Are standardized betas in multiple linear regression partial correlations? [duplicate]

Since standardized betas are correlation coefficients in bivariate regression, is it the case that standardized betas in multiple regression are partial correlations?


Longer answer.

If I have this right —

Partial correlation:

r_{y1.2} = \frac{r_{y1}-r_{y2}r_{12}}{\sqrt{(1-r^2_{y2})(1-r^2_{12})}}

equivalent standardized beta:

\beta_1 = \frac{r_{y1}-r_{y2}r_{12}}{(1-r^2_{12})}

As you see, the denominator is different.

Their relative size depends on whether $\sqrt{(1-r^2_{y2})}$ or $\sqrt{(1-r^2_{12})}$ is smaller.

Source : Link , Question Author : user20924 , Answer Author : Glen_b

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