This is an econometrics question with stata we have for a practice exam. Please

Question

This is an econometrics question with stata we have for a practice exam. Please help with working out thank you

Consider the following regression model to establish the relationship between graduating class size, race, being an athlete and students test scores sat 0 + 1hsize + 2hsize2 + A,black .athlete + u, (1) where sat is student SAT score, hsize is students' high school graduating class size (in hundreds), black is a race dummy variable equal to one for blacks and zero otherwise and athlete is a dummy equal to one if the student is an athlete. Consider also the alternative model where Isize log(hsize): 1. Below are reported OLS estimates for both specifications, which one do you prefer? Motivate your answer 2. Do you have evidence to say that athletes have, on average, lower scores? By how much? 3. Provide a 99% confidence interval for the effect of being an athlete on SAT scores 4. Is the effect of hsize on SAT scores constant 5. The third Table below shows the regression of the squared residuals from model (1) on hsize, hsize2, athlete and black. Is there any evidence of heterosckedasticity in the error term u? 6. How would potential heterosckedasticity in the errors u affect the OLS estimates reported above? In particular, would the point estimate and the confidence interval provided at points 2 and 3 above be correct?

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.

6. 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.

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