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ps2_solution - Problem Set 2 Solution Question 1 points 1 1...

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Problem Set 2 Solution Question 1 points HSGPA College GPA 1 a) Mean 3.7996 3.6124 1 b) Median 3.8250 3.7000 1 c) mode 3.7500 3.5000 1 d) std dev 0.5476 0.2760 2 e) corr coeff Question 2 points cov(y t ,x t ) var(x t ) β α 2 a) 0.0113 0.2998 0.0378 3.4687 1 b) gpa=3.4687 + 0.0378*hsgpa + u_hat alpha_hat means that the location of GPA score which is the mean of GPA conditional on high school GPA. 0.5 c) fitted value: gpa_hat = 3.4687 + 0.0378*hsgpa 1 d) residuals: resid = gpa - gpa_hat 0.5 e) 3.5942 0.0767 beta_hat means the scale or marginal effect of GPA with respect to high school GPA. In other words, it represents the amount of change in GPA corresponding to one unit change in high school GPA , holding others constant. Q3 1. Check your answers in question (1) in Stata? . sum hsgpa gpa, d HSGPA ------------------------------------------------------------- Percentiles Smallest 1% .97 .97
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5% 3 2.5 10% 3.6 3 Obs 46 25% 3.75 3.5 Sum of Wgt. 46 (Median)50% 3.825 Mean 3.799565 Largest Std. Dev. .5475682 75% 4 4.2 90% 4.2 4.3 Variance .2998309 95% 4.3 4.35 Skewness -3.148193 99% 5.02 5.02 Kurtosis 17.64842 GPA ------------------------------------------------------------- Percentiles Smallest 1% 3 3 5% 3.12 3 10% 3.2 3.12 Obs 46 25% 3.4 3.2 Sum of Wgt. 46 Median 50% 3.7 Mean 3.612391 Largest Std. Dev. .2760208 75% 3.86 3.91 90% 3.9 3.95 Variance .0761875 95% 3.95 4 Skewness -.5461125
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99% 4 4 Kurtosis 2.239417 . tab hsgpa
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