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Midterm 104 Q3&4

Midterm 104 Q3&4 - Midterm Solutions Molin Zhong 1...

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Midterm Solutions Molin Zhong October 28, 2011 1 Question 3 1.1 Part A d Testscore = 480 . 0 - 5 . 0 × 20 = 380 is the prediction of the classroom’s average test score. 1.2 Part B 2 × - 5 = - 10 The regression predicts that the average test score decreases by 10. 1.3 Part C 2 × 0 . 3 = 0 . 6 is the standard error. 1.4 Part D t-statistic = | - 5 0 . 3 | = | - 16 . 67 | = 16 . 67 > 1 . 96 The t-statistic is greater than 1.96, so we reject the null hypothesis. 1.5 Part E t-statistic = - 5 0 . 3 = - 16 . 67 < - 1 . 65 The t-statistic is less than -1.65, so we reject the null hypothesis. 1.6 Part F 95% confidence interval: - 5 . 0 ± 1 . 96 × 0 . 3 = ( - 5 . 59 , - 4 . 41) 1.7 Part G 90% confidence interval: 2 × ( - 5 . 0 ± 1 . 65 × 0 . 3) = ( - 10 . 99 , - 9 . 01) 1
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1.8 Part H 480 - 5 × 30 = 330 The sample average of test scores is 330. 1.9 Part I R 2 is the percentage of the variation in test score explained by the class size. In this case, the R 2 is 0.1, which means that 10 percent of the variation in test score is explained by class size. 1.10 Part J This is not true. The reason why this is not true is that with more variation in the class size data there is more information in order to fit an optimal line.
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