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).

2. (35 points) You have t a multiple linlar regression model and the (X 'X)'1 matrix is: 0.893758 0.0282448 0.0175641 (.X'X)'1 = -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 02 (3 points) (c) Please calculate the standard error of the regression coefcients 31 and 32 (5 points). (d) Assume the estimated regression coefcients 31 and 32 are 2.7442? 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 coefcients are 2.7442? and 0.012528. Please construct a 95% prediction interval when x.=4 and X2= 250 (16 points)