Please help with e-g. Thank you!

Consider a multiple linear regression problem with intercept (i.e., the design matrix X E RRXU'H) has a column of all ones, and 33 other columns corresponding to p covariates). Given the following information: 2 0 0 0 -lly |12 = 18.593, -( X X ) = 0 1 0.5 0 -3 0 0.5 1 0 n y = n = 16 O 0 O 0.1 answer the following questions: (a) Is 1(XTX) PSD? Justify your answer. (b) Is X full-rank? Justify your answer. (c) Find 3, the least-squares estimate (LSE) of B. (d) Find the covariance matrix of B. Is this matrix PSD? (e) Let us write B = (Bo, 31, 32, 33). What is cov (B1, B2)? (f) Find a 95% confidence interval for 32. Given this level of confidence should we accept or reject the hypothesis: 32 = 0? (g) Let H be the orthogonal projection matrix, projecting onto Im(X). What is the dimension of Im(I - H)