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Chapter%206%20and%207%20-%20Extra%20Practice%20Problems

# Chapter%206%20and%207%20-%20Extra%20Practice%20Problems -...

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Econ 120B Chapters 6 and 7 – Extra Practice Problems 1. You have obtained data on test scores and student-teacher ratios in region A and region B of your state. Region B, on average, has lower student-teacher ratios than region A. You decide to run the following regression Y i = β 0 + 1 X 1 i + 2 X 2 i + 3 X 3 i + u i where X 1 is the class size in region A, X 2 is the difference in class size between region A and B, and X 3 is the class size in region B. Your regression package shows a message indicating that it cannot estimate the above equation. What is the problem here and how can it be fixed? 2. Consider the following multiple regression model Y i = 0 + 1 X 1 i + 2 X 2 i + 3 X 3 i + u i You want to consider certain hypotheses involving more than one parameter. For each of the cases below transform the regression model so that you can use a t-statistic to test: (specify the t-stat you would compute for each case) a. 1 + 2 + 3 = 1 b. 1 = 2 3 c. 2 3 3 = 2 3. Females, on average, are shorter and weigh less than males. One of your friends, who is a pre-med student, tells you that in addition, females will weigh less for a given height. To test this hypothesis, you collect 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 females and is zero otherwise, yields the following result: , =0.50, SER = 20.99 ) 62 . 0 ( ) 74 . 5 ( ) 39 . 43 ( 58 . 5 36 . 6 21 . 229 ^ Height Female Studentw × + × = R 2 where Studentw is weight measured in pounds and Height is measured in inches (heteroskedasticity-robust standard errors in parentheses). a. Interpret the results. Does it make sense to have a negative intercept? 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 - statistic? Do you thing that the regression has changed? R 2 c. Carry out the hypothesis test that females weigh the same as males, on average, for a given height, using a 10% significance level (don’t forget to specify the alternative hypothesis).

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4. A subsample from the Current Population Survey is taken, on weekly earnings of individuals, their age, and their gender. You have read in the news that women make 70 cents to the \$1 that men earn. To test this
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Chapter%206%20and%207%20-%20Extra%20Practice%20Problems -...

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