This is an econometrics question about interpreting results from stata and regre

Question

This is an econometrics question about interpreting results from stata and regression:

Consider the following regression model to establish the relationship between graduating class size and students test scores A,female * hsize + 5female * hsize2 + ,black + u, where sat is student SAT score, hsize is students's high school graduating class size (in hundreds), female is a gender dummy variable and black is a race dummy variable equal to one for blacks and zero otherwise. Consider also the simpler models: sat-oa + .hsize+ 2hsize2 + 3female + 4black-+ u, (2) an I. How would you interpret 3 in equation (2)? 2. Stata output for each of the above regression is reported below. How would you formally test the hypothesis that hsize has no effect on SAT scores after controlling for gender and race? 3. Using results from equation (2) provide the predicted SAT score for a male black student graduated in a high school class of size 200 4. Do you have reasons to believe that the marginal effect of hsize on SAT scores is not constant? 5. Using results from your preferred model, provide an estimate of the marginal effect of hsize on SAT scores for a female student with ob- served hsize of 100

Explanation / Answer

1. This shows the change in the SAT score if the individual is female. The slope parameter.

2. To see the significance of hsize we will need to use the t stat and test that under the null H0: alpha1=alpha2=0. As against an alternative that H1: they are not equal. In the output we see that that the slope coefficients have t stats that are all greater than 2. and hence we can reject the null that hsize is not signifcant. Even for the first regression to see whether the hsize variable are insignificant we test that the beta coefficients are 0. In this case all t stats relating to hsize are greater than 2 and hence significant.

3. This can be obtained from the output: SAT=19.11454*(200) -2.189393*(200)^2 -139.2918 = -83892. The size squared variable is what is turning the SAT score negative.

4. This will not be constant. As the class size increases the increment to the SAT score will not always be the same. This will depend on the nature of the students coming in.

5. The third model is the best. The SAT score here would be SAT = -41.69324*1. Assuming the student is white the score will be SAT=-41.69324.

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