1. Consider the following STATA output on college distances. This dataset contains data from a random sample of high school seniors interviewed in 1980 and re-interviewed in 1986. In this exercise you will 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. The variable ed corresponds to years of education and dist is the distance to the nearest college and it is measured in tens of miles (For example dist = 3 means that the high school of the senior is 30 miles from the nearest college). . reg ed dist, robust Linear regression Number of obs F( 1, 3794) Prob > F R-squared Root MSE = = = = = 3796 29.83 0.0000 0.0074 1.8074 -----------------------------------------------------------------------------| Robust ed | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------dist | -.0733727 .0134334 -5.46 0.000 -.0997101 -.0470353 _cons | 13.95586 .0378112 369.09 0.000 13.88172 14.02999 ------------------------------------------------------------------------------ (a) A student's high school was 18 miles from the nearest college. Estimate the number of years of schooling completed. (b) Compute the 99% confidence interval for the difference in the predicted years of education between a high school senior who is 93 miles to the nearest college and another student who attends a high school that shares a campus with a college. Explain what your solution means in one sentence. (c) Does distance to the nearest college explain a lot of the variation in educational attainment? Explain. (d) Suppose distance was measured in kilometers such that 10 miles = 16 kilometers. Replicate the entire STATA output. (e) Interpret the coefficient of tuition below where the dependent variable, led, is the natural logarithm of years of education. Give one good explanation for your answer. (note that tuition is given in $1000) Linear regression Number of obs = 3796 F(3, 3792) = 151.91 Prob > F = 0.0000 R-squared = 0.1001 Root MSE = .12236 -----------------------------------------------------------------------------| Robust led | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------tuition | .0158511 .0069175 2.29 0.022 .0022887 .0294135 momcoll | .0474716 .0063938 7.42 0.000 .034936 .0600071 dadcoll | .0749874 .0055234 13.58 0.000 .0641583 .0858164 _cons | 2.582142 .0065834 392.22 0.000 2.569234 2.595049