Given the random variables X1, X2, and X3 having the joint density f(x1, x2, x3), show that if the regression of X3 on X1 and X2 is linear and written as Then Where micro i E(Xi), Iuml 2i var(Xi), and Iuml ij cov(Xi,Xj) Proceed as on pages 386 and 387, multiplying by (x1 micro 1) and (x2 micro 2), ...

Multiply by hx 1 x 2 and integrate over x 1 x 2 ...

Given the random variables X1, X2, and X3 having the joint density f(x1, x2, x3), show that

Question:

Given the random variables X1, X2, and X3 having the joint density f(x1, x2, x3), show that if the regression of X3 on X1 and X2 is linear and written as

Then

Given the random variables X1, X2, and X3 having the

Where µi = E(Xi), Ïƒ2i = var(Xi), and Ïƒij = cov(Xi,Xj). [Proceed as on pages 386 and 387, multiplying by (x1 €“ µ1) and (x2 €“ µ2), respectively, to obtain the second and third equations.]