PUBPOL5750 PROBLEM SET 1
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PUBPOL5750 PROBLEM SET 1
BIVARIATE REGRESSION REVIEW
Due date: Thursday, February 19th , at 23:59
1 Calculation Questions (30 points, equal weights)
In this question, you are asked to calculate a bivarite regression line manually.
The objective of this exercise is to show what it means to fit the best linear line to understand the relationship between two variables. Please do not attempt to use Stata for this exercise.
See the data on hours studied and test scores:
Student Hours studied Test Scores
|
1 |
2 |
75 |
|
2 |
3 |
80 |
|
3 |
1 |
65 |
|
4 |
4 |
90 |
|
5 |
2 |
70 |
1. (6 points): Calculate the intercept and slope coefficients for the regression on:
Testi = β0 + β1 Hoursi + ϵi
Show all your steps: Means of dependent and independent variables, co- variance between them, variance, etc. Use tables for these.
Show Work/Reasoning:
2. (6 points): Write down the estimated line. Now, use a table and get regression residuals.
Show Work/Reasoning:
3. (6 points): Calculate the standard error of the slope coefficient. Test the hypothesis that there is no relationship between hours of study and test scores.
Show Work/Reasoning:
4. (6 points): Draw the fitted line and place the actual data points around the graph. Illustrate the residuals on your graph.
5. (6 points): Calculate the R-square for your regression and interpret. Show Work/Reasoning:
2 Stata Questions (70 points, equal weights)
For this question, use the data on hourly wage and education of US residents in 2017 (for those individuals working “full time and full year”), given in the data set CPS-ASEC-2017.dta on the course webpage (in the ”Data” folder).
Please show your Stata output when relevant. Do not forget to hand in your do-file and your log-file along with your PS. You will lose 5 points for not submitting your do-file and 5 extra for not submitting your log-file.
1. Start creating a do-file (for example: yournamePS1.do) (There is no points for this item but you will lose 5 points if you don’t submit a nicely written do-file.)
2. (7 points): Examine the variables. Use “summarize” for the variables wage, age, education, and male and female, and “tabulate” for educa- tion. Do the summary statistics look consistent with your expectations? Explain.
3. (7 points): Run a linear regression of wage on years of education using the “regress” command. Interpret the slope coefficient – what does it tell us in words? Is this reasonable?
4. (7 points): Interpret the intercept coefficient. What does it tell us? Is this reasonable?
5. (7 points): Show the regression line as well as the actual data points using Stata [twoway (scatter depvar indepvar) (lfit depvar indepvar)]
6. (7 points): Test the null hypothesis that there is no relationship between wage and education. What is the relationship between the F statistic and the t statistic in this regression?
7. (7 points): Test the null hypothesis that the efect of education on wages is positive (one-sided test).
8. (7 points): Calculate the correlation between wage and years of education (use two diferent methods for this).
9. (7 points): Now, estimate the wage equation for age only where the pop- ulation model is:
Wagei = α + βAgei + ϵi
Predict the wage for ages 1, 35, 45 and 100. How can you make sense out of these numbers?
10. (7 points): Calculate the gender wage gap in the data (hint: diference in means of male and female wages).
11. (7 points): How can you formulate an empirical model to test whether there is a significant gender wage gap? If so, in favor of which gender?
2026-02-24
BIVARIATE REGRESSION REVIEW