Consider two variables, (y) and (x). Do a regression of (y) on (x) to get a slope
Question:
Consider two variables, \(y\) and \(x\). Do a regression of \(y\) on \(x\) to get a slope coefficient that we call \(b_{1, x, y}\). Do another regression of \(x\) on \(y\) to get a slope coefficient that we call \(b_{1, y, x}\). Show that the correlation coefficient between \(x\) and \(y\) is the geometric mean of the two slope coefficients up to sign; that is, show that \(|r|=\sqrt{b_{1, x, y} b_{1, y, x}}\).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Regression Modeling With Actuarial And Financial Applications
ISBN: 9780521135962
1st Edition
Authors: Edward W. Frees
Question Posted: