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# quiz ch 8 - Quiz 8 Introduction to Econometrics...

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Quiz 8 – Page 1 out of 4 Quiz 8 Introduction to Econometrics 01:220:322:02 Fall 2010 Instructor: Geoffrey Williams Name: _______________________ It is strongly encouraged that you clearly show your work to allow for partial credit. (24 points total) 1. (12 points) On the next page is the output from two regressions. The first regresses ln(TESTSCORE) on student teacher ratio (STR), percentage of students learning English as a second language (EL_PCT) and percentage of students who are qualified for subsidized meals (MEAL_PCT, a measure of poverty in the district). The second regression regresses TESTSCORE on the same three variables. a. (4 points) Which regression seems to do a better job, given the output? Are both about the same, or is one better? (Hint: Remember that the Y variable changes, don’t make the same mistake I made in class). b. (4 points) If we increased the student teacher ratio of a given school by 3, what does the first regression predict will happen? What is the 95% confidence interval? c. (4 points) If we increased the student teacher ratio of a given school by 3, what does the SECOND regression predict will happen? What is the 95% confidence interval? Answer a) First, remember that we can’t compare R^2 or adjusted R^2 between the two regressions, because for the first regression the Y variable is LNTESTSCR and for the second regression the Y variable is TESTSCR. Since R^2 is a measure of how much of the variation in the Y variable our regression explains, we can’t use it to compare two different (albeit related) Y variables. This is the mistake I made in class – remember to avoid it. Next, what we need to look at is SIGNIFICANCE – how do the t-stats compare? In this case, there is not much difference between the two regressions. No regressor changes from significant to insignificant, or vice versa, so that means that the two regressions are similar in that respect. What’s more, all regressors in both regressions are very highly significant – all would be rejected not just at the 5% level, not just at the 1% level, but at the 0.1% level.

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