c. (Optional) Get together with a classmate and take turns explainingthe assumptions to each other. In this exercise, try to go beyond the definition of the assumption to give your classmate a feeling for the real-world meaning of each assumption. 7. W. Bowen and T. Finegan' estimated the following regression equation for 78 cities (standard errors in parentheses): L : 5 94.2 2 0.24U; 1 0.20E; 2 0.691; 2 0.065: 1 0.0020; 2 0.80D; (0.08) (0.06) (0.16) (0.18) (0.03) (0.53) N 5 78R- 5.51 where: Li percent labor force participation (males ages 25 to 54) in the ith city U; percent unemployment rate in the ith city E; average earnings (hundreds of dollars/year) in the ith city Is average other income (hundreds of dollars/year) in the ith city S; average schooling completed (years) in the ith city Ci percent of the labor force that is nonwhite in the ith city Do a dummy equal to 1 if the city is in the South, 0 otherwise a. Interpret the estimated coefficients of C and D. What do theymean? b. How likely is perfect collinearity in this equation? Explain youranswer. c. Suppose that you were told that the data for this regression wereold and that estimates on new data yielded a much different coefficient of the dummy variable. Would this imply that one of the estimates was biased? If not, why not? If so, how would you determine which year's estimate was biased? d. Comment on the following statement. "I know that these results are not BLUE because the estimated coefficient of 5 is wrong. It's negative when it should be positive!" Do you agree or disagree? Why? 8. A typical exam question in a more advanced econometrics class is to prove the Gauss-Markov Theorem. How might you go about starting such a proof? What is the importance of such a proof: 9. For your first econometrics project you decide to model sales at the frozen yogurt store nearest your school. The owner of the store is glad to help you with data collection because she believes that students from your school make up the bulk of her business. After countless hours of data collection and an endless supply of frozen yogurt, you estimate the following regression equation (standard errors in parentheses): Y , 5 262.5 1 3.91, 2 46.94P, 1 134.3A, 2 152.10; (0.7) (20.0) (106.0) (138.3) N 5 29R-5.78 2 . W. G. Bowen and T. A. Finegan, "Labor Force Participation and Unemployment," in Arthur M. Ross (ed.), Employment Policy and Labor Markets (Berkeley: University of California Press, 1965), Table 4-2