INSTRUCTIONS: Answer all questions in the spaces provided (or indicate clearly where you have continued your answer). Calculators are NOT permitted. Reduce all computations to the simplest form so that anyone with a calculator could attain the answer easily. Show your work and reasoning to the fullest extent possible so that part marks can be assigned as warranted. You have 75 minutes to complete this exam. All parts of both questions are worth 10 points (and some are much easier than others). Total points = 150. This means roughly 5 minutes for each answer. Budget your time carefully. NOTE: these data are fictitious.

SCENARIO: The marketing sub-committee for a consortium of dealers of American-made luxury automobiles has hired your consulting firm to tell them about the determinants of demand for their products. For a random sample of 17 dealerships in different neighborhoods, you collect data on the average number of cars sold per month (cars_i), the median age of the population in the same zipcode as the dealership (age_i), the median household income (in thousands of dollars) from all sources in the same zipcode (inc_i), median price of luxury cars stocked at the dealership (in thousands of dollars) (price_i), and distance from the nearest foreign luxury car dealership (dist_i). The statistical analyses you perform are given in the Exhibits.

1. Fill in the blanks:

Across these 17 dealerships, what is the mean number of cars sold? ______
What is the highest observed median price of luxury cars across these dealerships? ________
What is the standard deviation in median zipcode incomes across the sample? ________
Do the descriptive statistics you have just provided refer to the joint distribution of these three variables, or to their marginal distributions? ______________
What is the correlation between age_i and inc_i in this sample? ________
What are the units for this correlation measure? ________
 
2. Using the descriptive statistics only, test the hypothesis that the true marginal mean value number of cars sold at ALL dealerships is 5 cars per month.
 

3. Does Regression 1 make sense? Why or why not?
 

4. The chairperson for the consortium says "I took Econ 1 and I know that demand curves slope downwards from left to right. I don't think much of your skills as an economist if the demand curve you estimate is not characterized by a negative slope." Based upon the relevant simple regression in the Exhibits, is it possible that there is a downward sloping demand curve for these cars? Explain how you have reached this conclusion.
 

5. Based on Regression 3, test the hypothesis that in order for a dealership to sell, on average, one additional luxury car per month, the neighborhood income needs to be $20,000 higher.
 

6. Based on Regression 3, what level of monthly sales would you expect for a dealership in a neighborhood with median income of $60,000? Give the formula for a point estimate and explain explicitly how a 95% confidence interval for this prediction would be constructed. Why should you use caution in making this prediction?
 

7. You finally remember that demand functions are functions of several variables, not just one at a time. You estimate Regression 6 in order to ascertain the joint effects of all available demand determinants on the number of cars sold per month. Describe what appears to happen to the apparent effect of the income variable when you include the other variables in your model. WHY is the apparent effect of income different in the more-complex specification?
 

8. In Regression 6, explain the use of the / auxrsqr option on the ols command. What does it tell you here?
 

9. For Regression 6, test the hypothesis that none of the explanatory variables has any effect on the dependent variable. Explain your reasoning.
 

10. On particularly self-assured dealer in the consortium brags that for years, he has claimed that in the luxury-car business, having a clientele that is older by 10 years is equivalent to having a clientele that is richer by $10,000. Do you have enough information in the output to test this informal "hypothesis"? Explain.

 
11. In the different specifications in the Exhibits, what fraction of the variation in cars sold across dealerships can be explained by a model that uses only age? _______ What fraction can be explained by a model that uses income, age, price and distance to nearest foreign luxury car dealership? ______ Can these be compared? Why or why not?

 
12. The demand function estimated in Regression 6 exhibits a negative intercept. Can demand functions have negative intercepts? Does this result and/or its statistical significance trouble you? Why or why not? Explain.

 
13. In Regression 6, are the apparent effects of inc_i and age_i individually statistically significantly different from zero? Could these coefficient both be zero? Explain carefully. Do you have adequate information?

 
14. Is a model to explain cars_i that uses only inc_i and age_i (leaving out price_i and dist_i) an adequate representation of the factors that influence sales of US-made luxury cars at the dealerships represented by this sample? Comment and explain.

 
15. (i.) Specifically, what do we call the distribution that appears in the histogram at the end of the Exhibits?

(ii.) Specifically, what do we call the scatterplot that appears at the end of the Exhibits?