Question: Problem 3 [12 points]: Consider the residuals {e; } from the simple linear regression: e; = yi - Vi = yi - Bo - Bix;,

Problem 3 [12 points]: Consider the residuals {e; } from the simple linear regression: e; = yi - Vi = yi - Bo - Bix;, i= 1, 2, ..., n where B, = SXY/SXX and Bo = y - Bix are the OLS estimates for B, and Bo. (a) [8 points] Show that Cov(x, e) [ ( x, - x ) ( e, - e) = 0, where e = - De. n-17=1 ni=1 (b) [4 points] Based on the results from part (a), show that ex, tex, +.tex, = 0

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