Need help with part(d)

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3. [14 pts] Consider a multiple linear regression With n observations and p predictors, Y = X + e, Where Y 2 (Y1, . . . ,Yn)T is the n X 1 vector of responses; X is the n X (19+ 1) matrix of predictors, including a column of 1's for the intercept; and e = (61, . . . , en)T is the n X 1 vector of statistical errors. Let Y = (171, . . . ,Yn)T denote the tted values and = (l, . . . , n)T denote the residuals. (Note: show all the derivation steps for the following questions) (a) [2 pts] Show that Cov(, Y) = 0. (b) [2 pts] Show that the sample covariance of and Y is 0. (c) [4 pts] What is the slope of the simple regression of on Y (that is, N Y)? [intercept term is included in the model] (d) [6 pts] What is the slope of the simple regression of 3 on Y (that is, N Y)? [intercept term is included in the model]