Question: We have often used the result that TSS = ExpSS + RSS, for example to justify the use of R2 and of F tests. The

We have often used the result that TSS = ExpSS + RSS, for example to justify the use of R2 and of F tests. The purpose of this question is to prove that result. (a) Prove that (yi y-bar)^2 = (yi yi-hat)^2 +( yi-hat y-bar)^2 +2(yi yi-hat)(yi-haty-bar). (Hint: forthispart, the denitions of yi and y are completely irrelevant; you may nd it easier to just call them a and b or something similar.)

(b) Use the result of part (a) to establish that TSS = ExpSS + RSS + 2(n1)Cov [e, y-hat].

(c) Prove that Cov [e, y-hat] = 0. You may take it as given that the residual is uncorrelated with each of the regressors. (d) Complete the proof that TSS = ExpSS + RSS.

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