(35 points) You have t a multiple linlar regression model and the (X 'X)'1 matrix is:893758 0.0282448 0.0175641 (.X'X)'1 = -0.028245 0.0013329...

You have fit a multiple linear regression model and the (????′????) −1 matrix is: (????′????) −1 = [ 0.893758 −0.0282448 −0.0175641 −0.028245 0.0013329 0.0001547 −0.0175641 0.0001547 0.0009108 ] (a) Please write the model of this multiple regression (2 points) (b) Assume the error sum of squares is 307, and there are 16 observations, what is the estimate of ???? 2 (3 points) (c) Please calculate the standard error of the regression coefficients ????̂ 1 and ????̂ 2 (5 points). (d) Assume the estimated regression coefficients ????̂ 1 and ????̂ 2 are 2.74427 and 0.012528, respectively. Please calculate the 95% confidence interval for each of them (9 points). (e) Assume the intercept is 2.264, the two estimated regression coefficients are 2.74427 and 0.012528. Please construct a 95% prediction interval when x1=4 and x2= 250 (16 points).