(a) Suppose we have the following regression result Dependent Variable: SAT Sample: 1 4137 Included observations: 4137 Variable Coefficient Std. Error t-Statistic Prob. C 1028.097 6.359652 161.6594 0.000 HSIZE 19.29706 3.816613 5.056069 0.0000 HSIZE 2 -2.194828 0.524200 -4.187009 0.0000 FEMALE -45.09145 4.229533 -10.661 10 0.0000 BLACK -169.8126 15.43402 -11.00249 0.0000 FEMALE*BLACK 62.30636 19.31951 3.225048 0.0013 R-squared 0.085783 Mean dependent var 1030.331 Adjusted R-squared 0.084677 S.D. dependent var 139.4014 S.E. of regression 133.3688 Akaike info criterion 12.62556 Sum squared resid 73479121 Schwarz criterion 12.63474 Log likelihood -26109.98 Hannan-Quinn criter. 12.62881 1.963199 F-statistic 77.52436 Durbin-Watson stat Prob(F-statistic) 0.000000 Here, Score is the combined SAT score, Hsize is size of the student's high school graduating class, in hundreds, Female is a gender dummy variable, and Black is a race dummy variable. Required [5 Marks] Fit the regression model and interpret the results. (2 Marks) ii) Compute the optimal score (SAT) iii) What is the estimated difference in SAT score between black females and 16 Marks) nonblack females? (b) Discuss Four (4) benefits of econometrics in the field of finance. (12 Marks]