19233:Intra-list Similarity
18761:Population statistics
18703:System identification
18437:Autocorrelation (ACF)
18365:Exponential smoothing
18279:Discriminant analysis
18274:Canonical correlation
18138:Partition of variance
18000:Regression validation
17844:(Jonckheere–Terpstra)
17743:Likelihood-ratio test
17432:Frequentist inference
17344:Location–scale family
17265:Sampling distribution
17230:Statistical inference
17197:Cross-sectional study
17184:Observational studies
17143:Randomized experiment
16972:Stem-and-leaf display
16774:Central limit theorem
16284:, Springer (pp. 110)
16062:Asymptotic Statistics
15707:Rahman, N. A. (1968)
15578:Rummel, R.J. (1976).
15278:10.1214/ss/1177012580
15042:bivariate correlation
14836:pandas.DataFrame.corr
14776:
14708:
14603:where an exponent of
14595:
14527:
14438:
14397:
14330:
14258:
14212:
14192:
14159:
14139:
14106:
14080:
14041:
14021:
13988:
13968:
13931:
13785:
13765:
13750:For two observables,
13706:
13677:
13645:
13570:
13501:
13402:
13314:Further information:
13301:
13222:
13138:
13115:
13095:
13093:{\displaystyle r_{k}}
13065:
13026:
12979:
12940:
12887:
12867:
12847:
12806:
12646:
12518:
12337:
12183:
12049:Weighted correlation
12042:
11859:
11706:
11529:are defined as above,
11524:
11473:
11364:
11222:
11160:are defined as above,
11155:
11110:
10962:
10935:
10758:Fisher transformation
10736:). Inspection of the
10597:Further information:
10585:(proportional to the
10576:
10543:
10510:
10429:
10334:
10245:
10137:
10012:
9958:
9785:
8694:
8645:
8599:that is explained by
8587:
8331:
8292:
8094:
8030:
7981:that is explained by
7949:
7914:
7859:
7686:
7571:
7569:{\displaystyle \rho }
7535:
7493:
7453:
7344:
7317:
7297:
7270:
7215:
7143:
7035:
7018:Fisher transformation
6996:Fisher transformation
6981:
6943:
6921:
6538:
6513:
6356:
6323:
6254:
6231:
5802:
5731:
5634:sampling distribution
5623:
5603:
5583:
5560:
5488:
5468:
5427:sampling distribution
5175:
5124:
5105:
4920:
4710:respectively. (Here,
4607:Regression lines for
4606:
4276:
4127:
4109:, with mean zero and
4097:
4095:{\displaystyle (X,Y)}
4056:
4054:{\displaystyle s_{y}}
4025:
3959:
3912:
3830:
3698:
3668:
3634:
3614:
3546:
3506:
3424:
3300:
3247:
3207:
3158:
2937:
2904:
2825:
2607:
2573:
2544:
2508:
2466:
2424:
2399:
2330:
2267:
2180:
2147:
2117:
2097:
2003:
1965:
1924:
1650:
1648:{\displaystyle \rho }
1627:
939:
937:{\displaystyle \rho }
915:
890:
870:
842:
822:
793:
766:
734:
608:
606:{\displaystyle \rho }
585:
470:
428:
408:
380:
356:
324:
299:
208:
206:{\displaystyle (X,Y)}
54:
42:
18684:Probabilistic design
18269:Principal components
18112:Exponential families
18064:Nonlinear regression
18043:General linear model
18005:Mixed effects models
17995:Errors and residuals
17972:Confounding variable
17874:Bayesian probability
17852:Van der Waerden test
17842:Ordered alternative
17607:Multiple comparisons
17486:Rao–Blackwellization
17449:Estimating equations
17405:Statistical distance
17123:Factorial experiment
16656:Arithmetic-Geometric
16525:. Linear regression.
16204:sci.tech-archive.net
15955:Information Sciences
14998:Quadrant count ratio
14973:Multiple correlation
14963:Distance correlation
14718:
14656:
14537:
14478:
14414:
14373:
14267:
14263:is symmetric, i.e.,
14224:
14201:
14170:
14148:
14117:
14089:
14052:
14030:
13999:
13977:
13946:
13797:
13774:
13754:
13686:
13657:
13383:
13242:
13170:
13127:
13104:
13077:
12991:
12984:is then computed as
12952:
12899:
12876:
12856:
12836:
12661:
12537:
12352:
12203:
12053:
11870:
11866:Weighted covariance
11766:
11754:(all of length
11612:
11585:has a bias of order
11507:
11400:
11257:
11166:
11138:
10988:
10948:
10844:
10686:law of large numbers
10682:consistent estimator
10628:population variances
10583:total sum of squares
10556:
10523:
10439:
10349:
10261:
10174:
10035:
9970:
9800:
8706:
8654:
8618:
8343:
8304:
8115:
8039:
7993:
7923:
7883:
7701:
7584:
7560:
7518:
7469:
7363:
7326:
7306:
7286:
7230:
7169:
7049:
7024:
7002:confidence intervals
6952:
6932:
6573:
6525:
6376:
6369:) can be written as
6339:
6267:
6243:
5855:
5754:
5659:
5592:
5572:
5504:
5477:
5457:
5319:}. The permutation
5141:
4987:
4821:
4309:stable distributions
4291:stochastic variables
4136:
4116:
4074:
4038:
3923:
3845:
3710:
3677:
3647:
3623:
3557:
3515:
3439:
3263:
3226:
3217:numerically unstable
3170:
2949:
2916:
2837:
2619:
2586:
2553:
2480:
2435:
2413:
2158:
2126:
2106:
2012:
1982:
1944:
1659:
1639:
951:
928:
900:
879:
852:
831:
804:
798:are defined as above
775:
748:
619:
597:
490:
441:
417:
390:
369:
338:
313:
223:
185:
121:It was developed by
18756:Official statistics
18679:Methods engineering
18360:Seasonal adjustment
18128:Poisson regressions
18048:Bayesian regression
17987:Regression analysis
17967:Partial correlation
17939:Regression analysis
17538:Prediction interval
17533:Likelihood interval
17523:Confidence interval
17515:Interval estimation
17476:Unbiased estimators
17294:Model specification
17174:Up-and-down designs
16862:Partial correlation
16818:Index of dispersion
16736:Interquartile range
15881:Weisstein, Eric W.
15363:Weisstein, Eric W.
15265:Statistical Science
15246:1895RSPS...58..240P
15189:Galton, F. (1886).
15130:1877Natur..15..492.
14988:Partial correlation
14842:Wolfram Mathematica
14633:is a row vector of
13739:partial correlation
13733:Partial correlation
13727:Partial correlation
13316:Circular statistics
12791:
12757:
12631:
12607:
11522:{\displaystyle r,n}
11339:
11153:{\displaystyle r,n}
10657:normal distribution
10632:Cauchy distribution
10623:is defined and the
7160:normal distribution
5431:confidence interval
5246:confidence interval
5186:prediction interval
4395:are constants with
4336:) = corr(
4313:normal distribution
4262:
4167:
3111:
3050:
2786:
2729:
1222:
1056:
920:is the expectation.
106:standard deviations
19303:Statistical ratios
19254:Euclidean distance
19220:Recommender system
19100:Similarity measure
18914:evaluation metrics
18776:Spatial statistics
18656:Medical statistics
18556:First hitting time
18510:Whittle likelihood
18161:Degrees of freedom
18156:Multivariate ANOVA
18089:Heteroscedasticity
17901:Bayesian estimator
17866:Bayesian inference
17715:Kolmogorov–Smirnov
17600:Randomization test
17570:Testing hypotheses
17543:Tolerance interval
17454:Maximum likelihood
17349:Exponential family
17282:Density estimation
17242:Statistical theory
17202:Natural experiment
17148:Scientific control
17065:Survey methodology
16751:Standard deviation
15621:Cohen, J. (1988).
14911:Anscombe's quartet
14903:Mathematics portal
14771:
14703:
14619:matrix square root
14590:
14522:
14461:correlation matrix
14433:
14392:
14369:be a matrix where
14325:
14253:
14207:
14187:
14154:
14134:
14101:
14075:
14036:
14016:
13983:
13963:
13926:
13780:
13760:
13701:
13672:
13640:
13296:
13217:
13161:Pearson's distance
13147:Pearson's distance
13133:
13110:
13090:
13060:
12974:
12935:
12882:
12872:for a given scale
12862:
12842:
12821:Scaled correlation
12801:
12777:
12743:
12641:
12617:
12593:
12513:
12332:
12178:
12037:
12020:
11915:
11854:
11837:
11805:
11701:
11519:
11468:
11359:
11325:
11217:
11150:
11105:
10957:
10930:
10829:, the expectation
10571:
10538:
10505:
10466:
10424:
10376:
10329:
10240:
10194:
10132:
10047:
10007:
9953:
9911:
9852:
9780:
9778:
9730:
9671:
9597:
9546:
9487:
9414:
9363:
9217:
9144:
9093:
8966:
8893:
8842:
8759:
8689:
8640:
8582:
8537:
8478:
8421:
8364:
8326:
8287:
8236:
8178:
8127:
8089:
8025:
7944:
7909:
7854:
7681:
7566:
7530:
7488:
7448:
7339:
7312:
7292:
7265:
7210:
7138:
7077:
7030:
6976:
6938:
6916:
6909:
6883:
6862:
6844:
6533:
6508:
6493:
6470:
6351:
6318:
6249:
6226:
6199:
6166:
6151:
6136:
6048:
5797:
5726:
5626:
5598:
5578:
5555:
5483:
5463:
5315:of the set {1,...,
5214:
5196:. For example, if
5170:
5100:
4915:
4648:
4594:Ratio of two means
4302:maximum likelihood
4271:
4265:
4248:
4153:
4122:
4092:
4051:
4020:
3907:
3825:
3693:
3663:
3629:
3609:
3541:
3501:
3419:
3242:
3202:
3153:
3097:
3036:
2932:
2899:
2820:
2772:
2771:
2715:
2714:
2650:
2602:
2568:
2539:
2461:
2419:
2394:
2142:
2112:
2092:
1998:
1960:
1919:
1645:
1622:
1620:
1208:
1042:
934:
910:
885:
865:
837:
817:
788:
761:
729:
603:
580:
465:
423:
403:
375:
363:standard deviation
351:
319:
294:
203:
117:Naming and history
78:
49:
19280:
19279:
19249:Cosine similarity
19085:Hopkins statistic
18878:
18877:
18816:
18815:
18812:
18811:
18751:National accounts
18721:Actuarial science
18713:Social statistics
18606:
18605:
18602:
18601:
18598:
18597:
18533:Survival function
18518:
18517:
18380:Granger causality
18221:Contingency table
18196:Survival analysis
18173:
18172:
18169:
18168:
18025:Linear regression
17920:
17919:
17916:
17915:
17891:Credible interval
17860:
17859:
17643:
17642:
17459:Method of moments
17328:Parametric family
17289:Statistical model
17219:
17218:
17215:
17214:
17133:Random assignment
17055:Statistical power
16989:
16988:
16985:
16984:
16834:Contingency table
16804:
16803:
16671:Generalized/power
16397:Physical Review A
16370:978-981-02-3778-3
16313:(10): 5966–5974.
16103:978-0-521-54985-1
16080:978-0-511-80225-6
16046:Robust Statistics
15995:. Academic Press.
15887:Wolfram MathWorld
15410:978-1-60021-976-4
15369:Wolfram MathWorld
15099:Statistics How To
14953:Correlation ratio
14764:
14679:
14583:
14501:
14339:Decorrelation of
14210:{\displaystyle Y}
14157:{\displaystyle X}
14039:{\displaystyle Y}
13986:{\displaystyle X}
13920:
13919:
13783:{\displaystyle Y}
13763:{\displaystyle X}
13698:
13669:
13638:
13635:
13622:
13566:
13553:
13491:
13454:
13393:
13136:{\displaystyle s}
13113:{\displaystyle k}
13024:
13004:
12965:
12926:
12885:{\displaystyle s}
12865:{\displaystyle T}
12845:{\displaystyle K}
12796:
12795:
12636:
12635:
12528:cosine similarity
12327:
12326:
12173:
12172:
12032:
12011:
11906:
11849:
11828:
11796:
11696:
11694:
11622:
11492:
11491:
11458:
11410:
11383:
11382:
11354:
11332:
11311:
11295:
11129:
11128:
11076:
11055:
11042:
10998:
10918:
10766:permutation tests
10568:
10563:
10535:
10530:
10492:
10457:
10451:
10446:
10411:
10390:
10367:
10361:
10356:
10327:
10324:
10319:
10312:
10307:
10285:
10221:
10185:
10180:
10120:
10099:
10074:
10038:
9994:
9951:
9937:
9902:
9887:
9866:
9843:
9824:
9771:
9770:
9756:
9721:
9706:
9685:
9662:
9646:
9645:
9632:
9611:
9588:
9572:
9537:
9522:
9501:
9478:
9463:
9462:
9449:
9428:
9405:
9389:
9354:
9336:
9315:
9293:
9272:
9247:
9208:
9193:
9192:
9179:
9158:
9135:
9119:
9084:
9076:
9055:
9036:
9015:
8993:
8957:
8942:
8941:
8928:
8907:
8884:
8868:
8833:
8825:
8804:
8785:
8750:
8734:
8680:
8631:
8577:
8563:
8528:
8513:
8492:
8469:
8461:
8447:
8412:
8391:
8355:
8317:
8271:
8250:
8227:
8205:
8169:
8153:
8118:
8080:
8052:
7942:
7941:
7846:
7790:
7728:
7676:
7611:
7540:, the p-value is
7446:
7390:
7389:
7384:
7315:{\displaystyle r}
7295:{\displaystyle n}
7260:
7259:
7239:
7175:
7114:
7076:
7033:{\displaystyle F}
6908:
6882:
6861:
6843:
6820:
6772:
6723:
6678:
6670:
6646:
6503:
6492:
6469:
6439:
6198:
6165:
6150:
6135:
6096:
6091:
6047:
6014:
6001:
5955:
5792:
5791:
5724:
5723:
5683:
5608:the sample size.
5601:{\displaystyle n}
5581:{\displaystyle r}
5553:
5552:
5486:{\displaystyle y}
5466:{\displaystyle x}
5441:of the resampled
5383:Using a bootstrap
5379:test is desired.
5265:Permutation tests
5168:
5133:with correlation
5073:
5070:
5063:
5047:
4930:cosine similarity
4907:
4904:
4897:
4881:
4790:= (1, 2, 3, 5, 8)
4018:
4005:
3957:
3904:
3889:
3823:
3782:
3770:
3632:{\displaystyle y}
3603:
3589:
3551:are defined below
3498:
3483:
3413:
3399:
3364:
3350:
3298:
3148:
3145:
3088:
3084:
2896:
2881:
2815:
2812:
2803:
2762:
2759:
2755:
2746:
2705:
2698:
2686:
2641:
2565:
2506:
2492:
2422:{\displaystyle n}
2392:
2389:
2376:
2326:
2313:
2257:
2226:
2115:{\displaystyle n}
1914:
1911:
1835:
1831:
888:{\displaystyle Y}
840:{\displaystyle X}
727:
426:{\displaystyle Y}
378:{\displaystyle X}
292:
55:Several sets of (
16:(Redirected from
19310:
19272:Confusion matrix
19047:Logarithmic Loss
18912:Machine learning
18905:
18898:
18891:
18882:
18881:
18866:
18865:
18854:
18853:
18843:
18842:
18828:
18827:
18731:Crime statistics
18625:
18624:
18612:
18611:
18529:
18528:
18495:Fourier analysis
18482:Frequency domain
18462:
18409:
18375:Structural break
18335:
18334:
18284:Cluster analysis
18231:Log-linear model
18204:
18203:
18179:
18178:
18120:
18094:Homoscedasticity
17950:
17949:
17926:
17925:
17845:
17837:
17829:
17828:(Kruskal–Wallis)
17813:
17798:
17753:Cross validation
17738:
17720:Anderson–Darling
17667:
17654:
17653:
17625:Likelihood-ratio
17617:Parametric tests
17595:Permutation test
17578:1- & 2-tails
17469:Minimum distance
17441:Point estimation
17437:
17436:
17388:Optimal decision
17339:
17238:
17237:
17225:
17224:
17207:Quasi-experiment
17157:Adaptive designs
17008:
17007:
16995:
16994:
16872:Rank correlation
16634:
16633:
16625:
16624:
16612:
16611:
16579:
16572:
16565:
16556:
16555:
16550:
16541:
16535:
16526:
16513:
16500:
16479:
16478:
16460:
16454:
16453:
16443:
16419:
16413:
16412:
16388:
16382:
16381:
16379:
16377:
16354:
16348:
16347:
16345:
16343:
16322:
16298:
16292:
16278:
16272:
16271:
16237:
16228:
16222:
16221:
16214:
16208:
16207:
16196:
16190:
16188:
16178:
16154:
16148:
16147:
16119:
16113:
16091:
16085:
16084:
16056:
16050:
16049:
16041:
16035:
16034:
16007:Devlin, Susan J.
16003:
15997:
15996:
15988:
15979:
15978:
15952:
15943:
15937:
15936:
15930:
15925:
15923:
15915:
15913:
15897:
15891:
15890:
15878:
15872:
15871:
15863:
15857:
15856:
15828:
15822:
15821:
15803:
15775:
15769:
15768:
15739:
15733:
15718:
15712:
15705:
15699:
15698:
15696:
15694:
15680:
15674:
15673:
15633:
15627:
15626:
15618:
15609:
15608:
15590:
15584:
15583:
15575:
15569:
15568:
15540:
15534:
15533:
15507:
15498:
15492:
15491:
15489:
15487:
15473:
15467:
15466:
15464:
15462:
15448:
15442:
15441:
15421:
15415:
15414:
15386:
15380:
15379:
15377:
15375:
15360:
15354:
15347:
15332:
15331:
15319:
15313:
15312:
15297:
15291:
15290:
15280:
15256:
15250:
15249:
15225:
15219:
15218:
15186:
15180:
15179:
15163:
15157:
15151:
15141:
15139:10.1038/015492a0
15109:
15103:
15102:
15091:
15085:
15084:
15077:
15061:
15054:
15048:
15023:
14905:
14900:
14899:
14882:
14878:has an in-built
14870:
14866:library via the
14854:
14848:
14837:
14824:
14808:
14803:
14780:
14778:
14777:
14772:
14767:
14766:
14765:
14757:
14744:
14743:
14742:
14712:
14710:
14709:
14704:
14696:
14695:
14680:
14672:
14616:
14615:
14611:
14608:
14599:
14597:
14596:
14591:
14586:
14585:
14584:
14576:
14563:
14562:
14561:
14531:
14529:
14528:
14523:
14518:
14517:
14502:
14494:
14442:
14440:
14439:
14434:
14432:
14431:
14401:
14399:
14398:
14393:
14391:
14390:
14343:random variables
14334:
14332:
14331:
14326:
14309:
14280:
14262:
14260:
14259:
14254:
14237:
14216:
14214:
14213:
14208:
14196:
14194:
14193:
14188:
14177:
14163:
14161:
14160:
14155:
14143:
14141:
14140:
14135:
14124:
14110:
14108:
14107:
14102:
14084:
14082:
14081:
14076:
14059:
14045:
14043:
14042:
14037:
14025:
14023:
14022:
14017:
14006:
13992:
13990:
13989:
13984:
13972:
13970:
13969:
13964:
13953:
13935:
13933:
13932:
13927:
13921:
13909:
13892:
13887:
13886:
13876:
13859:
13836:
13830:
13810:
13789:
13787:
13786:
13781:
13769:
13767:
13766:
13761:
13710:
13708:
13707:
13702:
13700:
13699:
13691:
13681:
13679:
13678:
13673:
13671:
13670:
13662:
13649:
13647:
13646:
13641:
13639:
13637:
13636:
13634:
13633:
13624:
13623:
13615:
13609:
13608:
13589:
13584:
13569:
13567:
13565:
13564:
13555:
13554:
13546:
13540:
13539:
13520:
13515:
13500:
13497:
13493:
13492:
13484:
13478:
13477:
13456:
13455:
13447:
13441:
13440:
13421:
13416:
13400:
13395:
13394:
13391:
13363:
13305:
13303:
13302:
13297:
13295:
13290:
13289:
13274:
13260:
13259:
13232:cluster analysis
13226:
13224:
13223:
13218:
13213:
13212:
13188:
13187:
13142:
13140:
13139:
13134:
13119:
13117:
13116:
13111:
13099:
13097:
13096:
13091:
13089:
13088:
13069:
13067:
13066:
13061:
13056:
13055:
13045:
13040:
13025:
13017:
13012:
13011:
13006:
13005:
12997:
12983:
12981:
12980:
12975:
12973:
12972:
12967:
12966:
12958:
12944:
12942:
12941:
12936:
12931:
12927:
12919:
12891:
12889:
12888:
12883:
12871:
12869:
12868:
12863:
12851:
12849:
12848:
12843:
12810:
12808:
12807:
12802:
12797:
12790:
12785:
12776:
12775:
12756:
12751:
12742:
12741:
12726:
12725:
12724:
12723:
12714:
12713:
12704:
12703:
12690:
12685:
12684:
12650:
12648:
12647:
12642:
12637:
12630:
12625:
12606:
12601:
12586:
12585:
12584:
12583:
12574:
12573:
12560:
12555:
12554:
12522:
12520:
12519:
12514:
12460:
12459:
12426:
12425:
12395:
12394:
12364:
12363:
12341:
12339:
12338:
12333:
12328:
12321:
12320:
12304:
12303:
12290:
12289:
12273:
12272:
12266:
12265:
12246:
12245:
12238:
12215:
12214:
12187:
12185:
12184:
12179:
12174:
12117:
12116:
12087:
12046:
12044:
12043:
12038:
12033:
12031:
12030:
12029:
12019:
12009:
11981:
11980:
11941:
11940:
11925:
11924:
11914:
11904:
11863:
11861:
11860:
11855:
11850:
11848:
11847:
11846:
11836:
11826:
11825:
11824:
11815:
11814:
11804:
11794:
11729:
11725:
11710:
11708:
11707:
11702:
11697:
11695:
11693:
11676:
11657:
11656:
11637:
11629:
11624:
11623:
11620:
11600:
11599:
11598:
11590:
11584:
11573:
11569:
11550:
11539:
11528:
11526:
11525:
11520:
11486:
11477:
11475:
11474:
11469:
11464:
11460:
11459:
11457:
11449:
11448:
11447:
11431:
11412:
11411:
11408:
11394:
11377:
11368:
11366:
11365:
11360:
11355:
11353:
11345:
11344:
11340:
11338:
11333:
11330:
11313:
11312:
11309:
11302:
11297:
11296:
11293:
11272:
11271:
11251:
11247:
11243:
11226:
11224:
11223:
11218:
11189:
11188:
11187:
11178:
11177:
11159:
11157:
11156:
11151:
11123:
11114:
11112:
11111:
11106:
11101:
11097:
11096:
11095:
11077:
11072:
11061:
11056:
11048:
11043:
11035:
11028:
11027:
11026:
11017:
11016:
11000:
10999:
10996:
10982:
10978:
10966:
10964:
10963:
10958:
10943:
10939:
10937:
10936:
10931:
10919:
10917:
10909:
10908:
10904:
10903:
10902:
10878:
10867:
10853:
10852:
10836:
10832:
10824:
10820:
10688:can be applied).
