The administrator of a new paralegal program at Seagate Technical College wants to estimate the grade point average (GPA) in the new program. He thought that high school GPA, the verbal score on the Scholastic Aptitude Test (SAT), and the mathematics score on the SAT would be good predictors of paralegal GPA. The data on 9 students are: (15 marks) High School SAT Verbal SAT Math Paralegal GPA GPA 480 410 3 .25 3 .21 l .80 290 270 1 .68 2.89 420 410 3 .58 3 .81 500 3 .92 3 .13 500 3 .00 2.81 430 2.20 320 2.14 530 2.63 469 440 2.33 VD Considering the following output. reg paralegalgpa highschoolgpa Source SS df MS Number of obs = 9 F( 1, 7) = 34. 35 Model 4 . 2060623 4. 2060623 Prob > F = 0 . 0006 Residual . 857026927 7 . 122432418 R-squared = 0. 8307 Adj R-squared = 0 . 8065 Total 5 . 06308922 8 . 632886153 Root MSE . 3499 paralegalgpa Coef. Std. Err. t P> It| [95% Conf. Interval] highschoolgpa 1 . 158886 . 1977203 5 . 86 0 . 001 . 6913522 1 . 626421 cons -. 4542376 . 5541665 -0. 82 0 . 439 -1. 764633 . 856158 c. The analysis has been rerun without "verbal" and "math". See the above output. How much has R-squared and adjusted R-squared changed from the previous analysis? (2 marks) d. Why do we prefer to use adjusted R-squared to measure goodness-of-fit of a multiple regression model? (5 marks)reg paralegalgpa highschoolgpa satverbal satmath Source SS df MS Number of obs = 9 F( 3 , 5) = 10.33 Model 4 . 3594607 3 1. 45315357 Prob > F = 0. 0139 Residual . 703628528 5 . 140725706 R-squared = 0 . 8610 Adj R-squared = 0. 7776 Total 5. 06308922 8 . 632886153 Root MSE = . 37513 paralegalgpa Coef. Std. Err. t P>ItI [95% Conf. Interval] highschoolgpa 1. 201374 295513 4. 07 0. 010 4417341 1. 961015 satverbal 0016293 . 0021471 0. 76 0 . 482 . 0038901 0071487 satmath - . 0019393 . 0020736 -0. 94 0. 393 - . 0072697 . 0033912 cons -. 4110716 . 7823005 -0.53 0. 622 -2. 422039 1 . 599896 a. Global test of hypothesis: Does it appear that any of the regression coefficients are not equal to zero? Explain or show your reasoning. (3 marks) b. Test of hypothesis on each independent variable. Would you consider eliminating the variables "verbal" and "math"? Let a = 0.05. Explain or show your reasoning. 5 marks)