1. (8 points) The superintendent of an elementary school district must decide whether to hire additional...

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1. (8 points) The superintendent of an elementary school district must decide whether to hire additional teachers and she wants your advice. If she hires the teachers, she will reduce the number of students per teacher (the student-teacher ratio) by two. She faces a trade-off. Parents want smaller classes so that their children can receive more individualized attention. But hiring more teachers means spending more money, which is not to the liking of those paying the bill! So she asks you: If she reduces the average class size by two students, what will the effect be on standardized test scores in her district? Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression: TestScore = 520.4-5.82 x CS, R2 = 0.08 a. (4 points) A classroom has 22 students. What is the regression's prediction for that classroom's average test score? b. (4 points) Last year a classroom had 19 students, and this year it has 23 students. What is the regression's prediction for the change in the classroom average test score? Appendix. Random Number Table 37 63 28 02 82 57 68 28 69 02 36 49 71 98 94 90 36 06 49 52 06 50 88 53 30 10 47 99 37 66 91 35 32 00 84 57 07 74 35 24 03 29 60 74 85 90 73 59 55 17 60 05 94 03 11 27 79 90 87 92 41 09 25 36 77 99 32 10 75 21 95 90 94 38 97 71 72 49 78 23 67 89 85 29 21 25 73 69 34 85 76 56 59 23 78 71 72 90 57 01 98 57 31 95 11 96 52 62 87 33 69 27 21 60 95 89 68 48 17 89 34 09 93 50 44 51 50 33 50 95 13 44 34 62 64 39 55 29 30 64 49 44 30 16 88 32 18 50 62 57 34 56 62 31 15 40 90 34 51 95 26 14 90 30 36 24 69 82 51 74 30 35 36 85 01 55 92 64 09 85 50 48 61 18 85 23 08 54 17 12 80 69 24 84 92 16 49 59 27 88 21 62 69 64 48 31 12 73 02 68 00 16 16 46 13 85 45 14 46 32 13 49 66 62 74 41 86 98 92 98 84 54 33 40 81 02 01 78 82 74 97 37 45 31 94 99 42 49 27 64 89 42 66 83 14 74 27 76 03 33 11 97 59 81 72 00 64 61 13 52 93 09 96 33 52 78 13 06 28 30 94 23 37 39 74 11 46 82 59 94 25 34 32 23 17 01 58 73 74 05 82 82 30 34 87 01 1. (8 points) The superintendent of an elementary school district must decide whether to hire additional teachers and she wants your advice. If she hires the teachers, she will reduce the number of students per teacher (the student-teacher ratio) by two. She faces a trade-off. Parents want smaller classes so that their children can receive more individualized attention. But hiring more teachers means spending more money, which is not to the liking of those paying the bill! So she asks you: If she reduces the average class size by two students, what will the effect be on standardized test scores in her district? Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression: TestScore = 520.4-5.82 x CS, R2 = 0.08 a. (4 points) A classroom has 22 students. What is the regression's prediction for that classroom's average test score? b. (4 points) Last year a classroom had 19 students, and this year it has 23 students. What is the regression's prediction for the change in the classroom average test score? Appendix. Random Number Table 37 63 28 02 82 57 68 28 69 02 36 49 71 98 94 90 36 06 49 52 06 50 88 53 30 10 47 99 37 66 91 35 32 00 84 57 07 74 35 24 03 29 60 74 85 90 73 59 55 17 60 05 94 03 11 27 79 90 87 92 41 09 25 36 77 99 32 10 75 21 95 90 94 38 97 71 72 49 78 23 67 89 85 29 21 25 73 69 34 85 76 56 59 23 78 71 72 90 57 01 98 57 31 95 11 96 52 62 87 33 69 27 21 60 95 89 68 48 17 89 34 09 93 50 44 51 50 33 50 95 13 44 34 62 64 39 55 29 30 64 49 44 30 16 88 32 18 50 62 57 34 56 62 31 15 40 90 34 51 95 26 14 90 30 36 24 69 82 51 74 30 35 36 85 01 55 92 64 09 85 50 48 61 18 85 23 08 54 17 12 80 69 24 84 92 16 49 59 27 88 21 62 69 64 48 31 12 73 02 68 00 16 16 46 13 85 45 14 46 32 13 49 66 62 74 41 86 98 92 98 84 54 33 40 81 02 01 78 82 74 97 37 45 31 94 99 42 49 27 64 89 42 66 83 14 74 27 76 03 33 11 97 59 81 72 00 64 61 13 52 93 09 96 33 52 78 13 06 28 30 94 23 37 39 74 11 46 82 59 94 25 34 32 23 17 01 58 73 74 05 82 82 30 34 87 01