We have collected data on GPA, demographic characteristics and drinking behavior of college students from 119 U.S. colleges in 2001. For this question you will use the same college.dta data set available on Latte but this time use it to explore the impact of drinking behavior on GPA. The main alcohol consumption variable is called drinks. This variable reflects student responses to the question: "In the past 30 days, on those occasions when you drank alcohol, how many drinks did you usually have?" Answers are coded as follows: 0 = did not drink in the past 30 days; 1 = 1 drink, 2=2 drinks, ... up to 9 = 9 or more drinks.

a. Write an equation (no need to estimate this in R, simply write down the equation you would like to estimate) that allows you to estimate the effects of alcohol consumption on GPA, while controlling for the other factors in the survey. What should be the functional form of this regression? (In other words, should GPA and/or drinks be in logs? Why or why not? Should a polynomial in drinks be considered?) Explain your reasoning.

b. Write an equation (again, no need to estimate this in R, simply write down the equation you would like to estimate) that would allow you to test whether alcohol consumption has different 5 effects on GPA for men and women (use the linear version of drinks). How would you test that there are no differences in the effects of alcohol consumption on GPA for men and women? Explain.

c. Estimate the equation in (b) in R and run the test. Is there a difference in how alcohol consumption affects GPA for men and women? Is the difference statistically significant?

d. Suppose you think it is better to measure alcohol consumption by putting students into one of four categories: abstainer, light drinker, moderate drinker and heavy drinker. Now, write a model that allows you to estimate the effects of alcohol consumption on GPA. (Assume there is no interaction effect with gender.) Using this model, explain clearly how to test the null hypothesis that alcohol consumption has no effect on GPA (write down your null and alternative hypotheses, and the number of restrictions).

e. Estimate the regression in (d) and run the test. What do you conclude about the impact of alcohol consumption on GPA based on these results?