Question Homework 5 100 points

Homework 5

100 points

The following two problems will require a lot of calculations in STATA. It will generate many pages of output. Here is how your should organize it. The first pages should contain your answers to all the questions, along with showing any key algebraic equations or explanations you need to use along the way. After that, include a printout of the output from the regressions you executed in support of your answers. Highlight any numbers in this output that you used in the first section. (You are encouraged to save paper here, you may print this section with a small font, double-sided and/or with 2-up format.) Last, include a copy of the DO file that contains the commands you asked STATA to execute. Be sure you organize these in a way that will be clear to the reader.

Problem 1

In the dataset Smoker, there is information on 1196 males from the United States. Data from this sample includes the variables:

smoke= 1 for smokers, and 0 for nonsmokers

age=age in years

educ= number of years of schooling

income= family income

pcigs= an index of the average price of cigarettes in the individual’s state

Part 1)

a) Create a dummy variable “hi_ed” that is a 1 if a person has ?17 years of education, zero otherwise.

b) Estimate a linear regression (which in this context is called a linear probability model (LPM)) for the binary variable smoke on the independent variable hi_ed. Report the beta coefficient on the dummy variable and its p-value. In words, express what the beta coefficient means in this case.

c) Create a frequency table for the smoke and hi_ed variables. The command in STATA istabulatesmoke hi_ed.

d) Calculate the probability that a person smokes if high education. Calculate the probability for smoking for low edcuation.

e) What is the relationship between the results for parts b and d?

f) Calculate the odds that a low education person smokes. Calculate the odds a high education person smokes. Calculate the odds ratio.

g) Estimate the logistic regression (logistic command) for smoke and hi_ed. Confirm that this equals the odds ratio. In words, express what the odds ratio coefficient means in this case.

Part 2)

a) Estimate the logistic regression for smoke on pcigs when hi_ed=0. Then, calculate the predicted values for Y. The command to do this is “predict yhat_0.” Repeat for when hi_ed=1, and also create a predicted value variable yhat_1.

b) Compare the coefficients for the two models. In words, explain what the model is saying about the impact of pcigs for the two different education groups.

c) Create a graph of the predicted values for the two versions. Use the following syntax:twoway (line yhat_0 pcigs, sort) (line yhat_1 pcigs, sort), legend(label(1 “low ed”) label(2 “hi ed”))

d) For a low education person, a 1 unit change of the price index of cigarettes will change the o

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