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Spring 2010 Midterm 2 Form C Solutions

Spring 2010 Midterm 2 Form C Solutions - Midterm 2 Form C...

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Midterm 2 - Form C - Spring 2010 Economics 203 Instructors: Petry and Sahakyan Name: 1. E. A positive residual is more likely to follow a positive residual when positive autocorrelation is present. Similarly, a negative residual is more likely to follow a negative residual when positive autocorrelation is present. In contrast, negative autocorrelation is characterized by adjacent residuals being likely to be of opposite signs. 2. D. R 2 can never decrease when adding independent variables. Adjusted R 2 R 2 and R 2 is always between zero and one. R 2 is not penalized by adding independent variables. The value of adjusted R 2 you are never sure about when adding variables. 3. A. R 2 of 0 means your SSR is 0 (with SST =50,000). That means your F -statistic is 0, since it has SSR on top and something positive on bottom. 4. C. P-values on the individual t-tests increase under serious multicollinearity, not decrease. This is due to inflated standard errors of the slope coefficients. 5. E. The pvalues for estimated coefficients are always two-tailed ( 6 =). The pvalue of 0.000402 is for the estimated coefficient b 1 yet hypotheses are always on the population parameters, thus β 1 . 6. C. The test implied by the Excel output is the two-sided test. To get the p-value for the one-sided test, we halve the p-value from the two-sided test. 7. A. The predicted sales is ˆ SALES = 8 . 7+5(4 . 2) = 29 . 7. The appropriate critical value is t 0 . 025 , 8 = 2 . 31. This gives everything that we need to put into the confidence interval formula: ˆ SALES ± t α/ 2 s ε s 1 /n + ( x g - ¯ x ) 2 ( n - 1) s 2 x = 29 . 7 ± (2 . 31)(3 . 234578798) s 1 / 10 + (5 - 5) 2 (10 - 1)2 . 22 = 29 . 7 ± (2 . 31)(3 . 234578798) p 1 / 10 = (27 . 337 , 32 . 063) 8. D. Under simple regression the overall F test statistic equals the (t-test stat) 2 , thus q 81700 . 4 792 . 05 and attach sign of estimated coefficient of b 1 so 10.156. You also have s x = 8 . 7458, so you could calculate s b 1 from that and do the standard t-test statistic formula of b 1 /s b 1 .
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