Following is the regression output for a data from a random sample of high school seniors in- terviewed in 1980 and re-interviewed in 1986. In this exercise, we use these data to investigate the relationship between the number of completed years of education for young adults and the distance from each student's high school to the nearest four-year college. (Proximity to college lowers the cost of education, so that students who live closer to a four-year college should, on average, complete more years of higher education.) Below are the results of a regression of years of completed education (ED) on distance to the nearest college (Dist), where Dist is measured in tens of miles. (For example, Dist = 2 means that the distance is 20 miles.) Dependent Variable: ED Sample: 1 3796 Method: Least Squares Included observations: 3796 Variable Std. Error C DIST Coefficient 13.95586 -0.073373 0.037724 0.01375 Mean dependent var S.D. dependent var R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) (a) Write the regression model using these results. 0.00745 0.007188 1.807438 12394.36 Schwarz criterion -7632.182 28.47582 0 Akaike info criterion Hannan-Quinn criter. Durbin-Watson stat 1-Statistic 369.9451 0 -5.336274 0 Prob. (c) Write the mathematical formula for-5.336274 13.82929 1.813969 4.022224 4.025513 4.023393 1.768991 (b) Write the mathematical formula for the intercept and the slope and the associated values from the above estimates. (d) Bob's high school was 20 miles from the nearest college. Predict Bob's years of completed education using the estimated regression. (e) Does distance to college explain a large fraction of the variance in educational attainment across individuals? Explain.