Module 3, Week 1, Paper and Pencil Assignment 5

1. You are interested in the relationship between the income of recent college graduates and the income of their parents. Below is a random sample containing information on the annual income of recent college graduates and the annual income of their top income earning parent. Income is measured in thousands of dollars.

Recent graduate annual income	Parent annual income
34	59
42	86
51	105
60	92
28	55
35	66
38	62
46	90

1. Write a first-order probabilistic simple linear regression model describing the relationship of interest.
2. Describe each component of the model.
3. Calculate (by hand) the least squares estimates of the model's parameters.
4. Interpret the estimated slope coefficient.
5. Interpret the estimated intercept. Is this a meaningful interpretation?
6. Use the estimated regression model to predict the annual income for a recent graduate whose parent earns 100.
7. What is a residual? Calculate the residual for the first observation in the table.
8. Test the hypothesis that there is a positive relationship between parent income and recent graduate income. Use a 10% level of significance.
9. Calculate a 90% confidence interval for the estimated slope coefficient.
10. Calculate and interpret the model's R-squared.
11. How would you describe the least squares procedure to someone with no background in statistics?
12. Do you think any important predictor variables have been left out of this model? If yes, give an example.