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Unformatted text preview: Econ 120B Chapters 4 and 5 – Extra Practice Problems 1. Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19 th century. It is from this study that the name “regression” originated. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship: 10 . ) ˆ ( , 2 . 7 ) ˆ ( , . 2 , 45 . , 73 . 6 . 19 ˆ 1 2 = = = = + = β β SE SE SER R X Y where Y is the height of students in inches, and X is the average of the parental heights (Following Galton’s methodology, both variables were adjusted so that the average female height was equal to the average male height.). The standard errors are heteroskedastic-robust. a. Interpret the estimated coefficients. b. What is the meaning of the regression ? What is the interpretation of the SER ? R 2 c. What is the prediction for the height of a child whose parents have an average height of 70.06 inches? d. Given the positive intercept and the fact that the slope lies between zero and one, what can you say about the height of students who have quite tall parents? Who have quite short parents? e. Test for the significance of the slope coefficient. f. Can you reject the null hypothesis that is zero? R 2 g. If children, on average, were expected to be of the same height as their parents, then this would imply two hypotheses, one for the slope and one for the intercept. i. What should the null hypothesis be for the intercept? Calculate the relevant t- statistic and carry out the hypothesis test at the 1% level. ii. What should the null hypothesis be for the slope? Calculate the relevant t- statistic and carry out the hypothesis test at the 5% level. h. Construct a 95% confidence interval for the predicted change in student height resulting from a 5 inches increase in the average of parental height. i. Galton was concerned about the height of the English aristocracy and referred to the above result as "regression towards mediocrity." Can you figure out what his concern was? Why do you think that we refer to this result today as "Galton's Fallacy?" 2. You have learned in one of your economics courses that one of the determinants of per capita income (the “Wealth of Nations”) is the population growth rate. Furthermore you also found out that the Penn World Tables contain income and population data for 104 countries of the world. To test this theory, you regress the GDP per worker (relative to the United States) in 1990 ( RelPersInc ) on the difference between the average population growth rate of that country ( n ) to the U.S. average population growth rate ( n us ) for the years 1980 to 1990. This results in the following regression output: ^ Re lPersInc = 0.518 – 18.831×( n – n us ) , R 2 =0.522, SER = 0.197 177 . 3 ) ˆ ( , 056 . ) ˆ ( 1 = = β β SE SE a. Interpret the results carefully. Is the relationship statistically significant? Is the relationship Interpret the results carefully....
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- Spring '08
- Regression Analysis, Statistical hypothesis testing, Human height, Sir Francis Galton, population growth rate