Consider the simple linear regression model yi beta0 beta1

Consider the simple linear regression model yi = beta_0 + beta_1x_i + e_i for i = 1,..., n where Ee = 0 and Cov(e) = sigma 2 I_n. Let denote the sample mean of the jth explanatory variable for j = 1,...,p. Show that (beta_0 and beta_1x_1 +...+ beta are estimable. What is the least squares estimate of beta_0 + beta_1x_1 +...+ beta_px_p and why? What is the variance of the least squares estimate in (b) and how would you estimate it from the regression data?

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