smoker.txt
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sat.txt
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How are high school graduates performing when enrolled in college?

The dataset sat.txt reports first-year college grade point average (G.P.A.), math and

verbal SAT scores (taken before enrolling in college, during high school), the private status

of high school and gender for 745 students in one incoming class at Bates College.

The file contains observations on the following variables:

1. gpa : First-year college grade point average (G.P.A).

2. female : =1 if female; =0 if male

3. math : Math SAT score (taken during high school)

4. verbal : Verbal SAT score (taken during high school)

5. priv : =1 for individuals who attended private high school; =0 for others

(i) Regress gpa on an intercept term, female, math, verbal and priv. Report the coefficients and standard errors.

(ii) Which of the explanatory variables are significant at the 5% level? at the 1% level?

(iii) What is the effect of an increase in the math SAT score of 200 points?

(iv) Test at the 5% level the null hypothesis that the coefficients on math and verbal are

equal, against the alternative that they are not.

(v) Give a confidence interval for the coefficient on female at the 5% level. From this

confidence interval, test the null hypothesis that the coefficient associated with the variable

female is equal to 0.5, against the alternative that it is different from 0.5.

第二题：

Who smokes? The dataset smoker.txt contains a random sample of 1,196 U.S. males.

The variables in the file are:

1. EDUC : education

2. AGE : age

3. INCOME : family income

4. PCIGS79 : price of cigarettes in individual’s state in 1979

5. SMOKER : =1 for smokers; =0 for non-smokers

(i) Estimate a logit model in which the dependent variable is smoker and the explanatory

variables are education, age, income and the price of cigarettes (include an intercept term).

Report the coefficients.

(ii) Interpret the sign of the estimated coefficients.

(iii) Determine the estimated effect of one additional year of education on the probability

of smoking, for an individual with average values for the explanatory variables. Interpret

this value.

(iv) What is the predicted probability of smoking for a 30 years old individual with 12 years of education, whose family income is 20000 dollars and for which the price of cigarettes was 60?

(v) How does this probability vary if education is now 16?