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1. Females, on average, are shorter and weigh less than males. One of your friends, who is a premed 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:
= -229.21 – 6.36 × Female + 5.58 × Height, =0.50, SER = 20.99 where Studentw is weight measured in pounds and Height is measured in inches.
(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? Do you thing that the regression has changed? What about the standard error of the regression?
(c) You have learned that correlation does not imply causation. Although this is true mathematically, does this always apply?
2. The cost of attending your college has once again gone up. Although you have been told that education is investment in human capital, which carries a return of roughly 10% a year, you (and your parents) are not pleased. One of the administrators at your university/college does not make the situation better by telling you that you pay more because the reputation of your institution is better than that of others. To investigate this hypothesis, you collect data randomly for 100 national universities and liberal arts colleges from the 2000-2001 U.S. News and World Report annual rankings. Next you perform the following regression
= 7,311.17 + 3,985.20 × Reputation – 0.20 × Size + 8,406.79 × Dpriv – 416.38 × Dlibart –
2,376.51 × Dreligion
R2=0.72, SER = 3,773.35
where Cost is Tuition, Fees, Room and Board in dollars, Reputation is the index used in U.S. News and World Report (based on a survey of university presidents and chief academic officers), which ranges from 1 (“marginal”) to 5 (“distinguished”), Size is the number of undergraduate students, and Dpriv, Dlibart, and Dreligion are binary variables indicating whether the institution is private, a liberal arts college, and has a religious affiliation.
(a) Interpret the results. Do the coefficients have the expected sign?
(b) What is the forecasted cost for a liberal arts college, which has no religious affiliation, a size of 1,500 students and a reputation level of 4.5? (All liberal arts colleges are private.)
(c) To save money, you are willing to switch from a private university to a public university, which has a ranking of 0.5 less and 10,000 more students. What is the effect on your cost? Is it substantial?
(d) Eliminating the Size and Dlibart variables from your regression, the estimation regression becomes
= 5,450.35 + 3,538.84 × Reputation + 10,935.70 × Dpriv – 2,783.31 × Dreligion;
=0.72, SER = 3,792.68
Why do you think that the effect of attending a private institution has increased now?
(e) What can you say about causation in the above relationship? Is it possible that Cost affects Reputation rather than the other way around?
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