assignment1_solution - University of California Santa...

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University of California, Santa Barbara Olivier Deschenes Department of Economics Winter 2011 Economics 140B Individual Assignment 1: Answer Key Due in class 01/20/11 Some of these exercises are from Stock and Watson. Question 1: Females are shorter and weigh less than males on average. One of your friends, a pre-med student, tells you that in addition, females will weigh less for a given height. To test this hypothesis, you collect the height and weight of 29 female and 81 male students at your university. A regression of the weight on a constant, height, and a binary variable, which takes a value of one for female and is zero otherwise, yields the follow result: 99 . 20 , 50 . 0 , 58 . 5 36 . 6 21 . 229 ˆ 2 SER R Height Female tudentw S (43.39) (5.74) (0.62) Where Studentw is weight measured in pounds and Height is measured in inches (heteroskedasticity-robust standard errors are in parentheses). (a) Interpret the results. Does it make sense to have a negative intercept? ANSWER: For every additional inch in height, weight increases by roughly 5.6 pounds. Female students weigh approximately 6.4 pounds less than male students, controlling for height. The regression explains 50 percent of the weight variation among students. It does not make sense to interpret the intercept, since there are no observations close to the origin, or, put differently, there are no individuals who are zero inches tall. (b) You decide that in order to give an interpretation to the intercept you should rescale the height variable. One possibility is to subtract 5 ft. or 60 inches from your Height , because the minimum height in your data set is 62 inches. The resulting new intercept is now 105.58. Can you interpret this number now? What effect do you think the rescaling had on the two slope coefficients and their t-statistics? Do you think that the R 2 has changed? What about the standard error of the regression? ANSWER: There are now observations close to the origin and you can therefore interpret the intercept. A student who is 5ft. tall will weight roughly 105.5 pounds, on average. The two slopes will be unaffected, as will be the regression R 2 . Since the explanatory power of the regression is unaffected by rescaling, and the dependent variable and the total sums of squares have remained unchanged, the sums of squared residuals, and hence the SER , must remain the same. (c) Use the information contained above to test the null hypothesis that males and females weigh the same (conditional on height).
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ANSWER: 108 . 1 74 . 5 36 . 6 0 ˆ Female Female se t Since 1.108 < 1.96, we cannot reject that males and females weight the same conditional on height at the 5% level. Question 2:
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