10580:
10578:
10577:
10572:
10570:
10569:
10566:
10564:
10561:
10547:
10545:
10544:
10539:
10537:
10536:
10533:
10531:
10528:
10514:
10512:
10511:
10506:
10504:
10503:
10494:
10493:
10485:
10479:
10478:
10465:
10453:
10452:
10449:
10447:
10444:
10433:
10431:
10430:
10425:
10423:
10422:
10413:
10412:
10404:
10398:
10397:
10392:
10391:
10383:
10375:
10363:
10362:
10359:
10357:
10354:
10338:
10336:
10335:
10330:
10328:
10326:
10325:
10322:
10320:
10317:
10314:
10313:
10310:
10308:
10305:
10302:
10297:
10296:
10287:
10286:
10278:
10249:
10247:
10246:
10241:
10239:
10238:
10229:
10228:
10223:
10222:
10214:
10207:
10206:
10193:
10181:
10178:
10152:
10141:
10139:
10138:
10133:
10122:
10121:
10113:
10107:
10106:
10101:
10100:
10092:
10082:
10081:
10076:
10075:
10067:
10060:
10059:
10046:
10016:
10014:
10013:
10008:
10006:
10005:
9996:
9995:
9987:
9962:
9960:
9959:
9954:
9952:
9950:
9949:
9948:
9939:
9938:
9930:
9924:
9923:
9910:
9900:
9899:
9898:
9889:
9888:
9880:
9874:
9873:
9868:
9867:
9859:
9851:
9841:
9836:
9835:
9826:
9825:
9817:
9789:
9787:
9786:
9781:
9779:
9772:
9769:
9768:
9767:
9758:
9757:
9749:
9743:
9742:
9729:
9719:
9718:
9717:
9708:
9707:
9699:
9693:
9692:
9687:
9686:
9678:
9670:
9660:
9659:
9651:
9647:
9644:
9643:
9634:
9633:
9625:
9619:
9618:
9613:
9612:
9604:
9596:
9584:
9583:
9574:
9573:
9565:
9559:
9558:
9545:
9536:
9535:
9534:
9533:
9524:
9523:
9515:
9509:
9508:
9503:
9502:
9494:
9486:
9476:
9468:
9464:
9461:
9460:
9451:
9450:
9442:
9436:
9435:
9430:
9429:
9421:
9413:
9401:
9400:
9391:
9390:
9382:
9376:
9375:
9362:
9353:
9352:
9348:
9347:
9338:
9337:
9329:
9323:
9322:
9317:
9316:
9308:
9295:
9294:
9286:
9280:
9279:
9274:
9273:
9265:
9255:
9254:
9249:
9248:
9240:
9233:
9232:
9216:
9206:
9198:
9194:
9191:
9190:
9181:
9180:
9172:
9166:
9165:
9160:
9159:
9151:
9143:
9131:
9130:
9121:
9120:
9112:
9106:
9105:
9092:
9083:
9082:
9078:
9077:
9069:
9063:
9062:
9057:
9056:
9048:
9038:
9037:
9029:
9023:
9022:
9017:
9016:
9008:
9001:
9000:
8995:
8994:
8986:
8979:
8978:
8965:
8955:
8947:
8943:
8940:
8939:
8930:
8929:
8921:
8915:
8914:
8909:
8908:
8900:
8892:
8880:
8879:
8870:
8869:
8861:
8855:
8854:
8841:
8832:
8831:
8827:
8826:
8818:
8812:
8811:
8806:
8805:
8797:
8787:
8786:
8778:
8772:
8771:
8758:
8748:
8736:
8735:
8727:
8698:
8696:
8695:
8690:
8688:
8687:
8682:
8681:
8673:
8666:
8665:
8649:
8647:
8646:
8641:
8639:
8638:
8633:
8632:
8624:
8591:
8589:
8588:
8583:
8578:
8576:
8575:
8574:
8565:
8564:
8556:
8550:
8549:
8536:
8526:
8525:
8524:
8515:
8514:
8506:
8500:
8499:
8494:
8493:
8485:
8477:
8467:
8462:
8460:
8459:
8458:
8449:
8448:
8440:
8434:
8433:
8420:
8410:
8409:
8408:
8399:
8398:
8393:
8392:
8384:
8377:
8376:
8363:
8353:
8335:
8333:
8332:
8327:
8325:
8324:
8319:
8318:
8310:
8296:
8294:
8293:
8288:
8283:
8282:
8273:
8272:
8264:
8258:
8257:
8252:
8251:
8243:
8235:
8223:
8222:
8213:
8212:
8207:
8206:
8198:
8191:
8190:
8177:
8165:
8164:
8155:
8154:
8146:
8140:
8139:
8126:
8098:
8096:
8095:
8090:
8088:
8087:
8082:
8081:
8073:
8060:
8059:
8054:
8053:
8045:
8034:
8032:
8031:
8026:
8024:
8023:
8005:
8004:
7953:
7951:
7950:
7945:
7943:
7937:
7933:
7918:
7916:
7915:
7910:
7902:
7863:
7861:
7860:
7855:
7847:
7844:
7842:
7841:
7837:
7791:
7788:
7786:
7785:
7781:
7729:
7726:
7690:
7688:
7687:
7682:
7677:
7674:
7672:
7671:
7667:
7612:
7609:
7575:
7573:
7572:
7567:
7543:
7539:
7537:
7536:
7531:
7497:
7495:
7494:
7489:
7487:
7486:
7457:
7455:
7454:
7449:
7447:
7436:
7428:
7427:
7391:
7387:
7386:
7385:
7382:
7373:
7348:
7346:
7345:
7340:
7338:
7337:
7321:
7319:
7318:
7313:
7301:
7299:
7298:
7293:
7274:
7272:
7271:
7266:
7261:
7249:
7245:
7240:
7237:
7222:
7219:
7217:
7216:
7211:
7176:
7173:
7147:
7145:
7144:
7139:
7119:
7115:
7113:
7102:
7091:
7078:
7069:
7039:
7037:
7036:
7031:
7006:hypothesis tests
6985:
6983:
6982:
6977:
6947:
6945:
6944:
6939:
6925:
6923:
6922:
6917:
6915:
6911:
6910:
6904:
6890:
6884:
6875:
6863:
6854:
6845:
6836:
6822:
6821:
6816:
6802:
6800:
6796:
6774:
6773:
6768:
6757:
6755:
6751:
6750:
6749:
6725:
6724:
6719:
6708:
6706:
6702:
6701:
6700:
6679:
6677:
6676:
6672:
6671:
6663:
6647:
6639:
6636:
6598:
6542:
6540:
6539:
6534:
6532:
6517:
6515:
6514:
6509:
6504:
6502:
6501:
6500:
6499:
6495:
6494:
6488:
6477:
6471:
6462:
6449:
6448:
6441:
6440:
6435:
6424:
6422:
6418:
6417:
6416:
6395:
6360:
6358:
6357:
6352:
6327:
6325:
6324:
6319:
6290:
6289:
6284:
6278:
6277:
6272:
6258:
6256:
6255:
6250:
6235:
6233:
6232:
6227:
6225:
6224:
6223:
6219:
6200:
6191:
6167:
6158:
6152:
6143:
6137:
6128:
6118:
6117:
6112:
6106:
6105:
6100:
6097:
6095:
6094:
6093:
6092:
6084:
6056:
6055:
6054:
6050:
6049:
6040:
6021:
6015:
6007:
6004:
6003:
6002:
5997:
5986:
5984:
5980:
5979:
5978:
5957:
5956:
5951:
5940:
5938:
5934:
5933:
5932:
5896:
5874:
5806:
5804:
5803:
5798:
5793:
5790:
5789:
5768:
5764:
5739:has a student's
5735:
5733:
5732:
5727:
5725:
5722:
5721:
5720:
5704:
5693:
5692:
5684:
5682:
5681:
5669:
5607:
5605:
5604:
5599:
5587:
5585:
5584:
5579:
5564:
5562:
5561:
5556:
5554:
5551:
5540:
5539:
5538:
5522:
5521:
5516:
5515:
5492:
5490:
5489:
5484:
5472:
5470:
5469:
5464:
5179:
5177:
5176:
5171:
5169:
5167:
5166:
5151:
5109:
5107:
5106:
5101:
5096:
5095:
5074:
5072:
5071:
5066:
5064:
5059:
5053:
5048:
5046:
5045:
5041:
5032:
5028:
5018:
5017:
5009:
5003:
4979:
4972:
4965:
4953:
4941:
4924:
4922:
4921:
4916:
4908:
4906:
4905:
4900:
4898:
4893:
4887:
4882:
4880:
4879:
4875:
4866:
4862:
4852:
4851:
4843:
4837:
4798:
4791:
4741:
4727:
4720:
4693:
4673:
4646:
4626:
4527:anti-correlation
4488:
4486:
4471:
4455:More generally,
4448:increases while
4434:regression slope
4405:
4378:
4364:
4285:Practical issues
4280:
4278:
4277:
4272:
4270:
4269:
4261:
4256:
4245:
4244:
4235:
4234:
4225:
4224:
4205:
4204:
4195:
4194:
4185:
4184:
4166:
4161:
4131:
4129:
4128:
4123:
4101:
4099:
4098:
4093:
4060:
4058:
4057:
4052:
4050:
4049:
4029:
4027:
4026:
4021:
4019:
4017:
4016:
4007:
4006:
3998:
3992:
3991:
3978:
3973:
3958:
3956:
3942:
3940:
3935:
3934:
3916:
3914:
3913:
3908:
3906:
3905:
3897:
3891:
3890:
3882:
3876:
3875:
3863:
3862:
3834:
3832:
3831:
3826:
3824:
3822:
3821:
3820:
3811:
3810:
3785:
3784:
3783:
3775:
3772:
3771:
3763:
3754:
3753:
3744:
3743:
3730:
3725:
3724:
3702:
3700:
3699:
3694:
3692:
3691:
3672:
3670:
3669:
3664:
3662:
3661:
3638:
3636:
3635:
3630:
3618:
3616:
3615:
3610:
3608:
3604:
3602:
3601:
3592:
3591:
3590:
3582:
3576:
3575:
3565:
3550:
3548:
3547:
3542:
3540:
3539:
3527:
3526:
3510:
3508:
3507:
3502:
3500:
3499:
3491:
3485:
3484:
3476:
3470:
3469:
3457:
3456:
3428:
3426:
3425:
3420:
3418:
3414:
3412:
3411:
3402:
3401:
3400:
3392:
3386:
3385:
3375:
3369:
3365:
3363:
3362:
3353:
3352:
3351:
3343:
3337:
3336:
3326:
3319:
3314:
3299:
3297:
3283:
3278:
3277:
3251:
3249:
3248:
3243:
3241:
3240:
3211:
3209:
3208:
3203:
3201:
3200:
3188:
3187:
3162:
3160:
3159:
3154:
3149:
3147:
3146:
3144:
3143:
3138:
3134:
3133:
3132:
3110:
3105:
3090:
3086:
3085:
3083:
3082:
3077:
3073:
3072:
3071:
3049:
3044:
3029:
3026:
3025:
3024:
3012:
3011:
2996:
2995:
2986:
2985:
2969:
2964:
2963:
2941:
2939:
2938:
2933:
2931:
2930:
2908:
2906:
2905:
2900:
2898:
2897:
2889:
2883:
2882:
2874:
2868:
2867:
2855:
2854:
2829:
2827:
2826:
2821:
2816:
2814:
2813:
2811:
2810:
2805:
2804:
2796:
2785:
2780:
2770:
2761:
2757:
2756:
2754:
2753:
2748:
2747:
2739:
2728:
2723:
2713:
2704:
2701:
2700:
2699:
2691:
2688:
2687:
2679:
2670:
2669:
2660:
2659:
2649:
2639:
2634:
2633:
2611:
2609:
2608:
2603:
2601:
2600:
2577:
2575:
2574:
2569:
2567:
2566:
2558:
2548:
2546:
2545:
2540:
2538:
2537:
2527:
2522:
2507:
2499:
2494:
2493:
2485:
2470:
2468:
2467:
2462:
2460:
2459:
2447:
2446:
2428:
2426:
2425:
2420:
2403:
2401:
2400:
2395:
2393:
2391:
2390:
2388:
2387:
2378:
2377:
2369:
2363:
2362:
2349:
2344:
2329:
2327:
2325:
2324:
2315:
2314:
2306:
2300:
2299:
2286:
2281:
2266:
2263:
2259:
2258:
2250:
2244:
2243:
2228:
2227:
2219:
2213:
2212:
2199:
2194:
2178:
2173:
2172:
2151:
2149:
2148:
2143:
2141:
2140:
2121:
2119:
2118:
2113:
2101:
2099:
2098:
2093:
2091:
2087:
2083:
2082:
2070:
2069:
2045:
2044:
2032:
2031:
2007:
2005:
2004:
1999:
1997:
1996:
1969:
1967:
1966:
1961:
1959:
1958:
1928:
1926:
1925:
1920:
1915:
1913:
1912:
1910:
1909:
1904:
1900:
1885:
1884:
1869:
1865:
1863:
1862:
1844:
1843:
1837:
1833:
1832:
1830:
1829:
1824:
1820:
1805:
1804:
1789:
1785:
1783:
1782:
1764:
1763:
1757:
1754:
1739:
1738:
1718:
1717:
1690:
1689:
1682:
1677:
1676:
1654:
1652:
1651:
1646:
1635:the formula for
1631:
1629:
1628:
1623:
1621:
1599:
1598:
1578:
1577:
1550:
1549:
1536:
1532:
1517:
1516:
1499:
1495:
1480:
1479:
1455:
1454:
1441:
1437:
1436:
1435:
1415:
1411:
1410:
1409:
1382:
1381:
1374:
1370:
1369:
1364:
1360:
1345:
1344:
1328:
1324:
1322:
1321:
1303:
1302:
1293:
1289:
1287:
1286:
1281:
1277:
1264:
1263:
1236:
1235:
1227:
1221:
1216:
1203:
1202:
1197:
1193:
1178:
1177:
1162:
1158:
1156:
1155:
1137:
1136:
1127:
1123:
1121:
1120:
1115:
1111:
1098:
1097:
1070:
1069:
1061:
1055:
1050:
1023:
1022:
1014:
1009:
1008:
981:
980:
972:
967:
966:
943:
941:
940:
935:
924:The formula for
919:
917:
916:
911:
909:
908:
894:
892:
891:
886:
874:
872:
871:
866:
864:
863:
846:
844:
843:
838:
826:
824:
823:
818:
816:
815:
797:
795:
794:
789:
787:
786:
770:
768:
767:
762:
760:
759:
738:
736:
735:
730:
728:
726:
725:
724:
715:
714:
704:
697:
696:
675:
674:
650:
649:
642:
637:
636:
612:
610:
609:
604:
593:the formula for
589:
587:
586:
581:
570:
569:
548:
547:
523:
522:
474:
472:
471:
466:
437:The formula for
432:
430:
429:
424:
412:
410:
409:
404:
402:
401:
384:
382:
381:
376:
360:
358:
357:
352:
350:
349:
328:
326:
325:
320:
303:
301:
300:
295:
293:
291:
290:
289:
280:
279:
269:
246:
241:
240:
212:
210:
209:
204:
161:For a population
21:
19318:
19317:
19313:
19312:
19311:
19309:
19308:
19307:
19283:
19282:
19281:
19276:
19263:
19237:
19214:
19205:Inception score
19193:
19170:
19148:Computer Vision
19142:
19114:
19051:
18983:
18915:
18909:
18879:
18874:
18837:
18808:
18770:
18707:
18693:quality control
18660:
18642:Clinical trials
18619:
18594:
18578:
18566:Hazard function
18560:
18514:
18476:
18460:
18423:
18419:Breusch–Godfrey
18407:
18384:
18324:
18299:Factor analysis
18245:
18226:Graphical model
18198:
18165:
18132:
18118:
18098:
18052:
18019:
17981:
17944:
17943:
17912:
17856:
17843:
17835:
17827:
17811:
17796:
17775:Rank statistics
17769:
17748:Model selection
17736:
17694:Goodness of fit
17688:
17665:
17639:
17611:
17564:
17509:
17498:Median unbiased
17426:
17337:
17270:Order statistic
17232:
17211:
17178:
17152:
17104:
17059:
17002:
17000:Data collection
16981:
16893:
16848:
16822:
16800:
16760:
16712:
16629:Continuous data
16619:
16606:
16588:
16583:
16545:
16533:
16529:
16517:
16504:
16491:
16488:
16483:
16482:
16475:
16461:
16457:
16420:
16416:
16389:
16385:
16375:
16373:
16371:
16355:
16351:
16341:
16339:
16320:10.1.1.642.9971
16299:
16295:
16279:
16275:
16235:
16229:
16225:
16216:
16215:
16211:
16198:
16197:
16193:
16155:
16151:
16120:
16116:
16092:
16088:
16081:
16057:
16053:
16042:
16038:
16004:
16000:
15989:
15982:
15950:
15944:
15940:
15928:
15926:
15917:
15916:
15898:
15894:
15879:
15875:
15864:
15860:
15829:
15825:
15776:
15772:
15740:
15736:
15732:(Section 31.19)
15719:
15715:
15706:
15702:
15692:
15690:
15688:Cross Validated
15682:
15681:
15677:
15654:10.2307/2277400
15634:
15630:
15625:(2nd ed.).
15619:
15612:
15605:
15591:
15587:
15576:
15572:
15541:
15537:
15522:10.2307/2685263
15505:
15499:
15495:
15485:
15483:
15475:
15474:
15470:
15460:
15458:
15450:
15449:
15445:
15422:
15418:
15411:
15387:
15383:
15373:
15371:
15361:
15357:
15348:
15335:
15320:
15316:
15299:
15298:
15294:
15257:
15253:
15226:
15222:
15207:10.2307/2841583
15187:
15183:
15178:(830): 507–510.
