ps3_solution

# ps3_solution - Problem Set 3- Solution Q1. a) regress gpa...

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Problem Set 3- Solution Q1. a) regress gpa hsgpa male white Source | SS df MS Number of obs = 45 -------------+------------------------------ F( 3, 41) = 0.26 Model | .063667477 3 .021222492 Prob > F = 0.8528 Residual | 3.32879035 41 .081190009 R-squared = 0.0188 -------------+------------------------------ Adj R-squared = -0.0530 Total | 3.39245783 44 .077101314 Root MSE = .28494 ------------------------------------------------------------------------------ gpa | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hsgpa | .0317284 .0785115 0.40 0.688 -.1268288 .1902857 male | -.0672294 .0870708 -0.77 0.444 -.2430724 .1086137 white | -.0198893 .0858711 -0.23 0.818 -.1933095 .153531 _cons | 3.537233 .3084067 11.47 0.000 2.914394 4.160073 ------------------------------------------------------------------------------ regress gpa hsgpa Source | SS df MS Number of obs = 46 -------------+------------------------------ F( 1, 44) = 0.26 Model | .02016819 1 .02016819 Prob > F = 0.6124 Residual | 3.40826881 44 .077460655 R-squared = 0.0059 -------------+------------------------------ Adj R-squared = -0.0167 Total | 3.428437 45 .076187489 Root MSE = .27832 ------------------------------------------------------------------------------ gpa | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hsgpa | .0386624 .0757698 0.51 0.612 -.1140416 .1913664 _cons | 3.465491 .2908022 11.92 0.000 2.879418 4.051564 ------------------------------------------------------------------------------ . Yes, the coefficient on HSGPA in the simple regression model is larger. Based on what we learned in the last class, this suggests that the omitted variable bias in the simple regression is positive because hsgpa is positively correlated with omitted variable (male and white).

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b) t-statistic = 0.40 < |1.96| do not reject the null hypothesis that the coefficient on HSGPA is equal to 0 at the 5% significance level. Therefore, HSGPA is not statistically significant. c) The errors don’t look normally distributed, because the probability density function is skewed to the right. d) 0 .5 1 1.5 2 -.6 -.4 -.2 0 .2 .4 Residuals .1 .2 .3 .4 1 2 3 4 5 HSGPA 0 .2 .4 .6 .8 1 male
The variance of the regression errors is lower for female students than for male students. It is lower for students with lower HSGPA than for students with higher HSGPA. The variance of the error term is about the same for white and non-white students.

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## ps3_solution - Problem Set 3- Solution Q1. a) regress gpa...

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