322Practice02Fall11 - Instructor H.H Kim 1 Econometrics...

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Unformatted text preview: Instructor : H.H. Kim 1 Econometrics Practice Questions II 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 19th 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: = 19.6 + 0.73 Midparh, R2 = 0.45, SER = 2.0 where Studenth is the height of students in inches, and Midparh is the average of the parental heights. (Following Galtons methodology, both variables were adjusted so that the average female height was equal to the average male height.) (a) Interpret the estimated coefficients. (less than 50 words) (b) What is the meaning of the regression R2? (in one sentence) (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? Those who have quite short parents? (less than 50 words) (e) 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 Galtons Fallacy? (less than 80 words) 2) You have obtained measurements of height in inches of 29 female and 81 male students (Studenth) at your university. A regression of the height on a constant and a binary variable (BFemme), which takes a value of one for females and is zero otherwise, yields the following result: = 71.0 4.84BFemme , R2 = 0.40, SER = 2.0 (0.3) (0.57) (a) What is the interpretation of the intercept? What is the interpretation of the slope? How tall are females, on average? (In one sentence each) (b) Test the hypothesis that females, on average, are shorter than males, at the 1% level. (c) Is it likely that the error term is homoskedastic here? (Less than 50 words) Fall 2011 2 Rutgers University ANSWER 1. (a) For every one inch increase in the average height of their parents, the students height increases by 0.73 of an inch. There is no reasonable interpretation for the intercept. (b) The model explains 45 percent of the variation in the height of students. (c) 19.6 + 0.73 70.06 = 70.74. (d) Tall parents will have, on average, tall students, but they will not be as tall as their parents. Short parents will have short students, although on average, they will be somewhat taller than their parents. (e) This is an example of mean reversion. Since the aristocracy was, on average, taller, he was concerned that their children would be shorter and resemble more the rest of the population. If this conclusion were true, then eventually everyone would be of the same height. However, we have not observed a decrease in the variance in height over time. 2. (a) The intercept gives you the average height of males, which is 71 inches in this sample. The slope tells you by how much shorter females are, on average (almost 5 inches). The average height of females is therefore approximately 66 inches. (b) The t-statistic for the difference in means is -8.49. For a one-sided test, the critical value is 2.33. Hence the difference is statistically significant. (c) It is safer to assume that the variances for males and females are different. In the underlying sample the standard deviation for females was smaller. ...
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