15164:
15160:
15110:
15106:
15093:
15092:
15088:
15079:
15078:
15074:
15069:
15064:
15055:
15051:
15024:
15020:
15016:
14901:
14894:
14891:
14880:
14868:
14853:CorrelationTest
14852:
14846:
14835:
14822:
14806:
14801:
14794:
14756:
14752:
14748:
14738:
14737:
14733:
14719:
14716:
14715:
14685:
14681:
14671:
14657:
14654:
14653:
14617:represents the
14613:
14609:
14606:
14604:
14575:
14571:
14567:
14557:
14556:
14552:
14538:
14535:
14534:
14507:
14503:
14493:
14479:
14476:
14475:
14421:
14417:
14415:
14412:
14411:
14380:
14376:
14374:
14371:
14370:
14351:
14345:
14299:
14270:
14268:
14265:
14264:
14227:
14225:
14222:
14221:
14202:
14199:
14198:
14173:
14171:
14168:
14167:
14149:
14146:
14145:
14120:
14118:
14115:
14114:
14090:
14087:
14086:
14055:
14053:
14050:
14049:
14031:
14028:
14027:
14002:
14000:
13997:
13996:
13978:
13975:
13974:
13949:
13947:
13944:
13943:
13905:
13888:
13872:
13855:
13832:
13831:
13829:
13800:
13798:
13795:
13794:
13775:
13772:
13771:
13755:
13752:
13751:
13748:
13735:
13729:
13690:
13689:
13687:
13684:
13683:
13661:
13660:
13658:
13655:
13654:
13629:
13625:
13614:
13613:
13604:
13600:
13585:
13574:
13568:
13560:
13556:
13545:
13544:
13535:
13531:
13516:
13505:
13499:
13498:
13483:
13482:
13473:
13469:
13446:
13445:
13436:
13432:
13417:
13406:
13401:
13399:
13390:
13386:
13384:
13381:
13380:
13361:
13359:
13350:
13339:
13330:
13318:
13312:
13291:
13279:
13275:
13270:
13249:
13245:
13243:
13240:
13239:
13202:
13198:
13177:
13173:
13171:
13168:
13167:
13149:
13128:
13125:
13124:
13105:
13102:
13101:
13084:
13080:
13078:
13075:
13074:
13051:
13047:
13041:
13030:
13016:
13007:
12996:
12995:
12994:
12992:
12989:
12988:
12968:
12957:
12956:
12955:
12953:
12950:
12949:
12918:
12914:
12900:
12897:
12896:
12877:
12874:
12873:
12857:
12854:
12853:
12837:
12834:
12833:
12823:
12817:
12786:
12781:
12771:
12767:
12752:
12747:
12737:
12733:
12719:
12715:
12709:
12705:
12699:
12695:
12691:
12689:
12671:
12667:
12662:
12659:
12658:
12626:
12621:
12602:
12597:
12579:
12575:
12569:
12565:
12561:
12559:
12547:
12543:
12538:
12535:
12534:
12455:
12451:
12421:
12417:
12390:
12386:
12359:
12355:
12353:
12350:
12349:
12316:
12312:
12299:
12298:
12285:
12281:
12268:
12267:
12241:
12240:
12239:
12237:
12210:
12206:
12204:
12201:
12200:
12194:
12088:
12086:
12054:
12051:
12050:
12025:
12021:
12015:
12010:
11976:
11972:
11936:
11932:
11920:
11916:
11910:
11905:
11903:
11871:
11868:
11867:
11842:
11838:
11832:
11827:
11820:
11816:
11810:
11806:
11800:
11795:
11793:
11767:
11764:
11763:
11762:Weighted mean:
11736:
11727:
11720:
11714:
11677:
11652:
11648:
11638:
11636:
11628:
11619:
11615:
11613:
11610:
11609:
11592:
11588:
11587:
11586:
11583:
11577:
11571:
11568:
11562:
11549:
11543:
11538:
11532:
11508:
11505:
11504:
11450:
11443:
11439:
11432:
11430:
11423:
11419:
11407:
11403:
11401:
11398:
11397:
11346:
11334:
11329:
11318:
11314:
11308:
11304:
11303:
11301:
11292:
11288:
11267:
11266:
11258:
11255:
11254:
11245:
11242:
11236:
11183:
11179:
11173:
11170:
11169:
11167:
11164:
11163:
11139:
11136:
11135:
11091:
11087:
11062:
11060:
11047:
11034:
11033:
11029:
11022:
11018:
11012:
11009:
11008:
10995:
10991:
10989:
10986:
10985:
10977:
10971:
10949:
10946:
10945:
10941:
10910:
10898:
10894:
10887:
10883:
10879:
10877:
10857:
10848:
10847:
10845:
10842:
10841:
10834:
10830:
10822:
10818:
10815:
10807:
10801:
10774:exchangeability
10713:
10652:
10606:
10601:
10595:
10565:
10560:
10559:
10557:
10554:
10553:
10532:
10527:
10526:
10524:
10521:
10520:
10499:
10495:
10484:
10483:
10474:
10470:
10461:
10448:
10443:
10442:
10440:
10437:
10436:
10418:
10414:
10403:
10402:
10393:
10382:
10381:
10380:
10371:
10358:
10353:
10352:
10350:
10347:
10346:
10321:
10316:
10315:
10309:
10304:
10303:
10301:
10292:
10288:
10277:
10276:
10262:
10259:
10258:
10234:
10230:
10224:
10213:
10212:
10211:
10202:
10198:
10189:
10177:
10175:
10172:
10171:
10166:
10159:
10150:
10112:
10111:
10102:
10091:
10090:
10089:
10077:
10066:
10065:
10064:
10055:
10051:
10042:
10036:
10033:
10032:
10001:
9997:
9986:
9985:
9971:
9968:
9967:
9944:
9940:
9929:
9928:
9919:
9915:
9906:
9901:
9894:
9890:
9879:
9878:
9869:
9858:
9857:
9856:
9847:
9842:
9840:
9831:
9827:
9816:
9815:
9801:
9798:
9797:
9777:
9776:
9763:
9759:
9748:
9747:
9738:
9734:
9725:
9720:
9713:
9709:
9698:
9697:
9688:
9677:
9676:
9675:
9666:
9661:
9658:
9649:
9648:
9639:
9635:
9624:
9623:
9614:
9603:
9602:
9601:
9592:
9579:
9575:
9564:
9563:
9554:
9550:
9541:
9529:
9525:
9514:
9513:
9504:
9493:
9492:
9491:
9482:
9477:
9475:
9466:
9465:
9456:
9452:
9441:
9440:
9431:
9420:
9419:
9418:
9409:
9396:
9392:
9381:
9380:
9371:
9367:
9358:
9343:
9339:
9328:
9327:
9318:
9307:
9306:
9305:
9285:
9284:
9275:
9264:
9263:
9262:
9250:
9239:
9238:
9237:
9228:
9224:
9212:
9207:
9205:
9196:
9195:
9186:
9182:
9171:
9170:
9161:
9150:
9149:
9148:
9139:
9126:
9122:
9111:
9110:
9101:
9097:
9088:
9068:
9067:
9058:
9047:
9046:
9045:
9028:
9027:
9018:
9007:
9006:
9005:
8996:
8985:
8984:
8983:
8974:
8970:
8961:
8956:
8954:
8945:
8944:
8935:
8931:
8920:
8919:
8910:
8899:
8898:
8897:
8888:
8875:
8871:
8860:
8859:
8850:
8846:
8837:
8817:
8816:
8807:
8796:
8795:
8794:
8777:
8776:
8767:
8763:
8754:
8749:
8747:
8740:
8726:
8725:
8709:
8707:
8704:
8703:
8683:
8672:
8671:
8670:
8661:
8657:
8655:
8652:
8651:
8634:
8623:
8622:
8621:
8619:
8616:
8615:
8570:
8566:
8555:
8554:
8545:
8541:
8532:
8527:
8520:
8516:
8505:
8504:
8495:
8484:
8483:
8482:
8473:
8468:
8466:
8454:
8450:
8439:
8438:
8429:
8425:
8416:
8411:
8404:
8400:
8394:
8383:
8382:
8381:
8372:
8368:
8359:
8354:
8352:
8344:
8341:
8340:
8320:
8309:
8308:
8307:
8305:
8302:
8301:
8278:
8274:
8263:
8262:
8253:
8242:
8241:
8240:
8231:
8218:
8214:
8208:
8197:
8196:
8195:
8186:
8182:
8173:
8160:
8156:
8145:
8144:
8135:
8131:
8122:
8116:
8113:
8112:
8107:
8083:
8072:
8071:
8070:
8055:
8044:
8043:
8042:
8040:
8037:
8036:
8019:
8015:
8000:
7996:
7994:
7991:
7990:
7967:
7960:
7932:
7924:
7921:
7920:
7892:
7884:
7881:
7880:
7843:
7833:
7829:
7825:
7787:
7777:
7773:
7769:
7725:
7702:
7699:
7698:
7673:
7663:
7659:
7655:
7608:
7585:
7582:
7581:
7561:
7558:
7557:
7541:
7519:
7516:
7515:
7482:
7478:
7470:
7467:
7466:
7463:null hypothesis
7435:
7423:
7419:
7381:
7374:
7372:
7364:
7361:
7360:
7333:
7329:
7327:
7324:
7323:
7307:
7304:
7303:
7287:
7284:
7283:
7244:
7236:
7231:
7228:
7227:
7220:
7172:
7170:
7167:
7166:
7103:
7092:
7090:
7086:
7067:
7050:
7047:
7046:
7025:
7022:
7021:
6998:
6992:
6953:
6950:
6949:
6933:
6930:
6929:
6891:
6888:
6873:
6852:
6834:
6833:
6829:
6803:
6801:
6783:
6779:
6778:
6758:
6756:
6745:
6741:
6734:
6730:
6729:
6709:
6707:
6696:
6692:
6685:
6681:
6680:
6662:
6655:
6651:
6638:
6637:
6599:
6597:
6574:
6571:
6570:
6557:
6528:
6526:
6523:
6522:
6478:
6475:
6460:
6459:
6455:
6454:
6453:
6444:
6443:
6442:
6425:
6423:
6412:
6408:
6401:
6397:
6396:
6394:
6377:
6374:
6373:
6340:
6337:
6336:
6285:
6280:
6279:
6273:
6271:
6270:
6268:
6265:
6264:
6244:
6241:
6240:
6189:
6156:
6141:
6126:
6125:
6121:
6120:
6119:
6113:
6108:
6107:
6101:
6099:
6098:
6083:
6076:
6072:
6038:
6031:
6027:
6026:
6025:
6017:
6006:
6005:
5987:
5985:
5974:
5970:
5963:
5959:
5958:
5941:
5939:
5928:
5924:
5917:
5913:
5912:
5892:
5875:
5873:
5856:
5853:
5852:
5830:
5785:
5781:
5763:
5755:
5752:
5751:
5716:
5712:
5705:
5694:
5691:
5677:
5673:
5668:
5660:
5657:
5656:
5618:
5593:
5590:
5589:
5573:
5570:
5569:
5541:
5534:
5530:
5523:
5520:
5511:
5507:
5505:
5502:
5501:
5478:
5475:
5474:
5458:
5455:
5454:
5451:
5412:
5403:
5385:
5306:
5297:
5288:
5279:
5262:
5231:null hypothesis
5223:
5162:
5158:
5150:
5142:
5139:
5138:
5119:
5088:
5084:
5065:
5058:
5057:
5052:
5037:
5033:
5024:
5020:
5019:
5013:
5005:
5004:
5002:
4988:
4985:
4984:
4974:
4967:
4959:
4947:
4933:
4899:
4892:
4891:
4886:
4871:
4867:
4858:
4854:
4853:
4847:
4839:
4838:
4836:
4822:
4819:
4818:
4793:
4786:
4729:
4722:
4715:
4687:
4675:
4667:
4655:
4640:
4628:
4620:
4608:
4601:
4546:
4537:
4524:
4515:
4506:
4497:
4482:
4480:
4467:
4465:
4456:
4418:
4396:
4370:
4356:
4321:
4287:
4264:
4263:
4257:
4252:
4246:
4240:
4236:
4230:
4226:
4214:
4210:
4207:
4206:
4200:
4196:
4190:
4186:
4174:
4170:
4168:
4162:
4157:
4146:
4145:
4137:
4134:
4133:
4117:
4114:
4113:
4075:
4072:
4071:
4068:
4045:
4041:
4039:
4036:
4035:
4012:
4008:
3997:
3996:
3987:
3983:
3974:
3963:
3946:
3941:
3939:
3930:
3926:
3924:
3921:
3920:
3896:
3895:
3881:
3880:
3871:
3867:
3858:
3854:
3846:
3843:
3842:
3816:
3812:
3806:
3802:
3786:
3774:
3773:
3762:
3761:
3749:
3745:
3739:
3735:
3731:
3729:
3717:
3713:
3711:
3708:
3707:
3684:
3680:
3678:
3675:
3674:
3654:
3650:
3648:
3645:
3644:
3624:
3621:
3620:
3597:
3593:
3581:
3580:
3571:
3567:
3566:
3564:
3560:
3558:
3555:
3554:
3535:
3531:
3522:
3518:
3516:
3513:
3512:
3490:
3489:
3475:
3474:
3465:
3461:
3452:
3448:
3440:
3437:
3436:
3407:
3403:
3391:
3390:
3381:
3377:
3376:
3374:
3370:
3358:
3354:
3342:
3341:
3332:
3328:
3327:
3325:
3321:
3315:
3304:
3287:
3282:
3270:
3266:
3264:
3261:
3260:
3254:standard scores
3233:
3229:
3227:
3224:
3223:
3196:
3192:
3183:
3179:
3171:
3168:
3167:
3139:
3128:
3124:
3120:
3116:
3115:
3106:
3101:
3089:
3078:
3067:
3063:
3059:
3055:
3054:
3045:
3040:
3028:
3027:
3020:
3016:
3007:
3003:
2991:
2987:
2981:
2977:
2970:
2968:
2956:
2952:
2950:
2947:
2946:
2923:
2919:
2917:
2914:
2913:
2888:
2887:
2873:
2872:
2863:
2859:
2850:
2846:
2838:
2835:
2834:
2806:
2795:
2794:
2793:
2781:
2776:
2766:
2760:
2749:
2738:
2737:
2736:
2724:
2719:
2709:
2703:
2702:
2690:
2689:
2678:
2677:
2665:
2661:
2655:
2651:
2645:
2640:
2638:
2626:
2622:
2620:
2617:
2616:
2593:
2589:
2587:
2584:
2583:
2557:
2556:
2554:
2551:
2550:
2533:
2529:
2523:
2512:
2498:
2484:
2483:
2481:
2478:
2477:
2455:
2451:
2442:
2438:
2436:
2433:
2432:
2414:
2411:
2410:
2383:
2379:
2368:
2367:
2358:
2354:
2345:
2334:
2328:
2320:
2316:
2305:
2304:
2295:
2291:
2282:
2271:
2265:
2264:
2249:
2248:
2239:
2235:
2218:
2217:
2208:
2204:
2195:
2184:
2179:
2177:
2165:
2161:
2159:
2156:
2155:
2133:
2129:
2127:
2124:
2123:
2107:
2104:
2103:
2078:
2074:
2065:
2061:
2040:
2036:
2027:
2023:
2019:
2015:
2013:
2010:
2009:
1989:
1985:
1983:
1980:
1979:
1951:
1947:
1945:
1942:
1941:
1934:
1905:
1880:
1879:
1878:
1874:
1873:
1858:
1854:
1852:
1848:
1839:
1838:
1836:
1825:
1800:
1799:
1798:
1794:
1793:
1778:
1774:
1772:
1768:
1759:
1758:
1756:
1755:
1734:
1733:
1713:
1712:
1685:
1684:
1683:
1681:
1666:
1662:
1660:
1657:
1656:
1640:
1637:
1636:
1619:
1618:
1594:
1593:
1573:
1572:
1545:
1544:
1512:
1511:
1504:
1500:
1475:
1474:
1467:
1463:
1450:
1449:
1431:
1427:
1420:
1416:
1405:
1401:
1394:
1390:
1377:
1376:
1372:
1371:
1365:
1340:
1339:
1337:
1333:
1332:
1317:
1313:
1311:
1307:
1298:
1297:
1282:
1259:
1258:
1251:
1247:
1246:
1244:
1240:
1231:
1230:
1228:
1226:
1217:
1212:
1205:
1204:
1198:
1173:
1172:
1171:
1167:
1166:
1151:
1147:
1145:
1141:
1132:
1131:
1116:
1093:
1092:
1085:
1081:
1080:
1078:
1074:
1065:
1064:
1062:
1060:
1051:
1046:
1039:
1038:
1018:
1017:
1015:
1013:
1004:
1000:
997:
996:
976:
975:
973:
971:
962:
958:
954:
952:
949:
948:
929:
926:
925:
904:
903:
901:
898:
897:
880:
877:
876:
875:is the mean of
859:
855:
853:
850:
849:
832:
829:
828:
827:is the mean of
811:
807:
805:
802:
801:
782:
778:
776:
773:
772:
755:
751:
749:
746:
745:
720:
716:
710:
706:
705:
692:
688:
670:
666:
645:
644:
643:
641:
626:
622:
620:
617:
616:
598:
595:
594:
565:
561:
543:
539:
518:
517:
491:
488:
487:
442:
439:
438:
418:
415:
414:
397:
393:
391:
388:
387:
370:
367:
366:
345:
341:
339:
336:
335:
314:
311:
310:
285:
281:
275:
271:
270:
247:
245:
230:
226:
224:
221:
220:
186:
183:
182:
163:
143:
131:Auguste Bravais
119:
35:
28:
23:
22:
15:
12:
11:
5:
19316:
19306:
19305:
19300:
19295:
19278:
19277:
19275:
19274:
19268:
19265:
19264:
19262:
19261:
19256:
19251:
19245:
19243:
19239:
19238:
19236:
19235:
19230:
19224:
19222:
19216:
19215:
19213:
19212:
19207:
19201:
19199:
19195:
19194:
19192:
19191:
19186:
19180:
19178:
19172:
19171:
19169:
19168:
19163:
19158:
19152:
19150:
19144:
19143:
19141:
19140:
19135:
19130:
19124:
19122:
19116:
19115:
19113:
19112:
19107:
19102:
19097:
19092:
19087:
19082:
19077:
19075:Davies-Bouldin
19072:
19067:
19061:
19059:
19053:
19052:
19050:
19049:
19044:
19039:
19034:
19029:
19024:
19019:
19014:
19009:
19004:
18999:
18993:
18991:
18989:Classification
18985:
18984:
18982:
18981:
18976:
18971:
18966:
18961:
18956:
18951:
18946:
18941:
18936:
18931:
18925:
18923:
18917:
18916:
18908:
18907:
18900:
18893:
18885:
18876:
18875:
18873:
18872:
18860:
18848:
18834:
18821:
18818:
18817:
18814:
18813:
18810:
18809:
18807:
18806:
18801:
18796:
18791:
18786:
18780:
18778:
18772:
18771:
18769:
18768:
18763:
18758:
18753:
18748:
18743:
18738:
18733:
18728:
18723:
18717:
18715:
18709:
18708:
18706:
18705:
18700:
18695:
18686:
18681:
18676:
18670:
18668:
18662:
18661:
18659:
18658:
18653:
18648:
18639:
18637:Bioinformatics
18633:
18631:
18621:
18620:
18608:
18607:
18604:
18603:
18600:
18599:
18596:
18595:
18593:
18592:
18586:
18584:
18580:
18579:
18577:
18576:
18570:
18568:
18562:
18561:
18559:
18558:
18553:
18548:
18543:
18537:
18535:
18526:
18520:
18519:
18516:
18515:
18513:
18512:
18507:
18502:
18497:
18492:
18486:
18484:
18478:
18477:
18475:
18474:
18469:
18464:
18456:
18451:
18446:
18445:
18444:
18442:partial (PACF)
18433:
18431:
18425:
18424:
18422:
18421:
18416:
18411:
18403:
18398:
18392:
18390:
18389:Specific tests
18386:
18385:
18383:
18382:
18377:
18372:
18367:
18362:
18357:
18352:
18347:
18341:
18339:
18332:
18326:
18325:
18323:
18322:
18321:
18320:
18319:
18318:
18303:
18302:
18301:
18291:
18289:Classification
18286:
18281:
18276:
18271:
18266:
18261:
18255:
18253:
18247:
18246:
18244:
18243:
18238:
18236:McNemar's test
18233:
18228:
18223:
18218:
18212:
18210:
18200:
18199:
18175:
18174:
18171:
18170:
18167:
18166:
18164:
18163:
18158:
18153:
18148:
18142:
18140:
18134:
18133:
18131:
18130:
18114:
18108:
18106:
18100:
18099:
18097:
18096:
18091:
18086:
18081:
18076:
18074:Semiparametric
18071:
18066:
18060:
18058:
18054:
18053:
18051:
18050:
18045:
18040:
18035:
18029:
18027:
18021:
18020:
18018:
18017:
18012:
18007:
18002:
17997:
17991:
17989:
17983:
17982:
17980:
17979:
17974:
17969:
17964:
17958:
17956:
17946:
17945:
17942:
17941:
17936:
17930:
17922:
17921:
17918:
17917:
17914:
17913:
17911:
17910:
17909:
17908:
17898:
17893:
17888:
17887:
17886:
17881:
17870:
17868:
17862:
17861:
17858:
17857:
17855:
17854:
17849:
17848:
17847:
17839:
17831:
17815:
17812:(Mann–Whitney)
17807:
17806:
17805:
17792:
17791:
17790:
17779:
17777:
17771:
17770:
17768:
17767:
17766:
17765:
17760:
17755:
17745:
17740:
17737:(Shapiro–Wilk)
17732:
17727:
17722:
17717:
17712:
17704:
17698:
17696:
17690:
17689:
17687:
17686:
17678:
17669:
17657:
17651:
17649:Specific tests
17645:
17644:
17641:
17640:
17638:
17637:
17632:
17627:
17621:
17619:
17613:
17612:
17610:
17609:
17604:
17603:
17602:
17592:
17591:
17590:
17580:
17574:
17572:
17566:
17565:
17563:
17562:
17561:
17560:
17555:
17545:
17540:
17535:
17530:
17525:
17519:
17517:
17511:
17510:
17508:
17507:
17502:
17501:
17500:
17495:
17494:
17493:
17488:
17473:
17472:
17471:
17466:
17461:
17456:
17445:
17443:
17434:
17428:
17427:
17425:
17424:
17419:
17414:
17413:
17412:
17402:
17397:
17396:
17395:
17385:
17384:
17383:
17378:
17373:
17363:
17358:
17353:
17352:
17351:
17346:
17341:
17325:
17324:
17323:
17318:
17313:
17303:
17302:
17301:
17296:
17286:
17285:
17284:
17274:
17273:
17272:
17262:
17257:
17252:
17246:
17244:
17234:
17233:
17221:
17220:
17217:
17216:
17213:
17212:
17210:
17209:
17204:
17199:
17194:
17188:
17186:
17180:
17179:
17177:
17176:
17171:
17166:
17160:
17158:
17154:
17153:
17151:
17150:
17145:
17140:
17135:
17130:
17125:
17120:
17114:
17112:
17106:
17105:
17103:
17102:
17100:Standard error
17097:
17092:
17087:
17086:
17085:
17080:
17069:
17067:
17061:
17060:
17058:
17057:
17052:
17047:
17042:
17037:
17032:
17030:Optimal design
17027:
17022:
17016:
17014:
17004:
17003:
16991:
16990:
16987:
16986:
16983:
16982:
16980:
16979:
16974:
16969:
16964:
16959:
16954:
16949:
16944:
16939:
16934:
16929:
16924:
16919:
16914:
16909:
16903:
16901:
16895:
16894:
16892:
16891:
16886:
16885:
16884:
16879:
16869:
16864:
16858:
16856:
16850:
16849:
16847:
16846:
16841:
16836:
16830:
16828:
16827:Summary tables
16824:
16823:
16821:
16820:
16814:
16812:
16806:
16805:
16802:
16801:
16799:
16798:
16797:
16796:
16791:
16786:
16776:
16770:
16768:
16762:
16761:
16759:
16758:
16753:
16748:
16743:
16738:
16733:
16728:
16722:
16720:
16714:
16713:
16711:
16710:
16705:
16700:
16699:
16698:
16693:
16688:
16683:
16678:
16673:
16668:
16663:
16661:Contraharmonic
16658:
16653:
16642:
16640:
16631:
16621:
16620:
16608:
16607:
16605:
16604:
16599:
16593:
16590:
16589:
16582:
16581:
16574:
16567:
16559:
16553:
16552:
16543:
16542:– large table.
