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 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: Suppose you are interested in learning about the determinants of demand for packs of cigarettes (per month) by young adult smokers between the ages of 18 and 30. An elected official with ties to the tobacco industry has claimed that falling real incomes in a mild recession that is likely to result from global economic instability will have a large negative effect on cigarette consumption by this group. Being aware of the commonly addictive properties of nicotine, you wish to determine the effect of a decrease in income on cigarette consumption. You have collected a random sample of 30 young adults and have recorded their ages (AGE_i in years), incomes (INC_i in thousands of dollars), the price they typically pay for a pack of cigarettes (PRICE_i in dollars), and the average number of packs per month they smoke (PACKS_i per month). The statistical analyses you perform are given in the Exhibits.

1. Fill in the blanks:

Across these 30 individuals, what is the mean number of packs of cigarettes consumed? ______
What is the highest observed price paid for cigarettes across these 30 people? ________
What is the standard deviation in incomes across the sample? ________
Do the descriptive statistics you have just provided refer to the joint distribution of these three variables, to their conditional distributions, 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 number of packs of cigarettes consumed across all young adults smokers in this age group is 10 packs per month.
 

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

4. Based on Regression 2, what is the verbal interpretation of the slope? Comment. Test the hypothesis that a $1,000 decrease in annual income (recession) will have no effect on the number of packs of cigarettes consumed per month by smokers in this age group. If the hypothesis can be rejected, comment upon the qualitative importance of the relationship, in terms of improved health outcomes for smokers as a consequence of recession.
 

5. Based upon the simple regression results the Regression 2, do cigarettes appear to be inferior (as opposed to normal) goods? Explain how you have reached this conclusion.
 

6. Based on Regression 2, what level of monthly cigarette consumption is expected for a smoker with a monthly income of $50,000? 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 3 in order to ascertain the effects of both income and price on the number of packs of cigarettes consumed per month. Controlling for income levels do cigarette prices have any statistically discernible effect on cigarette consumption? What will be the expected effect of a $0.50 additional tax on each pack of cigarettes?
 

8. What is the interpretation of the intercept term in Regression 3? Should you be interest in testing statistical hypotheses about the magnitude of the intercept in this model? Why or why not? Explain.
 

9. Being sensitized to the ever-present potential for omitted variables bias, you begin to wonder whether the results in Regression 3 are robust. You collected age data when you surveyed this sample of smokers, and cumulative time spent smoking might affect monthly demand for cigarettes, since this is widely understood to be an addictive product. Based on the results of Regression 4, on the Descriptive Statistics, and on the data displayed in Plot 1 and Plot 2, assess whether and why the coefficient on the income variable differs from that estimated in Regression 3. Is a recession likely to improve health outcomes by causing a statistically significant decrease in monthly cigarette consumption?
 

10. Does failure to include the age variable in Regression 3 lead to bias in the estimation of the effect of price on pack of cigarettes consumed per month? Explain carefully.
 

11. For Regression 4, explain the use of the / auxrsqr option on the OLS command. What does it tell you here?
 

12. For Regression 4, test the hypothesis that none of the explanatory variables has any effect on the dependent variable. Explain your reasoning.
 

13. For Regression 4, test the hypothesis that neither of the "economic" variables (i.e. PRICE_i and INC_i has any effect on the dependent variable. Explain your reasoning.
 

14. For Regression 4, test the hypothesis that being one year older, in this age group of smokers, means that you consume, on average, one more pack of cigarettes per month.
 

15. An expert in smoking behavior has asserted for years that "A recession that cuts gross incomes of smokers by $10,000 per year in this age group would have the same effect on cigarette consumption as turning back the clock by one year for these smokers. For Regression 4, assess the statistical validity of this assertion.
 

Bonus: (Trickier) Suppose you are trying to use the model in Regression 4 to predict how many packs per month each of these smokers will consume ten years from now. Is this possible?
  [Outlines of Solutions]