Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher's salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. Regression Statistics ANOVA Multiple R 0.79 df SS MS F significance F R Square 0.62 Regression 4 6548.49 1637.12 88.367068 1.384E-44 Adjusted R 0.61 Residual 219 4057.28 18.53 Standard Er 4.30 Total 223 10605.77 Observation 224.00 Coefficients Standard Errc t Stat P-value Lower 95% Upper 95% Lower 95.0%Jpper 95.0% Intercept 231.89 3.370 68.82 2.57E-150 225.253 238.535 225.25349 238.53537 STR -0.50 0. 131 -3.79 0.0001915 -0.754 -0.238 -0.7538457 -0.2384408 TSAL -0.02 0.075 -0.31 0.7546528 -0.170 0. 124 -0.17037 0.1236846 INC 0.29 0.034 8.51 2.776E-15 0.225 0.361 0.2250472 0.3607169 SGL -0.88 0.174 -5.06 9.052E-07 -1.220 -0.536 -1.2202964 -0.535734 (a) What proportion of the variation in MCAS score is explained by the explanatory variables? (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly. (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly. (d) Suppose a second regression model (Model 2) was generated using only the variables STR, INC, and SGL. For that model R2 = 0.70, Se = 3.68 , Adjusted R2 = 0.67. Which model is better, Model 2 or Model 1, the model given above in the table with explanatory variables STR, INC, TSAL, SGL? Explain briefly