16527:
16515:
16502:
16487:
16486:External links
16484:
16481:
16480:
16473:
16455:
16434:(13): 130401.
16414:
16403:(2): 913–923.
16383:
16369:
16349:
16293:
16273:
16223:
16209:
16191:
16169:(1): 201–211.
16149:
16130:(2): 193–232.
16114:
16086:
16079:
16051:
16036:
16017:(3): 531–545.
15998:
15980:
15938:
15929:|journal=
15892:
15873:
15858:
15839:(2): 193–232.
15823:
15770:
15759:(4): 328–413.
15734:
15713:
15700:
15675:
15648:(161): 31–34.
15628:
15610:
15603:
15585:
15570:
15551:(4): 311–313.
15535:
15493:
15468:
15443:
15432:(3): 281–288.
15416:
15409:
15381:
15355:
15333:
15314:
15292:
15251:
15220:
15181:
15158:
15104:
15086:
15071:
15070:
15068:
15065:
15063:
15062:
15049:
15025:Also known as
15017:
15015:
15012:
15011:
15010:
15005:
15003:RV coefficient
15000:
14995:
14990:
14985:
14980:
14975:
14970:
14965:
14960:
14958:Disattenuation
14955:
14950:
14945:
14940:
14935:
14934:
14933:
14928:
14918:
14913:
14907:
14906:
14890:
14887:
14886:
14885:
14873:
14857:
14839:
14827:
14823:pearsonr(x, y)
14811:
14807:cor.test(x, y)
14793:
14790:
14782:
14781:
14770:
14763:
14760:
14755:
14751:
14747:
14741:
14736:
14732:
14729:
14726:
14723:
14713:
14702:
14699:
14694:
14691:
14688:
14684:
14678:
14675:
14670:
14667:
14664:
14661:
14601:
14600:
14589:
14582:
14579:
14574:
14570:
14566:
14560:
14555:
14551:
14548:
14545:
14542:
14532:
14521:
14516:
14513:
14510:
14506:
14500:
14497:
14492:
14489:
14486:
14483:
14430:
14427:
14424:
14420:
14389:
14386:
14383:
14379:
14347:Main article:
14344:
14337:
14324:
14321:
14318:
14315:
14312:
14308:
14305:
14302:
14298:
14295:
14292:
14289:
14286:
14283:
14279:
14276:
14273:
14252:
14249:
14246:
14243:
14240:
14236:
14233:
14230:
14219:
14218:
14206:
14186:
14183:
14180:
14176:
14165:
14153:
14133:
14130:
14127:
14123:
14112:
14100:
14097:
14094:
14074:
14071:
14068:
14065:
14062:
14058:
14047:
14035:
14015:
14012:
14009:
14005:
13994:
13982:
13962:
13959:
13956:
13952:
13937:
13936:
13925:
13918:
13915:
13912:
13908:
13904:
13901:
13898:
13895:
13891:
13885:
13882:
13879:
13875:
13871:
13868:
13865:
13862:
13858:
13854:
13851:
13848:
13845:
13842:
13839:
13835:
13828:
13825:
13822:
13819:
13816:
13813:
13809:
13806:
13803:
13779:
13759:
13747:
13744:
13731:Main article:
13728:
13725:
13713:circular means
13697:
13694:
13668:
13665:
13651:
13650:
13632:
13628:
13621:
13618:
13612:
13607:
13603:
13599:
13596:
13593:
13588:
13583:
13580:
13577:
13573:
13563:
13559:
13552:
13549:
13543:
13538:
13534:
13530:
13527:
13524:
13519:
13514:
13511:
13508:
13504:
13496:
13490:
13487:
13481:
13476:
13472:
13468:
13465:
13462:
13459:
13453:
13450:
13444:
13439:
13435:
13431:
13428:
13425:
13420:
13415:
13412:
13409:
13405:
13398:
13389:
13355:
13348:
13335:
13328:
13320:For variables
13311:
13308:
13294:
13288:
13285:
13282:
13278:
13273:
13269:
13266:
13263:
13258:
13255:
13252:
13248:
13228:
13227:
13216:
13211:
13208:
13205:
13201:
13197:
13194:
13191:
13186:
13183:
13180:
13176:
13148:
13145:
13132:
13109:
13087:
13083:
13071:
13070:
13059:
13054:
13050:
13044:
13039:
13036:
13033:
13029:
13023:
13020:
13015:
13010:
13003:
13000:
12971:
12964:
12961:
12946:
12945:
12934:
12930:
12925:
12922:
12917:
12913:
12910:
12907:
12904:
12881:
12861:
12841:
12819:Main article:
12816:
12813:
12812:
12811:
12800:
12794:
12789:
12784:
12780:
12774:
12770:
12766:
12763:
12760:
12755:
12750:
12746:
12740:
12736:
12732:
12729:
12722:
12718:
12712:
12708:
12702:
12698:
12694:
12688:
12683:
12680:
12677:
12674:
12670:
12666:
12652:
12651:
12640:
12634:
12629:
12624:
12620:
12616:
12613:
12610:
12605:
12600:
12596:
12592:
12589:
12582:
12578:
12572:
12568:
12564:
12558:
12553:
12550:
12546:
12542:
12524:
12523:
12512:
12509:
12506:
12503:
12500:
12497:
12494:
12490:
12487:
12484:
12481:
12478:
12475:
12472:
12469:
12466:
12463:
12458:
12454:
12450:
12447:
12444:
12441:
12438:
12435:
12432:
12429:
12424:
12420:
12416:
12413:
12410:
12407:
12404:
12401:
12398:
12393:
12389:
12385:
12382:
12379:
12376:
12373:
12370:
12367:
12362:
12358:
12343:
12342:
12331:
12325:
12319:
12315:
12310:
12307:
12302:
12297:
12294:
12288:
12284:
12279:
12276:
12271:
12264:
12260:
12256:
12252:
12249:
12244:
12236:
12233:
12230:
12227:
12224:
12221:
12218:
12213:
12209:
12193:
12190:
12189:
12188:
12177:
12171:
12168:
12165:
12162:
12159:
12156:
12153:
12150:
12147:
12144:
12141:
12138:
12135:
12132:
12129:
12126:
12123:
12120:
12115:
12112:
12109:
12106:
12103:
12100:
12097:
12094:
12091:
12085:
12082:
12079:
12076:
12073:
12070:
12067:
12064:
12061:
12058:
12047:
12036:
12028:
12024:
12018:
12014:
12008:
12005:
12002:
11999:
11996:
11993:
11990:
11987:
11984:
11979:
11975:
11971:
11968:
11965:
11962:
11959:
11956:
11953:
11950:
11947:
11944:
11939:
11935:
11931:
11928:
11923:
11919:
11913:
11909:
11902:
11899:
11896:
11893:
11890:
11887:
11884:
11881:
11878:
11875:
11864:
11853:
11845:
11841:
11835:
11831:
11823:
11819:
11813:
11809:
11803:
11799:
11792:
11789:
11786:
11783:
11780:
11777:
11774:
11771:
11735:
11732:
11718:
11712:
11711:
11700:
11692:
11689:
11686:
11683:
11680:
11675:
11672:
11669:
11666:
11663:
11660:
11655:
11651:
11647:
11644:
11641:
11635:
11632:
11627:
11618:
11603:
11602:
11581:
11575:
11566:
11560:
11547:
11541:
11536:
11530:
11518:
11515:
11512:
11490:
11489:
11480:
11478:
11467:
11463:
11456:
11453:
11446:
11442:
11438:
11435:
11429:
11426:
11422:
11418:
11415:
11406:
11381:
11380:
11371:
11369:
11358:
11352:
11349:
11343:
11337:
11328:
11324:
11321:
11317:
11307:
11300:
11291:
11287:
11284:
11281:
11278:
11275:
11270:
11265:
11262:
11240:
11233:
11232:
11216:
11213:
11210:
11207:
11204:
11201:
11198:
11195:
11192:
11186:
11182:
11176:
11172:
11161:
11149:
11146:
11143:
11127:
11126:
11117:
11115:
11104:
11100:
11094:
11090:
11086:
11083:
11080:
11075:
11071:
11068:
11065:
11059:
11054:
11051:
11046:
11041:
11038:
11032:
11025:
11021:
11015:
11011:
11006:
11003:
10994:
10975:
10968:
10967:
10956:
10953:
10928:
10925:
10922:
10916:
10913:
10907:
10901:
10897:
10893:
10890:
10886:
10882:
10876:
10873:
10870:
10866:
10863:
10860:
10856:
10851:
10814:
10811:
10800:
10797:
10770:non-parametric
10712:
10709:
10708:
10707:
10700:
10689:
10678:
10675:
10665:asymptotically
10651:
10648:
10616:for which the
10605:
10602:
10594:
10591:
10589:of the data).
10517:
10516:
10502:
10498:
10491:
10488:
10482:
10477:
10473:
10469:
10464:
10460:
10456:
10434:
10421:
10417:
10410:
10407:
10401:
10396:
10389:
10386:
10379:
10374:
10370:
10366:
10340:
10339:
10300:
10295:
10291:
10284:
10281:
10275:
10272:
10269:
10266:
10252:
10251:
10237:
10233:
10227:
10220:
10217:
10210:
10205:
10201:
10197:
10192:
10188:
10184:
10164:
10157:
10143:
10142:
10131:
10128:
10125:
10119:
10116:
10110:
10105:
10098:
10095:
10088:
10085:
10080:
10073:
10070:
10063:
10058:
10054:
10050:
10045:
10041:
10004:
10000:
9993:
9990:
9984:
9981:
9978:
9975:
9964:
9963:
9947:
9943:
9936:
9933:
9927:
9922:
9918:
9914:
9909:
9905:
9897:
9893:
9886:
9883:
9877:
9872:
9865:
9862:
9855:
9850:
9846:
9839:
9834:
9830:
9823:
9820:
9814:
9811:
9808:
9805:
9791:
9790:
9775:
9766:
9762:
9755:
9752:
9746:
9741:
9737:
9733:
9728:
9724:
9716:
9712:
9705:
9702:
9696:
9691:
9684:
9681:
9674:
9669:
9665:
9657:
9654:
9652:
9650:
9642:
9638:
9631:
9628:
9622:
9617:
9610:
9607:
9600:
9595:
9591:
9587:
9582:
9578:
9571:
9568:
9562:
9557:
9553:
9549:
9544:
9540:
9532:
9528:
9521:
9518:
9512:
9507:
9500:
9497:
9490:
9485:
9481:
9474:
9471:
9469:
9467:
9459:
9455:
9448:
9445:
9439:
9434:
9427:
9424:
9417:
9412:
9408:
9404:
9399:
9395:
9388:
9385:
9379:
9374:
9370:
9366:
9361:
9357:
9351:
9346:
9342:
9335:
9332:
9326:
9321:
9314:
9311:
9304:
9301:
9298:
9292:
9289:
9283:
9278:
9271:
9268:
9261:
9258:
9253:
9246:
9243:
9236:
9231:
9227:
9223:
9220:
9215:
9211:
9204:
9201:
9199:
9197:
9189:
9185:
9178:
9175:
9169:
9164:
9157:
9154:
9147:
9142:
9138:
9134:
9129:
9125:
9118:
9115:
9109:
9104:
9100:
9096:
9091:
9087:
9081:
9075:
9072:
9066:
9061:
9054:
9051:
9044:
9041:
9035:
9032:
9026:
9021:
9014:
9011:
9004:
8999:
8992:
8989:
8982:
8977:
8973:
8969:
8964:
8960:
8953:
8950:
8948:
8946:
8938:
8934:
8927:
8924:
8918:
8913:
8906:
8903:
8896:
8891:
8887:
8883:
8878:
8874:
8867:
8864:
8858:
8853:
8849:
8845:
8840:
8836:
8830:
8824:
8821:
8815:
8810:
8803:
8800:
8793:
8790:
8784:
8781:
8775:
8770:
8766:
8762:
8757:
8753:
8746:
8743:
8741:
8739:
8733:
8730:
8724:
8721:
8718:
8715:
8712:
8711:
8686:
8679:
8676:
8669:
8664:
8660:
8637:
8630:
8627:
8593:
8592:
8581:
8573:
8569:
8562:
8559:
8553:
8548:
8544:
8540:
8535:
8531:
8523:
8519:
8512:
8509:
8503:
8498:
8491:
8488:
8481:
8476:
8472:
8465:
8457:
8453:
8446:
8443:
8437:
8432:
8428:
8424:
8419:
8415:
8407:
8403:
8397:
8390:
8387:
8380:
8375:
8371:
8367:
8362:
8358:
8351:
8348:
8323:
8316:
8313:
8298:
8297:
8286:
8281:
8277:
8270:
8267:
8261:
8256:
8249:
8246:
8239:
8234:
8230:
8226:
8221:
8217:
8211:
8204:
8201:
8194:
8189:
8185:
8181:
8176:
8172:
8168:
8163:
8159:
8152:
8149:
8143:
8138:
8134:
8130:
8125:
8121:
8103:
8086:
8079:
8076:
8069:
8066:
8063:
8058:
8051:
8048:
8022:
8018:
8014:
8011:
8008:
8003:
7999:
7959:
7956:
7940:
7936:
7931:
7928:
7908:
7905:
7901:
7898:
7895:
7891:
7888:
7865:
7864:
7853:
7850:
7840:
7836:
7832:
7828:
7824:
7821:
7818:
7815:
7812:
7809:
7806:
7803:
7800:
7797:
7794:
7784:
7780:
7776:
7772:
7768:
7765:
7762:
7759:
7756:
7753:
7750:
7747:
7744:
7741:
7738:
7735:
7732:
7724:
7721:
7718:
7715:
7712:
7709:
7706:
7692:
7691:
7680:
7670:
7666:
7662:
7658:
7654:
7651:
7648:
7645:
7642:
7639:
7636:
7633:
7630:
7627:
7624:
7621:
7618:
7615:
7607:
7604:
7601:
7598:
7595:
7592:
7589:
7565:
7529:
7526:
7523:
7485:
7481:
7477:
7474:
7459:
7458:
7445:
7442:
7439:
7434:
7431:
7426:
7422:
7418:
7415:
7412:
7409:
7406:
7403:
7400:
7397:
7394:
7380:
7377:
7371:
7368:
7336:
7332:
7311:
7291:
7276:
7275:
7264:
7258:
7255:
7252:
7248:
7243:
7235:
7225:standard error
7209:
7206:
7203:
7200:
7197:
7194:
7191:
7188:
7185:
7182:
7179:
7149:
7148:
7137:
7134:
7131:
7128:
7125:
7122:
7118:
7112:
7109:
7106:
7101:
7098:
7095:
7089:
7085:
7082:
7075:
7072:
7066:
7063:
7060:
7057:
7054:
7029:
6994:Main article:
6991:
6988:
6975:
6972:
6969:
6966:
6963:
6960:
6957:
6937:
6914:
6907:
6903:
6900:
6897:
6894:
6887:
6881:
6878:
6872:
6869:
6866:
6860:
6857:
6851:
6848:
6842:
6839:
6832:
6828:
6825:
6819:
6815:
6812:
6809:
6806:
6799:
6795:
6792:
6789:
6786:
6782:
6777:
6771:
6767:
6764:
6761:
6754:
6748:
6744:
6740:
6737:
6733:
6728:
6722:
6718:
6715:
6712:
6705:
6699:
6695:
6691:
6688:
6684:
6675:
6669:
6666:
6661:
6658:
6654:
6650:
6645:
6642:
6635:
6632:
6629:
6626:
6623:
6620:
6617:
6614:
6611:
6608:
6605:
6602:
6596:
6593:
6590:
6587:
6584:
6581:
6578:
6556:
6553:
6531:
6519:
6518:
6507:
6498:
6491:
6487:
6484:
6481:
6474:
6468:
6465:
6458:
6452:
6447:
6438:
6434:
6431:
6428:
6421:
6415:
6411:
6407:
6404:
6400:
6393:
6390:
6387:
6384:
6381:
6350:
6347:
6344:
6317:
6314:
6311:
6308:
6305:
6302:
6299:
6296:
6293:
6288:
6283:
6276:
6261:gamma function
6248:
6237:
6236:
6222:
6218:
6215:
6212:
6209:
6206:
6203:
6197:
6194:
6188:
6185:
6182:
6179:
6176:
6173:
6170:
6164:
6161:
6155:
6149:
6146:
6140:
6134:
6131:
6124:
6116:
6111:
6104:
6090:
6087:
6082:
6079:
6075:
6071:
6068:
6065:
6062:
6059:
6053:
6046:
6043:
6037:
6034:
6030:
6024:
6020:
6013:
6010:
6000:
5996:
5993:
5990:
5983:
5977:
5973:
5969:
5966:
5962:
5954:
5950:
5947:
5944:
5937:
5931:
5927:
5923:
5920:
5916:
5911:
5908:
5905:
5902:
5899:
5895:
5890:
5887:
5884:
5881:
5878:
5872:
5869:
5866:
5863:
5860:
5829:
5826:
5808:
5807:
5796:
5788:
5784:
5780:
5777:
5774:
5771:
5767:
5762:
5759:
5737:
5736:
5719:
5715:
5711:
5708:
5703:
5700:
5697:
5690:
5687:
5680:
5676:
5672:
5667:
5664:
5617:
5610:
5597:
5577:
5566:
5565:
5550:
5547:
5544:
5537:
5533:
5529:
5526:
5519:
5514:
5510:
5495:standard error
5482:
5462:
5450:
5449:Standard error
5447:
5408:
5399:
5384:
5381:
5360:
5359:
5352:
5302:
5293:
5284:
5275:
5261:
5258:
5254:
5253:
5242:
5222:
5219:
5165:
5161:
5157:
5154:
5149:
5146:
5118:
5115:
5111:
5110:
5099:
5094:
5091:
5087:
5083:
5080:
5077:
5069:
5062:
5056:
5051:
5044:
5040:
5036:
5031:
5027:
5023:
5016:
5012:
5008:
5001:
4998:
4995:
4992:
4937:= 0.10 + 0.01
4926:
4925:
4914:
4911:
4903:
4896:
4890:
4885:
4878:
4874:
4870:
4865:
4861:
4857:
4850:
4846:
4842:
4835:
4832:
4829:
4826:
4683:
4663:
4636:
4616:
4600:
4597:
4596:
4595:
4592:
4589:
4586:
4583:
4580:
4577:
4574:
4571:
4568:
4565:
4562:
4559:
4549:absolute value
4542:
4533:
4520:
4511:
4502:
4493:
4476:
4461:
4417:
4416:Interpretation
4414:
4365:and transform
4320:
4317:
4286:
4283:
4268:
4260:
4255:
4251:
4247:
4243:
4239:
4233:
4229:
4223:
4220:
4217:
4213:
4209:
4208:
4203:
4199:
4193:
4189:
4183:
4180:
4177:
4173:
4169:
4165:
4160:
4156:
4152:
4151:
4149:
4144:
4141:
4121:
4091:
4088:
4085:
4082:
4079:
4067:
4064:
4063:
4062:
4048:
4044:
4015:
