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can you help me with this question? thanks a lot! (ei represents the residuals) 2.a. Suppose that the true linear regression model has the form

can you help me with this question? thanks a lot! (ei represents the residuals)

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2.a. Suppose that the true linear regression model has the form Yi = Bo + Biki + B2xi2 + ci, ci ~N(0,62 ), while we have misspecified it such that E [Y;] = Bo + Bitu. Show that Ele] = B2(x12 + fxu + g). where e; is the residual left over after fitting the model, and f , g are functions of X1 and X12- 2.b. For the linear regression model Yi = Bo + BiXu + Bzx12 + 6i, Gi~N(0, 62 ) prove that 1 2r Var(Bo) = + + n 1 -2 CV2 CVx, CVxz CV2 where r is the correlation coefficient of (Xi1, X12) and the quantity CV is defined as CV, = El=1 (X1 - x)2 Sxx

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