## Regression and Dummy Variables

To determine the effects of computer ownership on college performance the following regression model has been proposed

(1)

where colGPA is a student's college GPA, hsGPA is the student's high school GPA, and ACT is the student's score on a standardized test, and PC is a dummy variable such that

.

The effect of PC ownership on college GPA is uncertain due to the fact that it serves two purposes: it can be a learning tool or it can be used for entertainment.

1. Use the EVIEWS workfile GPA1.wf1 to estimate the unknown coefficients of model (1). What is the magnitude of the effect of PC ownership on a student's college GPA? .157309 Is this effect significant? Yes, the t = 2.74.

2. In Model (1) what is the effect of PC ownership on a graph that has hsGPA on the horizontal axis and colGPA on the vertical? Using ACT equal to its mean value, draw a sketch of this effect.

3. If you drop hsGPA and ACT from the model what is the effect on the coefficient on PC?

New Coefficient = .1695, it is bigger.

4. Now add the dummy variables for mother (mothcoll) and father (fathcoll) having at least some college and report the results for the model

.                                  (2)

5. Are the coefficients on mothcoll and fathcoll individually different from zero? Use a 5% level of test for each.

The mothcoll variable is not significant since the p-value is .95, much larger than the specified 5% level of test.

The fathcoll variable is not significant since the p-value is .49, much larger than the specified 5% level of test.

One could also state the test in terms of the observed t-stats and critical value, but the conclusion would be the same.

6. Are the coefficients on mothcoll and fathcoll jointly different from zero at the 5% level?

This is an F-test. F = [(15.14868-15.094)/2]/[15.094/(141-4)] = 0.248. This is such a small F statistic that we fail to reject the null.

7. What is the effect on the PC coefficient of adding mathcoll and fathcoll?

It falls very slightly.

8. Now add the square of hsGPA to model (2) and report the results. Is the coefficient on the square of GPA different from zero at the 1% level?

The coefficient on the square of GPA is not different from zero at the 1% level.

9. After adding hsGPA2 what has happened to the PC coefficient?

There is a very small further decline.