4011:
4004:
4001:
3995:
3990:
3986:
3982:
3977:
3972:
3969:
3966:
3962:
3955:
3952:
3949:
3945:
3938:
3933:
3929:
3918:
3903:
3900:
3894:
3888:
3885:
3879:
3874:
3870:
3866:
3861:
3857:
3853:
3850:
3836:
3835:
3819:
3815:
3809:
3805:
3801:
3798:
3795:
3792:
3789:
3781:
3778:
3769:
3766:
3760:
3757:
3752:
3748:
3742:
3738:
3734:
3728:
3723:
3720:
3716:
3690:
3687:
3683:
3660:
3657:
3653:
3641:
3640:
3628:
3607:
3600:
3596:
3588:
3585:
3579:
3574:
3570:
3563:
3552:
3538:
3534:
3530:
3525:
3521:
3497:
3494:
3488:
3482:
3479:
3473:
3468:
3464:
3460:
3455:
3451:
3447:
3444:
3430:
3429:
3417:
3410:
3406:
3398:
3395:
3389:
3384:
3380:
3373:
3368:
3361:
3357:
3349:
3346:
3340:
3335:
3331:
3324:
3318:
3313:
3310:
3307:
3303:
3296:
3293:
3290:
3286:
3281:
3276:
3273:
3269:
3239:
3236:
3232:
3199:
3195:
3191:
3186:
3182:
3178:
3175:
3164:
3163:
3152:
3142:
3137:
3131:
3127:
3123:
3119:
3114:
3109:
3104:
3100:
3096:
3093:
3081:
3076:
3070:
3066:
3062:
3058:
3053:
3048:
3043:
3039:
3035:
3032:
3023:
3019:
3015:
3010:
3006:
3002:
2999:
2994:
2990:
2984:
2980:
2976:
2973:
2967:
2962:
2959:
2955:
2929:
2926:
2922:
2895:
2892:
2886:
2880:
2877:
2871:
2866:
2862:
2858:
2853:
2849:
2845:
2842:
2831:
2830:
2819:
2809:
2802:
2799:
2792:
2789:
2784:
2779:
2775:
2769:
2765:
2752:
2745:
2742:
2735:
2732:
2727:
2722:
2718:
2712:
2708:
2697:
2694:
2685:
2682:
2676:
2673:
2668:
2664:
2658:
2654:
2648:
2644:
2637:
2632:
2629:
2625:
2599:
2596:
2592:
2580:
2579:
2564:
2561:
2536:
2532:
2526:
2521:
2518:
2515:
2511:
2505:
2502:
2497:
2491:
2488:
2475:
2458:
2454:
2450:
2445:
2441:
2430:
2429:is sample size
2418:
2386:
2382:
2375:
2372:
2366:
2361:
2357:
2353:
2348:
2343:
2340:
2337:
2333:
2323:
2319:
2312:
2309:
2303:
2298:
2294:
2290:
2285:
2280:
2277:
2274:
2270:
2262:
2256:
2253:
2247:
2242:
2238:
2234:
2231:
2225:
2222:
2216:
2211:
2207:
2203:
2198:
2193:
2190:
2187:
2183:
2176:
2171:
2168:
2164:
2152:is defined as
2139:
2136:
2132:
2111:
2102:consisting of
2090:
2086:
2081:
2077:
2073:
2068:
2064:
2060:
2057:
2054:
2051:
2048:
2043:
2039:
2035:
2030:
2026:
2022:
2018:
1995:
1992:
1988:
1957:
1954:
1950:
1933:
1930:
1918:
1908:
1903:
1899:
1895:
1891:
1888:
1883:
1877:
1872:
1868:
1861:
1857:
1851:
1847:
1842:
1828:
1823:
1819:
1815:
1811:
1808:
1803:
1797:
1792:
1788:
1781:
1777:
1771:
1767:
1762:
1753:
1749:
1745:
1742:
1737:
1732:
1728:
1724:
1721:
1716:
1711:
1708:
1704:
1700:
1696:
1693:
1688:
1680:
1675:
1672:
1669:
1665:
1644:
1633:
1632:
1617:
1613:
1609:
1605:
1602:
1597:
1592:
1588:
1584:
1581:
1576:
1571:
1568:
1564:
1560:
1556:
1553:
1548:
1543:
1540:
1535:
1531:
1527:
1523:
1520:
1515:
1510:
1507:
1503:
1498:
1494:
1490:
1486:
1483:
1478:
1473:
1470:
1466:
1461:
1458:
1453:
1448:
1445:
1440:
1434:
1430:
1426:
1423:
1419:
1414:
1408:
1404:
1400:
1397:
1393:
1388:
1385:
1380:
1375:
1373:
1368:
1363:
1359:
1355:
1351:
1348:
1343:
1336:
1331:
1327:
1320:
1316:
1310:
1306:
1301:
1296:
1292:
1285:
1280:
1276:
1273:
1270:
1267:
1262:
1257:
1254:
1250:
1243:
1239:
1234:
1229:
1225:
1220:
1215:
1211:
1207:
1206:
1201:
1196:
1192:
1188:
1184:
1181:
1176:
1170:
1165:
1161:
1154:
1150:
1144:
1140:
1135:
1130:
1126:
1119:
1114:
1110:
1107:
1104:
1101:
1096:
1091:
1088:
1084:
1077:
1073:
1068:
1063:
1059:
1054:
1049:
1045:
1041:
1040:
1037:
1033:
1029:
1026:
1021:
1016:
1012:
1007:
1003:
999:
998:
995:
991:
987:
984:
979:
974:
970:
965:
961:
957:
956:
933:
922:
921:
907:
895:
884:
862:
858:
847:
836:
814:
810:
799:
785:
781:
758:
754:
723:
719:
713:
709:
703:
700:
695:
691:
687:
684:
681:
678:
673:
669:
665:
662:
659:
656:
653:
648:
640:
635:
632:
629:
625:
602:
591:
590:
579:
576:
573:
568:
564:
560:
557:
554:
551:
546:
542:
538:
535:
532:
529:
526:
521:
516:
513:
510:
507:
504:
501:
498:
495:
464:
461:
458:
455:
452:
449:
446:
435:
434:
422:
400:
396:
385:
374:
348:
344:
333:
318:
288:
284:
278:
274:
268:
265:
262:
259:
256:
253:
250:
244:
239:
236:
233:
229:
202:
199:
196:
193:
190:
162:
159:
155:product-moment
142:
139:
127:Francis Galton
118:
115:
96:that measures
26:
9:
6:
4:
3:
2:
19315:
19304:
19301:
19299:
19296:
19294:
19291:
19290:
19288:
19273:
19270:
19269:
19266:
19260:
19257:
19255:
19252:
19250:
19247:
19246:
19244:
19240:
19234:
19231:
19229:
19226:
19225:
19223:
19221:
19217:
19211:
19208:
19206:
19203:
19202:
19200:
19196:
19190:
19187:
19185:
19182:
19181:
19179:
19177:
19173:
19167:
19164:
19162:
19159:
19157:
19154:
19153:
19151:
19149:
19145:
19139:
19136:
19134:
19131:
19129:
19126:
19125:
19123:
19121:
19117:
19111:
19108:
19106:
19103:
19101:
19098:
19096:
19093:
19091:
19090:Jaccard index
19088:
19086:
19083:
19081:
19078:
19076:
19073:
19071:
19068:
19066:
19063:
19062:
19060:
19058:
19054:
19048:
19045:
19043:
19040:
19038:
19035:
19033:
19030:
19028:
19025:
19023:
19020:
19018:
19015:
19013:
19010:
19008:
19005:
19003:
19000:
18998:
18995:
18994:
18992:
18990:
18986:
18980:
18977:
18975:
18972:
18970:
18967:
18965:
18962:
18960:
18957:
18955:
18952:
18950:
18947:
18945:
18942:
18940:
18937:
18935:
18932:
18930:
18927:
18926:
18924:
18922:
18918:
18913:
18906:
18901:
18899:
18894:
18892:
18887:
18886:
18883:
18871:
18870:
18861:
18859:
18858:
18849:
18847:
18846:
18841:
18835:
18833:
18832:
18823:
18822:
18819:
18805:
18802:
18800:
18799:Geostatistics
18797:
18795:
18792:
18790:
18787:
18785:
18782:
18781:
18779:
18777:
18773:
18767:
18766:Psychometrics
18764:
18762:
18759:
18757:
18754:
18752:
18749:
18747:
18744:
18742:
18739:
18737:
18734:
18732:
18729:
18727:
18724:
18722:
18719:
18718:
18716:
18714:
18710:
18704:
18701:
18699:
18696:
18694:
18690:
18687:
18685:
18682:
18680:
18677:
18675:
18672:
18671:
18669:
18667:
18663:
18657:
18654:
18652:
18649:
18647:
18643:
18640:
18638:
18635:
18634:
18632:
18630:
18629:Biostatistics
18626:
18622:
18618:
18613:
18609:
18591:
18590:Log-rank test
18588:
18587:
18585:
18581:
18575:
18572:
18571:
18569:
18567:
18563:
18557:
18554:
18552:
18549:
18547:
18544:
18542:
18539:
18538:
18536:
18534:
18530:
18527:
18525:
18521:
18511:
18508:
18506:
18503:
18501:
18498:
18496:
18493:
18491:
18488:
18487:
18485:
18483:
18479:
18473:
18470:
18468:
18465:
18463:
18461:(Box–Jenkins)
18457:
18455:
18452:
18450:
18447:
18443:
18440:
18439:
18438:
18435:
18434:
18432:
18430:
18426:
18420:
18417:
18415:
18414:Durbin–Watson
18412:
18410:
18404:
18402:
18399:
18397:
18396:Dickey–Fuller
18394:
18393:
18391:
18387:
18381:
18378:
18376:
18373:
18371:
18370:Cointegration
18368:
18366:
18363:
18361:
18358:
18356:
18353:
18351:
18348:
18346:
18345:Decomposition
18343:
18342:
18340:
18336:
18333:
18331:
18327:
18317:
18314:
18313:
18312:
18309:
18308:
18307:
18304:
18300:
18297:
18296:
18295:
18292:
18290:
18287:
18285:
18282:
18280:
18277:
18275:
18272:
18270:
18267:
18265:
18262:
18260:
18257:
18256:
18254:
18252:
18248:
18242:
18239:
18237:
18234:
18232:
18229:
18227:
18224:
18222:
18219:
18217:
18216:Cohen's kappa
18214:
18213:
18211:
18209:
18205:
18201:
18197:
18193:
18189:
18185:
18180:
18176:
18162:
18159:
18157:
18154:
18152:
18149:
18147:
18144:
18143:
18141:
18139:
18135:
18129:
18125:
18121:
18115:
18113:
18110:
18109:
18107:
18105:
18101:
18095:
18092:
18090:
18087:
18085:
18082:
18080:
18077:
18075:
18072:
18070:
18069:Nonparametric
18067:
18065:
18062:
18061:
18059:
18055:
18049:
18046:
18044:
18041:
18039:
18036:
18034:
18031:
18030:
18028:
18026:
18022:
18016:
18013:
18011:
18008:
18006:
18003:
18001:
17998:
17996:
17993:
17992:
17990:
17988:
17984:
17978:
17975:
17973:
17970:
17968:
17965:
17963:
17960:
17959:
17957:
17955:
17951:
17947:
17940:
17937:
17935:
17932:
17931:
17927:
17923:
17907:
17904:
17903:
17902:
17899:
17897:
17894:
17892:
17889:
17885:
17882:
17880:
17877:
17876:
17875:
17872:
17871:
17869:
17867:
17863:
17853:
17850:
17846:
17840:
17838:
17832:
17830:
17824:
17823:
17822:
17819:
17818:Nonparametric
17816:
17814:
17808:
17804:
17801:
17800:
17799:
17793:
17789:
17788:Sample median
17786:
17785:
17784:
17781:
17780:
17778:
17776:
17772:
17764:
17761:
17759:
17756:
17754:
17751:
17750:
17749:
17746:
17744:
17741:
17739:
17733:
17731:
17728:
17726:
17723:
17721:
17718:
17716:
17713:
17711:
17709:
17705:
17703:
17700:
17699:
17697:
17695:
17691:
17685:
17683:
17679:
17677:
17675:
17670:
17668:
17663:
17659:
17658:
17655:
17652:
17650:
17646:
17636:
17633:
17631:
17628:
17626:
17623:
17622:
17620:
17618:
17614:
17608:
17605:
17601:
17598:
17597:
17596:
17593:
17589:
17586:
17585:
17584:
17581:
17579:
17576:
17575:
17573:
17571:
17567:
17559:
17556:
17554:
17551:
17550:
17549:
17546:
17544:
17541:
17539:
17536:
17534:
17531:
17529:
17526:
17524:
17521:
17520:
17518:
17516:
17512:
17506:
17503:
17499:
17496:
17492:
17489:
17487:
17484:
17483:
17482:
17479:
17478:
17477:
17474:
17470:
17467:
17465:
17462:
17460:
17457:
17455:
17452:
17451:
17450:
17447:
17446:
17444:
17442:
17438:
17435:
17433:
17429:
17423:
17420:
17418:
17415:
17411:
17408:
17407:
17406:
17403:
17401:
17398:
17394:
17393:loss function
17391:
17390:
17389:
17386:
17382:
17379:
17377:
17374:
17372:
17369:
17368:
17367:
17364:
17362:
17359:
17357:
17354:
17350:
17347:
17345:
17342:
17340:
17334:
17331:
17330:
17329:
17326:
17322:
17319:
17317:
17314:
17312:
17309:
17308:
17307:
17304:
17300:
17297:
17295:
17292:
17291:
17290:
17287:
17283:
17280:
17279:
17278:
17275:
17271:
17268:
17267:
17266:
17263:
17261:
17258:
17256:
17253:
17251:
17248:
17247:
17245:
17243:
17239:
17235:
17231:
17226:
17222:
17208:
17205:
17203:
17200:
17198:
17195:
17193:
17190:
17189:
17187:
17185:
17181:
17175:
17172:
17170:
17167:
17165:
17162:
17161:
17159:
17155:
17149:
17146:
17144:
17141:
17139:
17136:
17134:
17131:
17129:
17126:
17124:
17121:
17119:
17116:
17115:
17113:
17111:
17107:
17101:
17098:
17096:
17095:Questionnaire
17093:
17091:
17088:
17084:
17081:
17079:
17076:
17075:
17074:
17071:
17070:
17068:
17066:
17062:
17056:
17053:
17051:
17048:
17046:
17043:
17041:
17038:
17036:
17033:
17031:
17028:
17026:
17023:
17021:
17018:
17017:
17015:
17013:
17009:
17005:
17001:
16996:
16992:
16978:
16975:
16973:
16970:
16968:
16965:
16963:
16960:
16958:
16955:
16953:
16950:
16948:
16945:
16943:
16940:
16938:
16935:
16933:
16930:
16928:
16925:
16923:
16922:Control chart
16920:
16918:
16915:
16913:
16910:
16908:
16905:
16904:
16902:
16900:
16896:
16890:
16887:
16883:
16880:
16878:
16875:
16874:
16873:
16870:
16868:
16865:
16863:
16860:
16859:
16857:
16855:
16851:
16845:
16842:
16840:
16837:
16835:
16832:
16831:
16829:
16825:
16819:
16816:
16815:
16813:
16811:
16807:
16795:
16792:
16790:
16787:
16785:
16782:
16781:
16780:
16777:
16775:
16772:
16771:
16769:
16767:
16763:
16757:
16754:
16752:
16749:
16747:
16744:
16742:
16739:
16737:
16734:
16732:
16729:
16727:
16724:
16723:
16721:
16719:
16715:
16709:
16706:
16704:
16701:
16697:
16694:
16692:
16689:
16687:
16684:
16682:
16679:
16677:
16674:
16672:
16669:
16667:
16664:
16662:
16659:
16657:
16654:
16652:
16649:
16648:
16647:
16644:
16643:
16641:
16639:
16635:
16632:
16630:
16626:
16622:
16618:
16613:
16609:
16603:
16600:
16598:
16595:
16594:
16591:
16587:
16580:
16575:
16573:
16568:
16566:
16561:
16560:
16557:
16548:
16544:
16539:
16532:
16528:
16524:
16520:
16516:
16511:
16510:nagysandor.eu
16507:
16506:"Correlation"
16503:
16498:
16494:
16490:
16489:
16476:
16474:0-412-12420-3
16470:
16466:
16459:
16451:
16447:
16442:
16437:
16433:
16429:
16425:
16418:
16410:
16406:
16402:
16398:
16394:
16387:
16372:
16366:
16362:
16361:
16353:
16338:
16334:
16330:
16326:
16321:
16316:
16312:
16308:
16304:
16297:
16291:
16290:1-4020-8879-5
16287:
16283:
16277:
16269:
16265:
16261:
16257:
16253:
16249:
16245:
16241:
16234:
16227:
16219:
16213:
16205:
16201:
16195:
16186:
16182:
16177:
16172:
16168:
16164:
16160:
16153:
16145:
16141:
16137:
16133:
16129:
16125:
16118:
16112:
16111:0-521-54985-X
16108:
16104:
16100:
16096:
16090:
16082:
16076:
16072:
16068:
16064:
16063:
16055:
16047:
16040:
16032:
16028:
16024:
16020:
16016:
16012:
16008:
16002:
15994:
15987:
15985:
15976:
15972:
15968:
15964:
15960:
15956:
15949:
15942:
15934:
15921:
15912:
15907:
15903:
15896:
15888:
15884:
15877:
15869:
15862:
15854:
15850:
15846:
15842:
15838:
15834:
15827:
15819:
15815:
15811:
15807:
15802:
15797:
15793:
15789:
15785:
15781:
15774:
15766:
15762:
15758:
15754:
15753:
15748:
15744:
15738:
15731:
15730:0-85264-215-6
15727:
15723:
15717:
15710:
15704:
15689:
15685:
15679:
15671:
15667:
15663:
15659:
15655:
15651:
15647:
15643:
15639:
15632:
15624:
15617:
15615:
15606:
15604:9788391527290
15600:
15596:
15589:
15581:
15574:
15566:
15562:
15558:
15554:
15550:
15546:
15539:
15531:
15527:
15523:
15519:
15515:
15511:
15504:
15497:
15482:
15481:opentextbc.ca
15478:
15472:
15457:
15453:
15447:
15439:
15435:
15431:
15427:
15420:
15412:
15406:
15402:
15398:
15394:
15393:
15385:
15370:
15366:
15359:
15352:
15346:
15344:
15342:
15340:
15338:
15330:(7): 557–585.
