1. Fraser Institute produces school rankings that report the BC school performance (lately they also started producing the rankings for Alberta, Ontario, and Quebec}. You want to try explaining the differences in elementary school performances, do some reading on the subject and find that the BCTF [British Columbia Teacher's Federation] constantly campaign to reduce the class sizes because they believe that the students learn better in smaller classes. So, you nd the data about the class sizes and run a regression: FER: = n + 31-5113: 1\"} where 33.5% = the performance index (the number between I] and lilthat is proportional to the FSA (Foundation Skills Assessment) scores the students at school i obtain on the tests}; STE.- = average student-toteaeher ratio at school 1'. Your regression 111.1] yields a signicant positive estimate for 1. at Interpret E1. {1} But then a friend points out that in the Fraser Institute ranking the private schools consistently get to the top of the rankings {higher performance indicaes}1 and that the private schools tend to have smaller classes [lower student-to-teacher ratios). You believe that that's true. You can easily identify which school is private and which one is public, and you create another variable, PR3, or a school ownership status {private or public]. b. Explain how you 'onde dene the PM variable values. {3} You are going to 11.1.1.1 a new regression: FER: = 13o + 315113.: + 23135! {"1 c. Interpret $1 in this regression. {1} d. Interpret g in this regression [2] e. How do you expect the estimate of 31 change from equation F] to equation (")3 Try to explain all the relevant details (do you expect any bias in the estimates? what signJ'direetion of the bias do you expect if any\"? why'E'}. {5} f. Now suppose you suspect that the marginal effect of reducing the class size differs between the private and public schools. Construct the equation that would allow you to measure those differing marginal effect of reducing the class size and test your suspicion that the effects do differ. Try to present all the relevant details (give the equation and explain how you would use the estimates in this equation to measure those differing marginal effect)