14. Does it appear to be a reasonable assumption that u is distributed normally? Why or why not? Using this answer as a starting point, can you justify using this regression model? 15. Evaluate the claim that se (final) is decreasing at approximately rate 1. Suppose the population model is ecolbs = Bo+ Breglbs + Bregpre+3ecopre + Bafamine + seduc+u. Run the regression in R, and print a summary of your regression output. 2. Calculate Bregpre using the "partialing out" process. Use R to calculate the residuals necessary to use the "partialing out" formula, but calculate Bregprice itself by using the formula. Confirm that the estimate matches your regression output for question 1. 3. Interpret the F-statistic and the (Adjusted) R in your regression output. What do they tell us about the model? 1. Test the null hypothesis that B0 = 0, under alternative that Bo 0. Use 2% significance level. 5. Test the null hypothesis that B0 = 0, under alternative that ;>0. Use the 2% significance level. 6. What is the 95% confidence interval associated with Beduc? 7. Interpret the sign of the coefficients Bregpre and Becopre from a microeconomics perspective. 8. Consider the coefficient restriction of Bregpre = -Becopre as a null hypothesis, and Bregpre-Becopre as the alternative hypothesis. Interpret the hypothesis (that is, describe an economic relationship implied by the hypothesis). Implement a test of this hypothesis. 9. What might motivate a concern that famine and edu are potentially jointly significant. Use an F-test to evaluate the null hypothesis that these two parameters are jointly significant. Report the p-value of your test, and report the test result for a significance level of 5%. 10. Use the Lagrange Multiplier test to evaluate the same null hypothesis in question 9. Report the p-value of your test, and compare it to the p-value of your F-test in question 9. Use the Wooldridge data set 'attend' to answer questions 11-15. 11. Suppose the population model is attend = Bo+BtermGPA+BpriGPA+B3ACT+Bfinal +shwrte + Be frosh + Brsoph + u. Run the regression in R, and print a summary of your regression output. Suppose instead that the variable termGPA is not included in your regression. What is the impact of its exclusion on BpriGPA? Why is priGPA impacted this way? 12. What is the p-value associated with the null hypothesis that frosh = 2, under the alternative that Bfrosh #2? I do not have a good motivation for this hypothesis, I just want to make sure you know how to run this kind of test. 13. Report the p-value under the null hypothesis that priGPA = termGPA, under the alternative that this is not true.