15329:
15325:
15318:
15310:
15306:
15302:
15296:
15288:
15284:
15279:
15274:
15270:
15266:
15262:
15255:
15247:
15243:
15239:
15235:
15231:
15224:
15216:
15212:
15208:
15204:
15200:
15196:
15192:
15185:
15177:
15173:
15169:
15162:
15155:
15149:
15145:
15140:
15135:
15131:
15127:
15123:
15119:
15115:
15108:
15100:
15096:
15090:
15082:
15076:
15072:
15059:
15053:
15047:
15043:
15039:
15035:
15031:
15030:
15022:
15018:
15009:
15006:
15004:
15001:
14999:
14996:
14994:
14991:
14989:
14986:
14984:
14981:
14979:
14976:
14974:
14971:
14969:
14966:
14964:
14961:
14959:
14956:
14954:
14951:
14949:
14946:
14944:
14941:
14939:
14936:
14932:
14929:
14927:
14924:
14923:
14922:
14919:
14917:
14914:
14912:
14909:
14908:
14904:
14898:
14893:
14883:
14877:
14874:
14871:
14865:
14862:
14858:
14855:
14849:
14843:
14840:
14838:
14832:
14828:
14825:
14819:
14816:
14812:
14809:
14799:
14796:
14795:
14789:
14787:
14768:
14761:
14758:
14753:
14745:
14734:
14727:
14724:
14721:
14714:
14700:
14697:
14692:
14689:
14686:
14682:
14676:
14673:
14668:
14665:
14662:
14659:
14652:
14651:
14650:
14648:
14644:
14640:
14636:
14632:
14628:
14624:
14620:
14587:
14580:
14577:
14572:
14564:
14553:
14546:
14543:
14540:
14533:
14519:
14514:
14511:
14508:
14504:
14498:
14495:
14490:
14487:
14484:
14481:
14474:
14473:
14472:
14470:
14466:
14462:
14458:
14454:
14450:
14446:
14428:
14425:
14422:
14418:
14409:
14405:
14387:
14384:
14381:
14377:
14368:
14364:
14360:
14355:
14350:
14349:Decorrelation
14342:
14336:
14319:
14316:
14313:
14296:
14290:
14287:
14284:
14247:
14244:
14241:
14204:
14181:
14166:
14151:
14128:
14113:
14098:
14095:
14092:
14069:
14066:
14063:
14048:
14033:
14010:
13995:
13980:
13957:
13942:
13941:
13940:
13923:
13913:
13902:
13896:
13880:
13869:
13863:
13852:
13846:
13843:
13840:
13826:
13820:
13817:
13814:
13793:
13792:
13791:
13777:
13757:
13743:
13740:
13734:
13724:
13722:
13718:
13714:
13692:
13663:
13630:
13616:
13610:
13605:
13601:
13594:
13591:
13586:
13581:
13578:
13575:
13571:
13561:
13547:
13541:
13536:
13532:
13525:
13522:
13517:
13512:
13509:
13506:
13502:
13485:
13479:
13474:
13470:
13463:
13460:
13448:
13442:
13437:
13433:
13426:
13423:
13418:
13413:
13410:
13407:
13403:
13396:
13387:
13379:
13378:
13377:
13375:
13371:
13367:
13358:
13354:
13347:
13343:
13338:
13334:
13327:
13323:
13317:
13307:
13286:
13283:
13280:
13276:
13267:
13264:
13261:
13256:
13253:
13250:
13246:
13235:
13233:
13214:
13209:
13206:
13203:
13199:
13195:
13192:
13189:
13184:
13181:
13178:
13174:
13166:
13165:
13164:
13162:
13158:
13154:
13144:
13130:
13121:
13107:
13085:
13081:
13057:
13052:
13048:
13042:
13037:
13034:
13031:
13021:
13018:
13013:
13008:
12998:
12987:
12986:
12985:
12969:
12959:
12932:
12928:
12923:
12920:
12915:
12911:
12908:
12905:
12902:
12895:
12894:
12893:
12879:
12859:
12839:
12830:
12828:
12822:
12798:
12787:
12782:
12778:
12772:
12768:
12764:
12753:
12748:
12744:
12738:
12734:
12730:
12720:
12716:
12710:
12706:
12700:
12696:
12692:
12686:
12681:
12678:
12675:
12672:
12668:
12664:
12657:
12656:
12655:
12638:
12627:
12622:
12618:
12614:
12603:
12598:
12594:
12590:
12580:
12576:
12570:
12566:
12562:
12556:
12551:
12548:
12544:
12540:
12533:
12532:
12531:
12529:
12510:
12507:
12504:
12501:
12498:
12495:
12492:
12488:
12482:
12479:
12476:
12473:
12470:
12467:
12461:
12456:
12452:
12448:
12442:
12439:
12436:
12433:
12427:
12422:
12418:
12414:
12408:
12405:
12402:
12396:
12391:
12387:
12383:
12377:
12374:
12371:
12365:
12360:
12356:
12348:
12347:
12346:
12329:
12317:
12313:
12305:
12295:
12286:
12282:
12274:
12258:
12254:
12247:
12234:
12228:
12225:
12222:
12216:
12211:
12207:
12199:
12198:
12197:
12175:
12166:
12163:
12160:
12157:
12154:
12148:
12145:
12139:
12136:
12133:
12130:
12127:
12121:
12118:
12110:
12107:
12104:
12101:
12098:
12092:
12089:
12083:
12077:
12074:
12071:
12068:
12065:
12059:
12056:
12048:
12034:
12026:
12022:
12016:
12012:
12000:
11997:
11994:
11988:
11982:
11977:
11973:
11960:
11957:
11954:
11948:
11942:
11937:
11933:
11926:
11921:
11917:
11911:
11907:
11900:
11894:
11891:
11888:
11885:
11882:
11876:
11873:
11865:
11851:
11843:
11839:
11833:
11829:
11821:
11817:
11811:
11807:
11801:
11797:
11790:
11784:
11781:
11778:
11772:
11761:
11760:
11759:
11757:
11753:
11749:
11745:
11741:
11731:
11724:
11717:
11698:
11687:
11684:
11681:
11670:
11667:
11664:
11653:
11649:
11645:
11642:
11633:
11630:
11625:
11616:
11608:
11607:
11606:
11596:
11580:
11576:
11565:
11561:
11558:
11554:
11546:
11542:
11535:
11531:
11516:
11513:
11510:
11503:
11502:
11501:
11499:
11498:
11488:
11481:
11479:
11465:
11461:
11454:
11451:
11444:
11440:
11436:
11433:
11427:
11424:
11420:
11416:
11413:
11404:
11396:
11395:
11392:
11390:
11389:
11379:
11372:
11370:
11356:
11350:
11347:
11341:
11335:
11326:
11322:
11319:
11315:
11305:
11298:
11289:
11285:
11279:
11273:
11263:
11260:
11253:
11252:
11249:
11239:
11230:
11211:
11208:
11205:
11202:
11199:
11196:
11193:
11171:
11162:
11147:
11144:
11141:
11134:
11133:
11132:
11125:
11118:
11116:
11102:
11098:
11092:
11088:
11084:
11081:
11078:
11073:
11069:
11066:
11063:
11057:
11052:
11049:
11044:
11039:
11036:
11030:
11010:
11004:
11001:
10992:
10984:
10983:
10980:
10974:
10954:
10951:
10926:
10923:
10920:
10914:
10911:
10905:
10899:
10895:
10891:
10888:
10884:
10880:
10874:
10871:
10868:
10864:
10861:
10858:
10854:
10840:
10839:
10838:
10828:
10810:
10806:
10796:
10794:
10790:
10786:
10782:
10777:
10775:
10771:
10767:
10763:
10759:
10754:
10752:
10747:
10743:
10739:
10735:
10734:
10729:
10725:
10721:
10718:
10705:
10701:
10698:
10694:
10690:
10687:
10683:
10679:
10676:
10673:
10669:
10666:
10662:
10658:
10654:
10653:
10647:
10645:
10641:
10637:
10633:
10629:
10626:
10622:
10619:
10615:
10611:
10600:
10590:
10588:
10584:
10551:
10500:
10486:
10480:
10475:
10471:
10462:
10458:
10454:
10435:
10419:
10405:
10399:
10394:
10384:
10372:
10368:
10364:
10345:
10344:
10343:
10298:
10293:
10279:
10273:
10270:
10264:
10257:
10256:
10255:
10235:
10225:
10215:
10208:
10203:
10199:
10190:
10186:
10182:
10170:
10169:
10168:
10163:
10156:
10148:
10129:
10126:
10114:
10108:
10103:
10093:
10078:
10068:
10061:
10056:
10052:
10043:
10039:
10031:
10030:
10029:
10026:
10024:
10020:
10002:
9988:
9982:
9979:
9973:
9945:
9931:
9925:
9920:
9916:
9907:
9903:
9895:
9881:
9875:
9870:
9860:
9848:
9844:
9837:
9832:
9818:
9812:
9809:
9803:
9796:
9795:
9794:
9773:
9764:
9750:
9744:
9739:
9735:
9726:
9722:
9714:
9700:
9694:
9689:
9679:
9667:
9663:
9655:
9653:
9640:
9626:
9620:
9615:
9605:
9593:
9589:
9585:
9580:
9566:
9560:
9555:
9551:
9542:
9538:
9530:
9516:
9510:
9505:
9495:
9483:
9479:
9472:
9470:
9457:
9443:
9437:
9432:
9422:
9410:
9406:
9402:
9397:
9383:
9377:
9372:
9368:
9359:
9355:
9344:
9330:
9324:
9319:
9309:
9299:
9287:
9281:
9276:
9266:
9251:
9241:
9234:
9229:
9225:
9213:
9209:
9202:
9200:
9187:
9173:
9167:
9162:
9152:
9140:
9136:
9132:
9127:
9113:
9107:
9102:
9098:
9089:
9085:
9070:
9064:
9059:
9049:
9030:
9024:
9019:
9009:
9002:
8997:
8987:
8980:
8975:
8971:
8962:
8958:
8951:
8949:
8936:
8922:
8916:
8911:
8901:
8889:
8885:
8881:
8876:
8862:
8856:
8851:
8847:
8838:
8834:
8819:
8813:
8808:
8798:
8779:
8773:
8768:
8764:
8755:
8751:
8744:
8742:
8728:
8722:
8719:
8713:
8702:
8701:
8700:
8684:
8674:
8667:
8662:
8658:
8635:
8625:
8613:
8612:least squares
8608:
8606:
8602:
8598:
8579:
8571:
8557:
8551:
8546:
8542:
8533:
8529:
8521:
8507:
8501:
8496:
8486:
8474:
8470:
8463:
8455:
8441:
8435:
8430:
8426:
8417:
8413:
8405:
8395:
8385:
8378:
8373:
8369:
8360:
8356:
8349:
8346:
8339:
8338:
8337:
8321:
8311:
8284:
8279:
8265:
8259:
8254:
8244:
8232:
8228:
8224:
8219:
8209:
8199:
8192:
8187:
8183:
8174:
8170:
8166:
8161:
8147:
8141:
8136:
8132:
8123:
8119:
8111:
8110:
8109:
8106:
8102:
8084:
8074:
8067:
8064:
8061:
8056:
8046:
8020:
8016:
8012:
8009:
8006:
8001:
7997:
7988:
7984:
7980:
7976:
7972:
7965:
7955:
7938:
7934:
7929:
7926:
7906:
7903:
7899:
7896:
7893:
7889:
7886:
7878:
7874:
7870:
7838:
7834:
7830:
7826:
7822:
7816:
7810:
7807:
7801:
7798:
7795:
7782:
7778:
7774:
7770:
7766:
7760:
7754:
7751:
7745:
7742:
7736:
7733:
7730:
7716:
7713:
7710:
7704:
7697:
7696:
7695:
7668:
7664:
7660:
7656:
7652:
7646:
7640:
7637:
7631:
7625:
7619:
7616:
7613:
7599:
7596:
7593:
7587:
7580:
7579:
7578:
7576:
7563:
7554:
7549:
7547:
7527:
7524:
7521:
7513:
7509:
7505:
7502:and follow a
7501:
7483:
7479:
7475:
7472:
7464:
7443:
7440:
7437:
7424:
7420:
7413:
7410:
7404:
7398:
7392:
7378:
7375:
7369:
7366:
7359:
7358:
7357:
7355:
7350:
7334:
7330:
7309:
7289:
7281:
7262:
7256:
7253:
7250:
7246:
7241:
7233:
7226:
7204:
7198:
7195:
7192:
7186:
7180:
7177:
7165:
7164:
7163:
7161:
7157:
7153:
7132:
7126:
7123:
7120:
7116:
7110:
7107:
7104:
7099:
7096:
7093:
7087:
7083:
7080:
7073:
7070:
7064:
7058:
7052:
7045:
7044:
7043:
7042:
7027:
7019:
7015:
7011:
7007:
7003:
7000:In practice,
6997:
6987:
6973:
6970:
6967:
6964:
6961:
6958:
6955:
6926:
6912:
6905:
6901:
6898:
6895:
6892:
6885:
6879:
6876:
6870:
6867:
6864:
6858:
6855:
6849:
6846:
6840:
6837:
6830:
6826:
6817:
6813:
6810:
6807:
6804:
6797:
6793:
6790:
6787:
6784:
6780:
6775:
6769:
6765:
6762:
6759:
6752:
6746:
6742:
6738:
6735:
6731:
6726:
6720:
6716:
6713:
6710:
6703:
6697:
6693:
6689:
6686:
6682:
6673:
6667:
6664:
6659:
6656:
6652:
6643:
6640:
6630:
6627:
6624:
6612:
6609:
6606:
6600:
6594:
6588:
6585:
6582:
6576:
6568:
6566:
6562:
6552:
6550:
6546:
6545:beta function
6505:
6496:
6489:
6485:
6482:
6479:
6472:
6466:
6463:
6456:
6450:
6436:
6432:
6429:
6426:
6419:
6413:
6409:
6405:
6402:
6398:
6391:
6385:
6379:
6372:
6371:
6370:
6368:
6364:
6348:
6345:
6342:
6333:
6331:
6312:
6309:
6306:
6303:
6300:
6297:
6294:
6286:
6274:
6262:
6220:
6213:
6210:
6207:
6204:
6195:
6192:
6186:
6180:
6177:
6174:
6171:
6162:
6159:
6153:
6147:
6144:
6138:
6132:
6129:
6122:
6114:
6102:
6088:
6085:
6080:
6077:
6069:
6066:
6063:
6060:
6051:
6044:
6041:
6035:
6032:
6028:
6022:
6011:
6008:
5998:
5994:
5991:
5988:
5981:
5975:
5971:
5967:
5964:
5960:
5952:
5948:
5945:
5942:
5935:
5929:
5925:
5921:
5918:
5914:
5906:
5903:
5900:
5885:
5882:
5879:
5870:
5864:
5858:
5851:
5850:
5849:
5847:
5843:
5839:
5835:
5825:
5823:
5818:
5816:
5811:
5794:
5786:
5782:
5778:
5775:
5772:
5769:
5765:
5760:
5757:
5750:
5749:
5748:
5746:
5742:
5717:
5713:
5709:
5706:
5701:
5698:
5695:
5688:
5685:
5678:
5674:
5670:
5665:
5662:
5655:
5654:
5653:
5651:
5647:
5646:-distribution
5645:
5639:
5635:
5631:
5622:
5616:-distribution
5615:
5609:
5595:
5575:
5548:
5545:
5542:
5535:
5531:
5527:
5524:
5517:
5512:
5508:
5500:
5499:
5498:
5496:
5480:
5460:
5446:
5444:
5440:
5436:
5432:
5428:
5424:
5420:
5416:
5411:
5407:
5402:
5398:
5394:
5390:
5380:
5378:
5374:
5369:
5365:
5357:
5353:
5350:
5346:
5342:
5338:
5337:bootstrapping
5334:
5330:
5326:
5322:
5318:
5314:
5310:
5307:), where the
5305:
5301:
5296:
5292:
5287:
5283:
5278:
5274:
5270:
5269:
5268:
5266:
5257:
5251:
5247:
5243:
5240:
5236:
5232:
5228:
5227:
5226:
5218:
5211:
5207:
5203:
5199:
5195:
5191:
5187:
5183:
5163:
5159:
5155:
5152:
5147:
5144:
5136:
5132:
5128:
5123:
5114:
5113:as expected.
5097:
5092:
5089:
5085:
5081:
5078:
5075:
5067:
5060:
5054:
5049:
5010:
4999:
4996:
4993:
4990:
4983:
4982:
4981:
4980:, from which
4977:
4970:
4963:
4957:
4951:
4945:
4940:
4936:
4931:
4912:
4909:
4901:
4894:
4888:
4883:
4844:
4833:
4830:
4827:
4824:
4817:
4816:
4815:
4813:
4809:
4805:
4800:
4796:
4789:
4784:
4780:
4774:
4772:
4768:
4764:
4760:
4757:
4753:
4747:
4745:
4740:
4736:
4732:
4725:
4718:
4713:
4709:
4705:
4701:
4697:
4691:
4686:
4682:
4678:
4671:
4666:
4662:
4658:
4653:
4644:
4639:
4635:
4631:
4624:
4619:
4615:
4611:
4605:
4593:
4590:
4587:
4584:
4581:
4578:
4575:
4572:
4569:
4566:
4563:
4560:
4557:
4556:
4555:
4552:
4550:
4545:
4541:
4536:
4532:
4528:
4523:
4519:
4514:
4510:
4505:
4501:
4496:
4492:
4485:
4479:
4475:
4470:
4464:
4460:
4453:
4451:
4447:
4443:
4440:increases as
4439:
4435:
4431:
4427:
4423:
4413:
4411:
4410:
4403:
4399:
4394:
4390:
4386:
4382:
4377:
4373:
4368:
4363:
4359:
4354:
4350:
4345:
4343:
4339:
4335:
4331:
4327:
4316:
4314:
4311:other than a
4310:
4305:
4303:
4298:
4296:
4292:
4282:
4266:
4258:
4253:
4249:
4241:
4237:
4231:
4227:
4221:
4218:
4215:
4211:
4201:
4197:
4191:
4187:
4181:
4178:
4175:
4171:
4163:
4158:
4154:
4147:
4142:
4112:
4108:
4105:
4086:
4083:
4080:
4046:
4042:
4033:
4013:
3999:
3993:
3988:
3984:
3975:
3970:
3967:
3964:
3960:
3953:
3950:
3947:
3943:
3936:
3931:
3927:
3919:
3898:
3892:
3883:
3877:
3872:
3868:
3864:
3859:
3855:
3851:
3848:
3841:
3840:
3839:
3817:
3813:
3807:
3803:
3796:
3793:
3790:
3776:
3764:
3758:
3755:
3750:
3746:
3740:
3736:
3732:
3726:
3721:
3718:
3714:
3706:
3705:
3704:
3688:
3685:
3681:
3658:
3655:
3651:
3626:
3605:
3598:
3594:
3583:
3577:
3572:
3568:
3561:
3553:
3536:
3532:
3528:
3523:
3519:
3492:
3486:
3477:
3471:
3466:
3462:
3458:
3453:
3449:
3445:
3442:
3435:
3434:
3433:
3415:
3408:
3404:
3393:
3387:
3382:
3378:
3371:
3366:
3359:
3355:
3344:
3338:
3333:
3329:
3322:
3316:
3311:
3308:
3305:
3301:
3294:
3291:
3288:
3284:
3279:
3274:
3271:
3267:
3259:
3258:
3257:
3255:
3237:
3234:
3230:
3220:
3218:
3213:
3197:
3193:
3189:
3184:
3180:
3176:
3173:
3150:
3140:
3135:
3129:
3125:
3121:
3117:
3112:
3107:
3102:
3098:
3094:
3091:
3079:
3074:
3068:
3064:
3060:
3056:
3051:
3046:
3041:
3037:
3033:
3030:
3021:
3017:
3013:
3008:
3004:
3000:
2997:
2992:
2988:
2982:
2978:
2974:
2971:
2965:
2960:
2957:
2953:
2945:
2944:
2943:
2927:
2924:
2920:
2910:
2890:
2884:
2875:
2869:
2864:
2860:
2856:
2851:
2847:
2843:
2840:
2817:
2807:
2797:
2790:
2787:
2782:
2777:
2773:
2767:
2763:
2750:
2740:
2733:
2730:
2725:
2720:
2716:
2710:
2706:
2692:
2680:
2674:
2671:
2666:
2662:
2656:
2652:
2646:
2642:
2635:
2630:
2627:
2623:
2615:
2614:
2613:
2597:
2594:
2590:
2559:
2534:
2530:
2524:
2519:
2516:
2513:
2509:
2503:
2500:
2495:
2486:
2476:
2474:
2456:
2452:
2448:
2443:
2439:
2431:
2416:
2409:
2408:
2407:
2404:
2384:
2370:
2364:
2359:
2355:
2346:
2341:
2338:
2335:
2331:
2321:
2307:
2301:
2296:
2292:
2283:
2278:
2275:
2272:
2268:
2251:
2245:
2240:
2236:
2220:
2214:
2209:
2205:
2196:
2191:
2188:
2185:
2181:
2174:
2169:
2166:
2162:
2153:
2137:
2134:
2130:
2109:
2088:
2079:
2075:
2071:
2066:
2062:
2055:
2052:
2049:
2041:
2037:
2033:
2028:
2024:
2016:
1993:
1990:
1986:
1977:
1973:
1955:
1952:
1948:
1939:
1929:
1916:
1906:
1901:
1893:
1886:
1875:
1870:
1866:
1859:
1855:
1849:
1845:
1826:
1821:
1813:
1806:
1795:
1790:
1786:
1779:
1775:
1769:
1765:
1747:
1740:
1726:
1719:
1709:
1702:
1698:
1691:
1678:
1673:
1670:
1667:
1663:
1642:
1615:
1607:
1600:
1586:
1579:
1569:
1562:
1558:
1551:
1541:
1533:
1525:
1518:
1508:
1505:
1501:
1496:
1488:
1481:
1471:
1468:
1464:
1456:
1446:
1438:
1432:
1428:
1424:
1421:
1417:
1412:
1406:
1402:
1398:
1395:
1391:
1383:
1366:
1361:
1353:
1346:
1334:
1329:
1325:
1318:
1314:
1308:
1304:
1294:
1290:
1283:
1278:
1271:
1265:
1255:
1252:
1248:
1241:
1237:
1223:
1218:
1213:
1209:
1199:
1194:
1186:
1179:
1168:
1163:
1159:
1152:
1148:
1142:
1138:
1128:
1124:
1117:
1112:
1105:
1099:
1089:
1086:
1082:
1075:
1071:
1057:
1052:
1047:
1043:
1031:
1024:
1010:
1005:
1001:
989:
982:
968:
963:
959:
947:
946:
945:
931:
896:
882:
860:
856:
848:
834:
812:
808:
800:
783:
779:
756:
752:
744:
743:
742:
739:
721:
717:
711:
707:
693:
689:
685:
682:
671:
667:
663:
660:
651:
638:
633:
630:
627:
623:
614:
600:
577:
566:
562:
558:
555:
544:
540:
536:
533:
524:
514:
508:
505:
502:
496:
493:
486:
485:
484:
482:
478:
459:
456:
453:
447:
444:
420:
398:
394:
386:
372:
364:
346:
342:
334:
332:
316:
309:
308:
307:
304:
286:
282:
276:
272:
263:
260:
257:
251:
248:
242:
237:
234:
231:
227:
218:
216:
197:
194:
191:
180:
176:
172:
168:
158:
157:in the name.
156:
152:
148:
138:
136:
135:Stigler's Law
132:
128:
124:
114:
111:
107:
103:
99:
95:
91:
87:
83:
75:
70:
66:
62:
58:
53:
46:
41:
37:
33:
19:
19258:
18867:
18855:
18836:
18829:
18741:Econometrics
18691: /
18674:Chemometrics
18651:Epidemiology
18644: /
18617:Applications
18459:ARIMA model
18406:Q-statistic
18355:Stationarity
18251:Multivariate
18194: /
18190: /
18188:Multivariate
18186: /
18126: /
18122: /
17896:Bayes factor
17795:Signed rank
17707:
17681:
17673:
17661:
17356:Completeness
17192:Cohort study
17090:Opinion poll
17025:Missing data
17012:Study design
16967:Scatter plot
16889:Scatter plot
16882:Spearman's ρ
16866:
16844:Grouped data
16537:
16523:hackmath.net
16522:
16509:
16496:
16464:
16458:
16431:
16427:
16417:
16400:
16396:
16386:
16376:21 September
16374:. Retrieved
16359:
16352:
16340:. Retrieved
16310:
16306:
16296:
16281:
16276:
16243:
16239:
16226:
16212:
16203:
16194:
16166:
16162:
16152:
16127:
16123:
16117:
16094:
16089:
16061:
16054:
16045:
16039:
16014:
16010:
16001:
15992:
15958:
15954:
15941:
15920:cite journal
15895:
15886:
15876:
15867:
15861:
15836:
15832:
15826:
15783:
15779:
15773:
15756:
15750:
15737:
15721:
15716:
15708:
15703:
15691:. Retrieved
15687:
15678:
15645:
15641:
15631:
15622:
15594:
15588:
15573:
15548:
15544:
15538:
15516:(1): 59–66.
15513:
15509:
15496:
15484:. Retrieved
15480:
15471:
15459:. Retrieved
15455:
15446:
15429:
15425:
15419:
15390:
15384:
15372:. Retrieved
15368:
15358:
15327:
15323:
15317:
15308:
15304:
15295:
15271:(2): 73–79.
15268:
15264:
15254:
15237:
15233:
15223:
15198:
15194:
15184:
15175:
15171:
15161:
15153:
15121:
15117:
15107:
15098:
15089:
15075:
15057:
15052:
15045:
15041:
15037:
15033:
15028:
15026:
15021:
14820:library via
14783:
14646:
14642:
14638:
14634:
14630:
14626:
14602:
14464:
14456:
14452:
14448:
14444:
14407:
14403:
14366:
14362:
14358:
14356:
14352:
14340:
14220:
13938:
13749:
13736:
13720:
13716:
13652:
13369:
13365:
13356:
13352:
13345:
13341:
13336:
13332:
13325:
13321:
13319:
13236:
13229:
13160:
13156:
13152:
13150:
13122:
13072:
12947:
12831:
12824:
12653:
12525:
12344:
12195:
11755:
11751:
11747:
11743:
11739:
11737:
11722:
11715:
11713:
11604:
11594:
11578:
11563:
11556:
11552:
11544:
11533:
11495:
11493:
11482:
11386:
11384:
11373:
11237:
11234:
11130:
11119:
10979:is given by
10972:
10969:
10816:
10808:
10792:
10788:
10780:
10778:
10755:
10745:
10741:
10731:
10719:
10714:
10696:
10692:
10639:
10635:
10607:
10518:
10341:
10253:
10161:
10154:
10144:
10027:
10022:
10018:
9965:
9792:
8609:
8604:
8600:
8596:
8594:
8299:
8104:
8100:
7982:
7978:
7970:
7968:
7876:
7872:
7868:
7866:
7693:
7556:
7552:
7550:
7511:
7460:
7351:
7279:
7277:
7155:
7151:
7150:
7040:
7009:
7008:relating to
6999:
6927:
6569:
6564:
6558:
6520:
6366:
6362:
6334:
6238:
5845:
5841:
5837:
5831:
5821:
5819:
5814:
5812:
5809:
5744:
5740:
5738:
5649:
5643:
5627:
5613:
5567:
5452:
5442:
5434:
5422:
5418:
5414:
5409:
5405:
5400:
5396:
5392:
5386:
5367:
5361:
5355:
5348:
5344:
5340:
5332:
5328:
5324:
5320:
5316:
5308:
5303:
5299:
5294:
5290:
5285:
5281:
5276:
5272:
5263:
5255:
5249:
5238:
5234:
5224:
5215:
5209:
5205:
5201:
5197:
5193:
5189:
5181:
5134:
5130:
5126:
5112:
4975:
4968:
4961:
4955:
4949:
4943:
4938:
4934:
4927:
4913:0.920814711.
