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Unformatted text preview: Midterm 2  Form A  Fall 2009 Economics 203 Instructor: Petry Name: 1. C. Of the above steps, you would first develop a model with a sound theoretical basis. You would next decide to gather data appropriate for your model. Finally you would estimate the coefficients. 2. E. With income as your dependent variable (y) and education as your independent variable (x) you should plug the values into your calculator. Using your calculator you would find that the intercept was 93 and the slope was 7. If using the BAII, this corresponds to a and b respectively. 3. E. Residuals are found as y ˆ y for the observation of interest. Steve has an income of 200 and ˆ y = 93 + 7 * 16 = 205 which implies the residual is equal to 5. 4. C. The test statistic is found when you grab r from your calculator and plug into the test statistic formula. r = .45957 so the test statistic is . 45957 * q 5 2 1 . 45957 2 = 0 . 8962 5. A. This is a twotailed test on the tdistribution with 3 degrees of freedom. The assumed test statistic of 2.5 is less extreme than the appropriate critical values of 3.18 and 3.18. So we do not reject the null hypothesis, and have found insufficient evidence of a linear relationship between income and education for this data. 6. B. SSE is equal to 1786 and SST is equal to SSR+SSE=1786+432=2218. Further, n = total degrees of freedom + 1 = 40 and k = 1 (the regression degrees of freedom). Adjusted R 2 then is equal to 1 SSE/ ( n k 1) SST/ ( n 1) = 1 SSE * ( n 1) SST * ( n k 1) = 1 1786 * 39 2218 * 38 = . 17358 7. B. The standard error of the estimate is s ε = q SSE n k 1 = q 1786 38 = 6 . 8556 8. D. The correlation coefficient under simple regression is equal to Multiple R with the correct sign attached. The correct sign can be found by looking at the sign of the estimated slope coefficient. Since the coefficient is negative, the correlation coefficient is .7809. 9. A. As number of employees change, profits change by 3.3*(the change in the number of employees) so profits are higher when you have fewer employees. Also, the pvalue is much less than the standard .05, so the relationship is in fact significant. 10. E. The standard error of the estimate is the sample standard deviation of the points around the regression line. Using the empirical rule, we can say that within ± 2 s ε we expect 95% of the data. 1 11. D. The expected sign on Baskets is positive as more baskets is believed to result in more sales. The expected sign on Front is positive since the dummy variable is equal to 1 when papayas are up front and this is believed to result in selling better. The expected sign on Mango is negative since the dummy variable is equal to 1 when mangoes are on sales and this is believed to result in lower sales. Finally, the price of papayas impacts sales of papayas, and as price increases, sales go down, all else constant so the expected sign would be negative....
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 Spring '10
 Petry
 Economics, Regression Analysis, SST

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