Please solve all parts a-e of the question below. Please note that there should be 43 data observations labeled (Y, X₁, X₂). Please show all work and all steps for all questions a-e. Use an SAS software to get any numbers needed for the formulas.

2. (7.5 points) Consider the following data for the response 1' and two predictors, X1 and X 2. 47 287 111 38 236 135 47 255 98 39 135 63 44 121 46 64 171 103 58 260 227 49 237 157 55 261 266 52 397 167 49 259 164 47 261 119 40 258 145 40 248 92 58 285 153 43 361 126 40 248 226 46 289 176 50 270 180 (a) (1.5 points) Construct 95% confidence interval for the unknown parameter B2 (do the calculations).(b) (1.5 points) Test if the mean response differs from 50 if X, = 300 and X2 = 150 (do the calculations). (c) (1.5 points) Construct 95% confidence interval for the mean response when X1 = 300 and X2 = 150 (do the calculations). (d) (1.5 points) Construct 95% prediction interval for a new value of the response when X1 = 300 and X2 = 150 (use SAS output). (e) (1.5 points) Compare points (c) and (d). Explain