4811:
4803:
4801:
4794:
4787:
4782:
4778:
4775:
4770:
4766:
4758:
4748:
4738:
4734:
4730:
4723:
4716:
4711:
4707:
4703:
4699:
4695:
4689:
4684:
4680:
4676:
4669:
4664:
4660:
4656:
4651:
4649:
4642:
4637:
4633:
4629:
4622:
4617:
4613:
4609:
4553:
4543:
4539:
4534:
4530:
4521:
4517:
4512:
4508:
4503:
4499:
4494:
4490:
4483:
4477:
4473:
4468:
4462:
4458:
4454:
4449:
4445:
4441:
4437:
4425:
4421:
4419:
4407:
4401:
4397:
4392:
4388:
4384:
4380:
4375:
4371:
4366:
4361:
4357:
4352:
4346:
4341:
4337:
4333:
4329:
4322:
4306:
4299:
4288:
4069:
3837:
3642:
3431:
3256:as follows:
3221:
3214:
3165:
2911:
2832:
2581:
2472:
2405:
2154:
1975:
1971:
1935:
1932:For a sample
1634:
923:
740:
615:
592:
436:
305:
219:
214:
178:
174:
170:
164:
154:
144:
123:Karl Pearson
120:
89:
85:
79:
73:
68:
64:
60:
56:
44:
36:
18869:WikiProject
18784:Cartography
18746:Jurimetrics
18698:Reliability
18429:Time domain
18408:(Ljung–Box)
18330:Time-series
18208:Categorical
18192:Time-series
18184:Categorical
18119:(Bernoulli)
17954:Correlation
17934:Correlation
17730:Jarque–Bera
17702:Chi-squared
17464:M-estimator
17417:Asymptotics
17361:Sufficiency
17128:Interaction
17040:Replication
17020:Effect size
16977:Violin plot
16957:Radar chart
16937:Forest plot
16927:Correlogram
16877:Kendall's τ
16342:11 February
16246:(5): 1–21.
15801:11343/44035
15786:: 728–740.
15743:Soper, H.E.
15724:, Griffin.
15240:: 240–242.
15201:: 246–263.
14847:Correlation
14469:independent
14365:times. Let
13362:[0, 2π)
12827:time series
10738:scatterplot
10704:dichotomous
10650:Sample size
10519:The symbol
6549:studentized
5638:studentized
5313:permutation
4808:dot product
4304:estimator.
481:expectation
110:correlation
19287:Categories
19242:Similarity
19184:Perplexity
19095:Rand index
19080:Dunn index
19065:Silhouette
19057:Clustering
18921:Regression
18736:Demography
18454:ARMA model
18259:Regression
17836:(Friedman)
17797:(Wilcoxon)
17735:Normality
17725:Lilliefors
17672:Student's
17548:Resampling
17422:Robustness
17410:divergence
17400:Efficiency
17338:(monotone)
17333:Likelihood
17250:Population
17083:Stratified
17035:Population
16854:Dependence
16810:Count data
16741:Percentile
16718:Dispersion
16651:Arithmetic
16586:Statistics
16011:Biometrika
15780:NeuroImage
15752:Biometrika
15067:References
15027:Pearson's
14983:Odds ratio
11494:where in (
10940:therefore
10803:See also:
10711:Robustness
10621:covariance
10618:population
8300:where the
7461:under the
7302:and small
5642:Student's
5439:percentile
4812:uncentered
331:covariance
167:population
147:covariance
141:Definition
102:covariance
82:statistics
19012:Precision
18964:RMSE/RMSD
18117:Logistic
17884:posterior
17810:Rank sum
17558:Jackknife
17553:Bootstrap
17371:Bootstrap
17306:Parameter
17255:Statistic
17050:Statistic
16962:Run chart
16947:Pie chart
16942:Histogram
16932:Fan chart
16907:Bar chart
16789:L-moments
16676:Geometric
16441:1408.6851
16315:CiteSeerX
15961:: 58–77.
15818:207184701
15662:0162-1459
15486:21 August
15399:pp.
15374:22 August
15014:Footnotes
14872:function.
14802:cor(x, y)
14754:−
14669:−
14573:−
14491:−
14096:⊗
14067:⊗
13903:⋅
13870:⋅
13853:−
13844:⊗
13719:and
13696:¯
13667:¯
13620:¯
13611:−
13595:
13572:∑
13551:¯
13542:−
13526:
13503:∑
13489:¯
13480:−
13464:
13452:¯
13443:−
13427:
13404:∑
13277:ρ
13268:−
13200:ρ
13196:−
13159:known as
13028:∑
13002:¯
12963:¯
12912:
12765:∑
12731:∑
12693:∑
12615:∑
12591:∑
12563:∑
12496:≠
12462:
12449:≠
12428:
12397:
12366:
12306:
12296:⋅
12275:
12248:
12217:
12149:
12122:
12093:
12060:
12013:∑
11989:
11983:−
11949:
11943:−
11927:⋅
11908:∑
11877:
11830:∑
11798:∑
11773:
11685:−
11668:−
11646:−
11634:−
11437:−
11414:≈
11323:−
11299:−
11286:≈
11274:
11085:−
11067:−
10952:ρ
10924:⋯
10896:ρ
10892:−
10881:ρ
10875:−
10872:ρ
10855:
10762:bootstrap
10717:statistic
10672:efficient
10604:Existence
10490:¯
10481:−
10459:∑
10409:¯
10400:−
10388:^
10369:∑
10283:^
10219:^
10209:−
10187:∑
10118:¯
10109:−
10097:^
10072:^
10062:−
10040:∑
9992:^
9935:¯
9926:−
9904:∑
9885:¯
9876:−
9864:^
9845:∑
9822:^
9754:¯
9745:−
9723:∑
9704:¯
9695:−
9683:^
9664:∑
9630:¯
9621:−
9609:^
9590:∑
9586:⋅
9570:¯
9561:−
9539:∑
9520:¯
9511:−
9499:^
9480:∑
9447:¯
9438:−
9426:^
9407:∑
9403:⋅
9387:¯
9378:−
9356:∑
9334:¯
9325:−
9313:^
9291:¯
9282:−
9270:^
9245:^
9235:−
9210:∑
9177:¯
9168:−
9156:^
9137:∑
9133:⋅
9117:¯
9108:−
9086:∑
9074:¯
9065:−
9053:^
9034:¯
9025:−
9013:^
8991:^
8981:−
8959:∑
8926:¯
8917:−
8905:^
8886:∑
8882:⋅
8866:¯
8857:−
8835:∑
8823:¯
8814:−
8802:^
8783:¯
8774:−
8752:∑
8732:^
8678:^
8668:−
8629:^
8561:¯
8552:−
8530:∑
8511:¯
8502:−
8490:^
8471:∑
8445:¯
8436:−
8414:∑
8389:^
8379:−
8357:∑
8315:^
8269:¯
8260:−
8248:^
8229:∑
8203:^
8193:−
8171:∑
8151:¯
8142:−
8120:∑
8078:^
8065:…
8050:^
8010:…
7930:±
7890:
7831:α
7811:
7802:
7775:α
7767:−
7755:
7746:
7737:∈
7734:ρ
7723:%
7717:α
7714:−
7661:α
7653:±
7641:
7632:∈
7626:ρ
7620:
7606:%
7600:α
7597:−
7564:ρ
7522:ρ
7480:ρ
7473:ρ
7441:−
7421:ρ
7411:−
7379:−
7331:ρ
7254:−
7205:ρ
7199:
7187:ρ
7127:
7108:−
7084:
7065:≡
6965:−
6956:ν
6902:ρ
6868:ν
6850:−
6827:
6814:ν
6808:−
6794:ρ
6788:−
6776:⋅
6763:−
6760:ν
6743:ρ
6739:−
6727:⋅
6714:−
6711:ν
6690:−
6657:ν
6649:Γ
6644:π
6628:−
6625:ν
6619:Γ
6610:−
6607:ν
6601:ν
6586:∣
6583:ρ
6577:π
6483:−
6451:
6430:−
6406:−
6343:ρ
6247:Γ
6205:ρ
6178:−
6081:−
6067:ρ
6064:−
6036:−
6023:
6019:Γ
6012:π
5992:−
5968:−
5946:−
5926:ρ
5922:−
5904:−
5894:Γ
5883:−
5773:−
5710:−
5699:−
5675:σ
5546:−
5528:−
5509:σ
5389:bootstrap
5377:one-sided
5373:two-sided
5221:Inference
5160:ρ
5156:−
5148:−
5086:ρ
5011:⋅
4997:θ
4994:
4966:) yields
4964:) = 0.138
4845:⋅
4831:θ
4828:
4349:invariant
4326:supported
4250:σ
4238:σ
4228:σ
4212:ρ
4198:σ
4188:σ
4172:ρ
4155:σ
4140:Σ
4120:Σ
4003:¯
3994:−
3961:∑
3951:−
3902:¯
3887:¯
3794:−
3780:¯
3768:¯
3756:−
3733:∑
3587:¯
3578:−
3496:¯
3481:¯
3397:¯
3388:−
3348:¯
3339:−
3302:∑
3292:−
3122:∑
3113:−
3095:∑
3061:∑
3052:−
3034:∑
3014:∑
3001:∑
2998:−
2975:∑
2894:¯
2879:¯
2801:¯
2788:−
2764:∑
2744:¯
2731:−
2707:∑
2696:¯
2684:¯
2672:−
2643:∑
2563:¯
2510:∑
2490:¯
2374:¯
2365:−
2332:∑
2311:¯
2302:−
2269:∑
2255:¯
2246:−
2224:¯
2215:−
2182:∑
2053:…
1887:
1871:−
1846:
1807:
1791:−
1766:
1741:
1720:
1710:−
1692:
1664:ρ
1643:ρ
1601:
1580:
1570:−
1552:
1519:
1509:−
1482:
1472:−
1457:
1429:μ
1425:−
1403:μ
1399:−
1384:
1347:
1330:−
1305:
1266:
1256:−
1238:
1210:σ
1180:
1164:−
1139:
1100:
1090:−
1072:
1044:σ
1025:
1002:μ
983:
960:μ
932:ρ
857:μ
809:μ
780:σ
753:σ
718:σ
708:σ
690:μ
686:−
668:μ
664:−
652:
624:ρ
601:ρ
563:μ
559:−
541:μ
537:−
525:
497:
448:
395:σ
343:σ
283:σ
273:σ
252:
228:ρ
19228:Coverage
19007:Accuracy
18831:Category
18524:Survival
18401:Johansen
18124:Binomial
18079:Isotonic
17666:(normal)
17311:location
17118:Blocking
17073:Sampling
16952:Q–Q plot
16917:Box plot
16899:Graphics
16794:Skewness
16784:Kurtosis
16756:Variance
16686:Heronian
16681:Harmonic
16260:22324876
16048:. Wiley.
15975:52878443
15810:22939874
15565:27528906
15456:STAT 462
14931:Yule's Y
14926:Yule's Q
14889:See also
14844:via the
13711:are the
13392:circular
10799:Variants
10785:stratify
10740:between
10728:outliers
10668:unbiased
10625:marginal
10587:variance
8607:(left).
5445:values.
5345:i′
5343:and the
5329:i′
5321:i′
5309:i′
5304:i′
5043:‖
5035:‖
5030:‖
5022:‖
4877:‖
4869:‖
4864:‖
4856:‖
4379:, where
4111:variance
4107:gaussian
483:. Since
76:is zero.
19120:Ranking
19110:SimHash
18997:F-score
18857:Commons
18804:Kriging
18689:Process
18646:studies
18505:Wavelet
18338:General
17505:Plug-in
17299:L space
17078:Cluster
16779:Moments
16597:Outline
16493:"cocor"
16337:1027502
16268:4694570
16185:2237306
16144:2983768
16031:2335508
15853:2983768
15693:30 July
15670:2277400
15530:2685263
15461:10 July
15401:223–260
15287:2245329
15242:Bibcode
15215:2841583
15148:4136393
15126:Bibcode
15040:), the
14623:inverse
14621:of the
14612:⁄
14402:is the
13372:with a
11591:⁄
11227:is the
11131:where:
10722:is not
10610:moments
10581:is the
10153:) over
7887:arctanh
7508:p-value
7354:z-score
6543:is the
6328:is the
6259:is the
5636:of the
5404:,
5395:pairs (
5364:p-value
5335:}. In
5298:,
5280:,
5068:0.00308
4952:) = 3.8
4810:), the
4763:vectors
4754:of the
4132:, then
4104:jointly
2122:pairs,
1974:or the
361:is the
329:is the
177:or the
92:) is a
59:,
19017:Recall
18726:Census
18316:Normal
18264:Manova
18084:Robust
17834:2-way
17826:1-way
17664:-test
17335:
16912:Biplot
16703:Median
16696:Lehmer
16638:Center
16471:
16367:
16335:
16317:
16288:
16266:
16258:
16183:
16142:
16109:
16101:
16077:
16029:
15973:
15851:
15816:
15808:
15728:
15668:
15660:
15601:
15563:
15528:
15407:
15285:
15213:
15172:Nature
15146:
15118:Nature
15032:, the
14831:Pandas
14818:Python
14443:be an
14410:. Let
13939:where
13653:where
13340:} and
13073:where
10724:robust
10552:, and
10342:where
9966:where
7927:0.8673
7907:0.8673
7808:artanh
7752:artanh
7638:artanh
7617:artanh
7278:where
7196:artanh
7124:artanh
6928:where
6521:where
6239:where
5632:, the
5568:where
5311:are a
5204:|
4902:0.0983
4752:cosine
4737:− tan
4733:= sec
4726:< 0
4719:> 0
4404:> 0
4391:, and
3838:where
3432:where
3166:where
3087:
2833:where
2758:
2406:where
1938:sample
1834:
741:where
306:where
151:moment
98:linear
84:, the
19022:Kappa
18939:sMAPE
18350:Trend
17879:prior
17821:anova
17710:-test
17684:-test
17676:-test
17583:Power
17528:Pivot
17321:shape
17316:scale
16766:Shape
16746:Range
16691:Heinz
16666:Cubic
16602:Index
16534:(PDF)
16436:arXiv
16333:S2CID
16264:S2CID
16236:(PDF)
16181:JSTOR
16140:JSTOR
16027:JSTOR
15971:S2CID
15951:(PDF)
15849:JSTOR
15814:S2CID
15666:JSTOR
15561:JSTOR
15526:JSTOR
15506:(PDF)
15283:JSTOR
15211:JSTOR
15144:S2CID
15038:PPMCC
14876:Excel
14861:Boost
14815:SciPy
14164:, and
13351:,...,
13331:,...,
12909:round
11391:) is
9793:Thus
7985:in a
7465:that
7162:with
5055:0.308
4756:angle
4529:) if
4030:(the
19189:BLEU
19161:SSIM
19156:PSNR
19133:NDCG
18954:MSPE
18949:MASE
18944:MAPE
18583:Test
17783:Sign
17635:Wald
16708:Mode
16646:Mean
16469:ISBN
16378:2016
16365:ISBN
16344:2018
16286:ISBN
16256:PMID
16107:ISBN
16099:ISBN
16075:ISBN
15933:help
15806:PMID
15726:ISBN
15695:2021
15658:ISSN
15599:ISBN
15488:2020
15463:2021
15405:ISBN
15376:2020
14859:The
14829:The
14813:The
14645:and
13770:and
13682:and
13374:sine
13368:and
13155:and
12832:Let
12508:>
12453:corr
12419:corr
12388:corr
12357:corr
12208:corr
12057:corr
11746:and
11597:− 1)
10744:and
10670:and
10160:and
8650:and
7935:1.96
7799:tanh
7743:tanh
7383:mean
7322:and
7223:and
7174:mean
7004:and
6971:>
6263:and
5473:and
5433:for
5387:The
5188:for
5061:30.8
4973:and
4954:and
4889:2.93
4792:and
4781:and
4702:and
4674:and
4627:and
4538:and
4516:and
4498:and
4430:line
4424:and
771:and
479:and
477:mean
365:of
67:and
19210:FID
19176:NLP
19166:IoU
19128:MRR
19105:SMC
19037:ROC
19032:AUC
19027:MCC
18979:MAD
18974:MDA
18959:RMS
18934:MAE
18929:MSE
17763:BIC
17758:AIC
16446:doi
16432:114
16405:doi
16325:doi
16248:doi
16171:doi
16132:doi
16067:doi
16019:doi
15963:doi
15959:470
15906:doi
15841:doi
15796:hdl
15788:doi
15761:doi
15650:doi
15553:doi
15518:doi
15434:doi
15273:doi
15203:doi
15134:doi
14864:C++
14463:of
14447:by
13715:of
13592:sin
13523:sin
13461:sin
13424:sin
13344:= {
13324:= {
12146:cov
12119:cov
12090:cov
11874:cov
11758:),
11719:adj
11621:adj
11582:adj
11567:adj
11559:)),
11548:adj
11537:adj
11409:adj
11331:adj
11310:adj
11294:adj
11241:adj
10997:adj
10976:adj
10638:or
10567:tot
10534:reg
10450:tot
10360:reg
10323:tot
10311:reg
10179:RSS
10151:RSS
7705:100
7588:100
7577:):
7356:is
6567:is
5453:If
5375:or
4991:cos
4958:by
4946:by
4895:103
4825:cos
4765:in
4706:on
4698:on
4369:to
4355:to
4344:).
4102:is
4070:If
494:cov
445:cov
317:cov
249:cov
217:is
90:PCC
80:In
19289::
19138:AP
19002:P4
16536:.
16521:.
16508:.
16495:.
16444:.
16430:.
16426:.
16401:40
16399:.
16395:.
16331:.
16323:.
16311:60
16309:.
16305:.
16262:.
16254:.
16244:35
16242:.
16238:.
16202:.
16179:.
16167:29
16165:.
16161:.
16138:.
16128:15
16126:.
16105:.
16073:.
16025:.
16015:62
16013:.
15983:^
15969:.
15957:.
15953:.
15924::
15922:}}
15918:{{
15904:.
15885:.
15847:.
15837:15
15812:.
15804:.
15794:.
15784:64
15782:.
15757:11
15755:.
15749:.
15686:.
15664:.
15656:.
15646:23
15644:.
15640:.
15613:^
15559:.
15549:41
15547:.
15524:.
15514:42
15512:.
15508:.
15479:.
15454:.
15430:38
15428:.
15403:.
15395:.
15367:.
15336:^
15328:20
15326:.
15303:.
15281:.
15267:.
15263:.
15238:58
15236:.
15232:.
15209:.
15199:15
15197:.
15193:.
15176:32
15174:.
15170:.
15142:.
15132:.
15122:15
15120:.
15116:.
15097:.
14649::
14471:.
13120:.
12892::
12530::
12511:0.
11730:.
11721:≈
11500:)
10795:.
10562:SS
10529:SS
10445:SS
10355:SS
10318:SS
10306:SS
10025:.
7939:47
7845:SE
7789:SE
7727:CI
7675:SE
7610:CI
7548:.
7388:SE
7238:SE
7081:ln
7020:,
7016:,
6986:.
6332:.
5351:};
5137:,
5129:,
4960:ℰ(
4948:ℰ(
4799:.
4746:.
4679:=
4659:=
4632:=
4612:=
4481:−
4472:)(
4466:−
4400:,
4387:,
4383:,
4376:dY
4374:+
4362:bX
4360:+
4281:.
3703::
3639:).
3219:.
2942::
2612::
137:.
18969:R
18904:e
18897:t
18890:v
17708:G
17682:F
17674:t
17662:Z
17381:V
17376:U
16578:e
16571:t
16564:v
16549:.
16540:.
16512:.
16499:.
16477:.
16452:.
16448::
16438::
16411:.
16407::
16380:.
16346:.
16327::
16270:.
16250::
16220:.
16206:.
16189:.
16187:.
16173::
16146:.
16134::
16083:.
16069::
16033:.
16021::
15977:.
15965::
15935:)
15931:(
15914:.
15908::
15889:.
15855:.
15843::
15820:.
15798::
15790::
15767:.
15763::
15697:.
15672:.
15652::
15607:.
15567:.
15555::
15532:.
15520::
15490:.
15465:.
15440:.
15436::
15413:.
15378:.
15309:9
15289:.
15275::
15269:4
15248:.
15244::
15217:.
15205::
15156:.
15154:r
15150:.
15136::
15128::
15101:.
15083:.
15058:r
15036:(
15029:r
14856:.
14826:.
14810:.
14798:R
14769:.
14762:2
14759:1
14750:)
14746:D
14740:T
14735:D
14731:(
14728:d
14725:=
14722:t
14701:,
14698:X
14693:m
14690:,
14687:1
14683:Z
14677:m
14674:1
14666:x
14663:=
14660:d
14647:t
14643:d
14639:x
14635:n
14631:x
14627:T
14614:2
14610:1
14607:+
14605:−
14588:,
14581:2
14578:1
14569:)
14565:D
14559:T
14554:D
14550:(
14547:D
14544:=
14541:T
14520:X
14515:m
14512:,
14509:m
14505:Z
14499:m
14496:1
14488:X
14485:=
14482:D
14465:T
14457:T
14453:D
14449:m
14445:m
14429:m
14426:,
14423:m
14419:Z
14408:i
14404:j
14388:j
14385:,
14382:i
14378:X
14367:X
14363:m
14359:n
14341:n
14323:)
14320:X
14317:,
14314:Y
14311:(
14307:r
14304:o
14301:C
14297:=
14294:)
14291:Y
14288:,
14285:X
14282:(
14278:r
14275:o
14272:C
14251:)
14248:Y
14245:,
14242:X
14239:(
14235:r
14232:o
14229:C
14217:.
