Multiple and Partial Correlation

最新推荐文章于 2024-08-11 22:44:19 发布

HonganW

最新推荐文章于 2024-08-11 22:44:19 发布

阅读量430

点赞数

CC 4.0 BY-SA版权

分类专栏：统计学习文章标签：复相关与偏相关

本文链接：https://blog.youkuaiyun.com/weixin_39415812/article/details/89350428

1. With only two predictors
a) The beta weights can be computed as follows:
$\beta_{Y1.2} = \frac{r_{Y1}-r_{Y2}r_{12}}{1-r_{12}^2}\tag{1}$
$\beta_{Y2.1} = \frac{r_{Y2}-r_{Y1}r_{12}}{1-r_{12}^2}\tag{2}$
b) Multiple R can be computed several ways. From the simple correlations, as
$\textbf{R}_{Y.12} = \sqrt{\frac{r_{Y1}^2+r_{Y2}^2-2r_{Y1}r_{Y2}r_{12}}{1-r_{12}^2}}\tag{3}$
or from the beta weights and validities as
$\textbf{R}_{Y.12} = \sqrt{\beta_{Y1.2}r_{Y1}\beta_{Y2.1}r_{Y2}}\tag{4}$
c) Semipartial correlations in general equal the square root of $R2\boldsymbol{R}^2$ complete minus $R2\boldsymbol{R}^2$ reduced. These are called semipartial correlations because the variance of the other controlled variable(s) is removed from the predictor, but not from the criterion. Therefore, in the two predictor case, they are equal
$r_{Y(1.2)}^2 = \textbf{R}_{Y.12}^2 - r_{Y2}^2\tag{5}$