Please show your work in good detail! In class, we discussed the connection between covariance and linear regression....

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In class, we discussed the connection between covariance and linear regression. If X and Y are two random variables, then the

(a) E[Z 0 (b) Cov (X, Z) 0.

Please show your work in good detail!

In class, we discussed the connection between covariance and linear regression. If X and Y are two random variables, then the best linear approximation to Y is given by aX +b, where a = b E[Y] E[X]: If ZY- aX - b, then show that Cov(X.Y) x and Var X Cov(X,Y)
(a) E[Z 0 (b) Cov (X, Z) 0.

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Answer 1

Answer #1

cov (x,y) Var x) cov (x,ッ) E() - ECx) Var (x) 2=y-ax- E(2 E (-ax-b 01 E(2) El)-a E)-1o El4) cev ECx)- El) - ECK) cov, Var (x) Var (x) 4(2) £ (2)- E lx) Rovy) - ()3 Var ) + Elx) co Vaul £(2) ah (X2 Cev ECK-ECx(-E( E ( 2- 2E0) EC ELx)E(2) = E (X2) nandom and tired xs EC ECE() ane

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Answer 2

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Please show your work in good detail! In class, we discussed the connection between covariance and linear regression....