14205:Y
14185:]
14182:Y
14179:[
14175:V
14152:X
14132:]
14129:X
14126:[
14122:V
14111:,
14099:Y
14093:X
14073:]
14070:Y
14064:X
14061:[
14057:E
14046:,
14034:Y
14014:]
14011:Y
14008:[
14004:E
13993:,
13981:X
13961:]
13958:X
13955:[
13951:E
13924:,
13917:]
13914:Y
13911:[
13907:V
13900:]
13897:X
13894:[
13890:V
13884:]
13881:Y
13878:[
13874:E
13867:]
13864:X
13861:[
13857:E
13850:]
13847:Y
13841:X
13838:[
13834:E
13827:=
13824:)
13821:Y
13818:,
13815:X
13812:(
13808:r
13805:o
13802:C
13778:Y
13758:X
13721:Y
13717:X
13693:y
13664:x
13631:2
13627:)
13617:y
13606:i
13602:y
13598:(
13587:n
13582:1
13579:=
13576:i
13562:2
13558:)
13548:x
13537:i
13533:x
13529:(
13518:n
13513:1
13510:=
13507:i
13495:)
13486:y
13475:i
13471:y
13467:(
13458:)
13449:x
13438:i
13434:x
13430:(
13419:n
13414:1
13411:=
13408:i
13397:=
13388:r
13370:Y
13366:X
13357:n
13353:y
13349:1
13346:y
13342:Y
13337:n
13333:x
13329:1
13326:x
13322:X
13293:|
13287:Y
13284:,
13281:X
13272:|
13265:1
13262:=
13257:Y
13254:,
13251:X
13247:d
13215:.
13210:Y
13207:,
13204:X
13193:1
13190:=
13185:Y
13182:,
13179:X
13175:d
13157:Y
13153:X
13131:s
13108:k
13086:k
13082:r
13058:,
13053:k
13049:r
13043:K
13038:1
13035:=
13032:k
13022:K
13019:1
13014:=
13009:s
12999:r
12970:s
12960:r
12933:.
12929:)
12924:s
12921:T
12916:(
12906:=
12903:K
12880:s
12860:T
12840:K
12799:.
12793:)
12788:2
12783:i
12779:y
12773:i
12769:w
12762:(
12759:)
12754:2
12749:i
12745:x
12739:i
12735:w
12728:(
12721:i
12717:y
12711:i
12707:x
12701:i
12697:w
12687:=
12682:w
12679:,
12676:y
12673:x
12669:r
12665:r
12639:.
12633:)
12628:2
12623:i
12619:y
12612:(
12609:)
12604:2
12599:i
12595:x
12588:(
12581:i
12577:y
12571:i
12567:x
12557:=
12552:y
12549:x
12545:r
12541:r
12505:b
12502:,
12499:0
12493:a
12489:,
12486:)
12483:Y
12480:b
12477:+
12474:a
12471:,
12468:X
12465:(
12457:r
12446:)
12443:Y
12440:b
12437:,
12434:X
12431:(
12423:r
12415:=
12412:)
12409:X
12406:,
12403:Y
12400:(
12392:r
12384:=
12381:)
12378:Y
12375:,
12372:X
12369:(
12361:r
12330:.
12324:]
12318:2
12314:Y
12309:[
12301:E
12293:]
12287:2
12283:X
12278:[
12270:E
12263:]
12259:Y
12255:X
12251:[
12243:E
12235:=
12232:)
12229:Y
12226:,
12223:X
12220:(
12212:r
12176:.
12170:)
12167:w
12164:;
12161:y
12158:,
12155:y
12152:(
12143:)
12140:w
12137:;
12134:x
12131:,
12128:x
12125:(
12114:)
12111:w
12108:;
12105:y
12102:,
12099:x
12096:(
12084:=
12081:)
12078:w
12075:;
12072:y
12069:,
12066:x
12063:(
12035:.
12027:i
12023:w
12017:i
12007:)
12004:)
12001:w
11998:;
11995:y
11992:(
11986:m
11978:i
11974:y
11970:(
11967:)
11964:)
11961:w
11958:;
11955:x
11952:(
11946:m
11938:i
11934:x
11930:(
11922:i
11918:w
11912:i
11901:=
11898:)
11895:w
11892:;
11889:y
11886:,
11883:x
11880:(
11852:.
11844:i
11840:w
11834:i
11822:i
11818:x
11812:i
11808:w
11802:i
11791:=
11788:)
11785:w
11782:;
11779:x
11776:(
11770:m
11756:n
11752:w
11748:y
11744:x
11740:w
11728:n
11723:r
11716:r
11699:.
11691:)
11688:2
11682:n
11679:(
11674:)
11671:1
11665:n
11662:(
11659:)
11654:2
11650:r
11643:1
11640:(
11631:1
11626:=
11617:r
11601:.
11595:n
11593:(
11589:1
11579:r
11574:,
11572:n
11564:r
11557:r
11555:(
11553:f
11545:r
11534:r
11517:n
11514:,
11511:r
11497:3
11487:)
11485:3
11483:(
11466:,
11462:]
11455:n
11452:2
11445:2
11441:r
11434:1
11428:+
11425:1
11421:[
11417:r
11405:r
11388:2
11378:)
11376:2
11374:(
11357:.
11351:n
11348:2
11342:)
11336:2
11327:r
11320:1
11316:(
11306:r
11290:r
11283:]
11280:r
11277:[
11269:E
11264:=
11261:r
11246:E
11238:r
11231:.
11215:)
11212:z
11209:;
11206:c
11203:;
11200:b
11197:,
11194:a
11191:(
11185:1
11181:F
11175:2
11148:n
11145:,
11142:r
11124:)
11122:1
11120:(
11103:,
11099:)
11093:2
11089:r
11082:1
11079:;
11074:2
11070:1
11064:n
11058:;
11053:2
11050:1
11045:,
11040:2
11037:1
11031:(
11024:1
11020:F
11014:2
11005:r
11002:=
10993:r
10973:r
10955:.
10942:r
10927:,
10921:+
10915:n
10912:2
10906:)
10900:2
10889:1
10885:(
10869:=
10865:]
10862:r
10859:[
10850:E
10835:r
10831:E
10823:ρ
10819:r
10793:W
10789:W
10781:W
10746:Y
10742:X
10720:r
10697:ρ
10693:r
10640:Y
10636:X
10515:.
10501:2
10497:)
10487:Y
10476:i
10472:Y
10468:(
10463:i
10455:=
10420:2
10416:)
10406:Y
10395:i
10385:Y
10378:(
10373:i
10365:=
10299:=
10294:2
10290:)
10280:Y
10274:,
10271:Y
10268:(
10265:r
10250:.
10236:2
10232:)
10226:i
10216:Y
10204:i
10200:Y
10196:(
10191:i
10183:=
10165:1
10162:β
10158:0
10155:β
10149:(
10130:0
10127:=
10124:)
10115:Y
10104:i
10094:Y
10087:(
10084:)
10079:i
10069:Y
10057:i
10053:Y
10049:(
10044:i
10023:X
10019:Y
10003:2
9999:)
9989:Y
9983:,
9980:Y
9977:(
9974:r
9946:2
9942:)
9932:Y
9921:i
9917:Y
9913:(
9908:i
9896:2
9892:)
9882:Y
9871:i
9861:Y
9854:(
9849:i
9838:=
9833:2
9829:)
9819:Y
9813:,
9810:Y
9807:(
9804:r
9774:.
9765:2
9761:)
9751:Y
9740:i
9736:Y
9732:(
9727:i
9715:2
9711:)
9701:Y
9690:i
9680:Y
9673:(
9668:i
9656:=
9641:2
9637:)
9627:Y
9616:i
9606:Y
9599:(
9594:i
9581:2
9577:)
9567:Y
9556:i
9552:Y
9548:(
9543:i
9531:2
9527:)
9517:Y
9506:i
9496:Y
9489:(
9484:i
9473:=
9458:2
9454:)
9444:Y
9433:i
9423:Y
9416:(
9411:i
9398:2
9394:)
9384:Y
9373:i
9369:Y
9365:(
9360:i
9350:]
9345:2
9341:)
9331:Y
9320:i
9310:Y
9303:(
9300:+
9297:)
9288:Y
9277:i
9267:Y
9260:(
9257:)
9252:i
9242:Y
9230:i
9226:Y
9222:(
9219:[
9214:i
9203:=
9188:2
9184:)
9174:Y
9163:i
9153:Y
9146:(
9141:i
9128:2
9124:)
9114:Y
9103:i
9099:Y
9095:(
9090:i
9080:)
9071:Y
9060:i
9050:Y
9043:(
9040:)
9031:Y
9020:i
9010:Y
9003:+
8998:i
8988:Y
8976:i
8972:Y
8968:(
8963:i
8952:=
8937:2
8933:)
8923:Y
8912:i
8902:Y
8895:(
8890:i
8877:2
8873:)
8863:Y
8852:i
8848:Y
8844:(
8839:i
8829:)
8820:Y
8809:i
8799:Y
8792:(
8789:)
8780:Y
8769:i
8765:Y
8761:(
8756:i
8745:=
8738:)
8729:Y
8723:,
8720:Y
8717:(
8714:r
8685:i
8675:Y
8663:i
8659:Y
8636:i
8626:Y
8605:X
8601:X
8597:Y
8580:.
8572:2
8568:)
8558:Y
8547:i
8543:Y
8539:(
8534:i
8522:2
8518:)
8508:Y
8497:i
8487:Y
8480:(
8475:i
8464:+
8456:2
8452:)
8442:Y
8431:i
8427:Y
8423:(
8418:i
8406:2
8402:)
8396:i
8386:Y
8374:i
8370:Y
8366:(
8361:i
8350:=
8347:1
8322:i
8312:Y
8285:,
8280:2
8276:)
8266:Y
8255:i
8245:Y
8238:(
8233:i
8225:+
8220:2
8216:)
8210:i
8200:Y
8188:i
8184:Y
8180:(
8175:i
8167:=
8162:2
8158:)
8148:Y
8137:i
8133:Y
8129:(
8124:i
8105:i
8101:Y
8085:n
8075:Y
8068:,
8062:,
8057:1
8047:Y
8021:n
8017:Y
8013:,
8007:,
8002:1
7998:Y
7983:X
7979:Y
7971:r
7966:.
7904:=
7900:)
7897:r
7894:(
7877:ρ
7873:n
7869:r
7852:]
7849:)
7839:2
7835:/
7827:z
7823:+
7820:)
7817:r
7814:(
7805:(
7796:,
7793:)
7783:2
7779:/
7771:z
7764:)
7761:r
7758:(
7749:(
7740:[
7731::
7720:)
7711:1
7708:(
7679:]
7669:2
7665:/
7657:z
7650:)
7647:r
7644:(
7635:[
7629:)
7623:(
7614::
7603:)
7594:1
7591:(
7555:(
7553:F
7528:0
7525:=
7512:z
7484:0
7476:=
7444:3
7438:n
7433:]
7430:)
7425:0
7417:(
7414:F
7408:)
7405:r
7402:(
7399:F
7396:[
7393:=
7376:x
7370:=
7367:z
7335:0
7310:r
7290:n
7280:n
7263:,
7257:3
7251:n
7247:1
7242:=
7234:=
7208:)
7202:(
7193:=
7190:)
7184:(
7181:F
7178:=
7156:r
7154:(
7152:F
7136:)
7133:r
7130:(
7121:=
7117:)
7111:r
7105:1
7100:r
7097:+
7094:1
7088:(
7074:2
7071:1
7062:)
7059:r
7056:(
7053:F
7041::
7028:F
7010:ρ
6974:1
6968:1
6962:n
6959:=
6936:F
6913:)
6906:2
6899:r
6896:+
6893:1
6886:;
6880:2
6877:1
6871:+
6865:;
6859:2
6856:1
6847:,
6841:2
6838:3
6831:(
6824:F
6818:2
6811:2
6805:1
6798:)
6791:r
6785:1
6781:(
6770:2
6766:2
6753:)
6747:2
6736:1
6732:(
6721:2
6717:1
6704:)
6698:2
6694:r
6687:1
6683:(
6674:)
6668:2
6665:1
6660:+
6653:(
6641:2
6634:)
6631:1
6622:(
6616:)
6613:1
6604:(
6595:=
6592:)
6589:r
6580:(
6565:ρ
6530:B
6506:,
6497:)
6490:2
6486:2
6480:n
6473:,
6467:2
6464:1
6457:(
6446:B
6437:2
6433:4
6427:n
6420:)
6414:2
6410:r
6403:1
6399:(
6392:=
6389:)
6386:r
6383:(
6380:f
6367:r
6365:(
6363:f
6349:0
6346:=
6316:)
6313:z
6310:;
6307:c
6304:;
6301:b
6298:,
6295:a
6292:(
6287:1
6282:F
6275:2
6221:)
6217:)
6214:1
6211:+
6208:r
6202:(
6196:2
6193:1
6187:;
6184:)
6181:1
6175:n
6172:2
6169:(
6163:2
6160:1
6154:;
6148:2
6145:1
6139:,
6133:2
6130:1
6123:(
6115:1
6110:F
6103:2
6089:2
6086:3
6078:n
6074:)
6070:r
6061:1
6058:(
6052:)
6045:2
6042:1
6033:n
6029:(
6009:2
5999:2
5995:4
5989:n
5982:)
5976:2
5972:r
5965:1
5961:(
5953:2
5949:1
5943:n
5936:)
5930:2
5919:1
5915:(
5910:)
5907:1
5901:n
5898:(
5889:)
5886:2
5880:n
5877:(
5871:=
5868:)
5865:r
5862:(
5859:f
5846:r
5842:r
5840:(
5838:f
5822:t
5815:ρ
5795:.
5787:2
5783:t
5779:+
5776:2
5770:n
5766:t
5761:=
5758:r
5745:r
5741:t
5718:2
5714:r
5707:1
5702:2
5696:n
5689:r
5686:=
5679:r
5671:r
5666:=
5663:t
5650:n
5644:t
5614:t
5596:n
5576:r
5549:2
5543:n
5536:2
5532:r
5525:1
5518:=
5513:r
5481:y
5461:x
5443:r
5435:ρ
5423:r
5419:r
5415:n
5410:i
5406:y
5401:i
5397:x
5393:n
5368:r
5356:r
5349:n
5341:i
5333:n
5325:n
5317:n
5300:y
5295:i
5291:x
5286:i
5282:y
5277:i
5273:x
5252:.
5250:ρ
5241:.
5239:r
5235:ρ
5212:.
5210:Y
5206:X
5202:Y
5198:ρ
5194:X
5190:Y
5182:ρ
5164:2
5153:1
5145:1
5135:ρ
5131:Y
5127:X
5098:,
5093:y
5090:x
5082:=
5079:1
5076:=
5050:=
5039:y
5026:x
5015:y
5007:x
5000:=
4976:y
4969:x
4962:y
4956:y
4950:x
4944:x
4939:x
4935:y
4910:=
4884:=
4873:y
4860:x
4849:y
4841:x
4834:=
4804:θ
4795:y
4788:x
4783:y
4779:x
4771:N
4767:N
4759:θ
4739:φ
4735:φ
4731:r
4724:r
4717:r
4712:φ
4708:y
4704:x
4700:x
4696:y
4692:)
4690:y
4688:(
4685:Y
4681:g
4677:x
4672:)
4670:x
4668:(
4665:X
4661:g
4657:y
4652:φ
4645:)
4643:y
4641:(
4638:Y
4634:g
4630:x
4625:)
4623:x
4621:(
4618:X
4614:g
4610:y
4544:i
4540:Y
4535:i
4531:X
4522:i
4518:Y
4513:i
4509:X
4504:i
4500:Y
4495:i
4491:X
4487:)
4484:Y
4478:i
4474:Y
4469:X
4463:i
4459:X
4457:(
4450:X
4446:Y
4442:X
4438:Y
4426:Y
4422:X
4402:d
4398:b
4393:d
4389:c
4385:b
4381:a
4372:c
4367:Y
4358:a
4353:X
4342:X
4340:,
4338:Y
4334:Y
4332:,
4330:X
4267:]
4259:2
4254:Y
4242:Y
4232:X
4222:Y
4219:,
4216:X
4202:Y
4192:X
4182:Y
4179:,
4176:X
4164:2
4159:X
4148:[
4143:=
4090:)
4087:Y
4084:,
4081:X
4078:(
4061:.
4047:y
4043:s
4014:2
4010:)
4000:x
3989:i
3985:x
3981:(
3976:n
3971:1
3968:=
3965:i
3954:1
3948:n
3944:1
3937:=
3932:x
3928:s
3899:y
3893:,
3884:x
3878:,
3873:i
3869:y
3865:,
3860:i
3856:x
3852:,
3849:n
3818:y
3814:s
3808:x
3804:s
3800:)
3797:1
3791:n
3788:(
3777:y
3765:x
3759:n
3751:i
3747:y
3741:i
3737:x
3727:=
3722:y
3719:x
3715:r
3689:y
3686:x
3682:r
3659:y
3656:x
3652:r
3627:y
3606:)
3599:x
3595:s
3584:x
3573:i
3569:x
3562:(
3537:y
3533:s
3529:,
3524:x
3520:s
3493:y
3487:,
3478:x
3472:,
3467:i
3463:y
3459:,
3454:i
3450:x
3446:,
3443:n
3416:)
3409:y
3405:s
3394:y
3383:i
3379:y
3372:(
3367:)
3360:x
3356:s
3345:x
3334:i
3330:x
3323:(
3317:n
3312:1
3309:=
3306:i
3295:1
3289:n
3285:1
3280:=
3275:y
3272:x
3268:r
3238:y
3235:x
3231:r
3198:i
3194:y
3190:,
3185:i
3181:x
3177:,
3174:n
3151:,
3141:2
3136:)
3130:i
3126:y
3118:(
3108:2
3103:i
3099:y
3092:n
3080:2
3075:)
3069:i
3065:x
3057:(
3047:2
3042:i
3038:x
3031:n
3022:i
3018:y
3009:i
3005:x
2993:i
2989:y
2983:i
2979:x
2972:n
2966:=
2961:y
2958:x
2954:r
2928:y
2925:x
2921:r
2891:y
2885:,
2876:x
2870:,
2865:i
2861:y
2857:,
2852:i
2848:x
2844:,
2841:n
2818:,
2808:2
2798:y
2791:n
2783:2
2778:i
2774:y
2768:i
2751:2
2741:x
2734:n
2726:2
2721:i
2717:x
2711:i
2693:y
2681:x
2675:n
2667:i
2663:y
2657:i
2653:x
2647:i
2636:=
2631:y
2628:x
2624:r
2598:y
2595:x
2591:r
2578:.
2560:y
2535:i
2531:x
2525:n
2520:1
2517:=
2514:i
2504:n
2501:1
2496:=
2487:x
2473:i
2457:i
2453:y
2449:,
2444:i
2440:x
2417:n
2385:2
2381:)
2371:y
2360:i
2356:y
2352:(
2347:n
2342:1
2339:=
2336:i
2322:2
2318:)
2308:x
2297:i
2293:x
2289:(
2284:n
2279:1
2276:=
2273:i
2261:)
2252:y
2241:i
2237:y
2233:(
2230:)
2221:x
2210:i
2206:x
2202:(
2197:n
2192:1
2189:=
2186:i
2175:=
2170:y
2167:x
2163:r
2138:y
2135:x
2131:r
2110:n
2089:}
2085:)
2080:n
2076:y
2072:,
2067:n
2063:x
2059:(
2056:,
2050:,
2047:)
2042:1
2038:y
2034:,
2029:1
2025:x
2021:(
2017:{
1994:y
1991:x
1987:r
1956:y
1953:x
1949:r
1917:.
1907:2
1902:)
1898:]
1894:Y
1890:[
1882:E
1876:(
1867:]
1860:2
1856:Y
1850:[
1841:E
1827:2
1822:)
1818:]
1814:X
1810:[
1802:E
1796:(
1787:]
1780:2
1776:X
1770:[
1761:E
1752:]
1748:Y
1744:[
1736:E
1731:]
1727:X
1723:[
1715:E
1707:]
1703:Y
1699:X
1695:[
1687:E
1679:=
1674:Y
1671:,
1668:X
1616:,
1612:]
1608:Y
1604:[
1596:E
1591:]
1587:X
1583:[
1575:E
1567:]
1563:Y
1559:X
1555:[
1547:E
1542:=
1539:]
1534:)
1530:]
1526:Y
1522:[
1514:E
1506:Y
1502:(
1497:)
1493:]
1489:X
1485:[
1477:E
1469:X
1465:(
1460:[
1452:E
1447:=
1444:]
1439:)
1433:Y
1422:Y
1418:(
1413:)
1407:X
1396:X
1392:(
1387:[
1379:E
1367:2
1362:)
1358:]
1354:Y
1350:[
1342:E
1335:(
1326:]
1319:2
1315:Y
1309:[
1300:E
1295:=
1291:]
1284:2
1279:)
1275:]
1272:Y
1269:[
1261:E
1253:Y
1249:(
1242:[
1233:E
1224:=
1219:2
1214:Y
1200:2
1195:)
1191:]
1187:X
1183:[
1175:E
1169:(
1160:]
1153:2
1149:X
1143:[
1134:E
1129:=
1125:]
1118:2
1113:)
1109:]
1106:X
1103:[
1095:E
1087:X
1083:(
1076:[
1067:E
1058:=
1053:2
1048:X
1036:]
1032:Y
1028:[
1020:E
1011:=
1006:Y
994:]
990:X
986:[
978:E
969:=
964:X
906:E
883:Y
861:Y
835:X
813:X
784:X
757:Y
722:Y
712:X
702:]
699:)
694:Y
683:Y
680:(
677:)
672:X
661:X
658:(
655:[
647:E
639:=
634:Y
631:,
628:X
578:,
575:]
572:)
567:Y
556:Y
553:(
550:)
545:X
534:X
531:(
528:[
520:E
515:=
512:)
509:Y
506:,
503:X
500:(
463:)
460:Y
457:,
454:X
451:(
433:.
421:Y
399:Y
373:X
347:X
287:Y
277:X
267:)
264:Y
261:,
258:X
255:(
243:=
238:Y
235:,
232:X
215:ρ
201:)
198:Y
195:,
192:X
189:(
171:ρ
88:(
74:Y
69:y
65:x
61:y
57:x
47:)
45:ρ
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
