Question

4. Let $hat{eta}_{yx}$ and $hat{eta}_{xy}$ represent the slopes in the regression of Y on X ($Y = eta_0 + hat{eta}_{yx}X + u$) and X on Y ($X = alpha_0 + hat{eta}_{xy}Y + v$), respectively. Show that $hat{eta}_{yx}hat{eta}_{xy} = r^2$ (see the formula for $r$ in Problem 5 below).

          4. Let $hat{eta}_{yx}$ and $hat{eta}_{xy}$ represent the slopes in the regression of Y on X ($Y = eta_0 + hat{eta}_{yx}X + u$) and X on Y ($X = alpha_0 + hat{eta}_{xy}Y + v$), respectively. Show that $hat{eta}_{yx}hat{eta}_{xy} = r^2$ (see the formula for $r$ in Problem 5 below).

4. Let hatetayx and hatetaxy represent the slopes in the regression of Y on X (Y = eta0 + hatetayxX + u) and X on Y (X = alpha0 + hatetaxyY + v), respectively. Show that hatetayxhatetaxy = r^2 (see the formula for r in Problem 5 below).

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

03/14/2023

Step 1

Step 1: We know that the slope in the regression of Y on X is given by: Byx = Cov(X, Y) / Var(X) Show more…

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Let hat{eta}_{yx} and hat{eta}_{xy} represent the slopes in the regression of Y on X (Y = eta_0 + hat{eta}_{yx}X + u) and X on Y (X = alpha_0 + hat{eta}_{xy}Y + v), respectively. Show that hat{eta}_{yx}hat{eta}_{xy} = r^2 (see the formula for r in Problem 5 below).