Fall09Midterm2BSols

Fall09Midterm2BSols - Midterm 2 - Form B - Fall 2009...

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Midterm 2 - Form B - Fall 2009 Economics 203 Instructor: Petry Name: 1. E. The underlying model for linear regression is Y = β 0 + β 1 X + ± Hence, β 1 is a population parameter. 2. D. This is the null hypothesis for the overall validity of the model. The alternative hypothesis is that at least one of the independent variables is not equal to zero so that there is at least some explanatory power among at least one of the independent variables. 3. E. 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. 4. A. 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 5. A. The standard error of the estimate is s ε = q SSE n - k - 1 = q 1786 38 = 6 . 8556 6. E. 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. 7. B. 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 p-value is much less than the standard .05, so the relationship is in fact significant. 8. D. 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. 9. A. 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. 1
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10. C. The numerator is found by subtracting consecutive residuals, squaring them and adding them up: ( - 1 - 1) 2 + ( . 5 - ( - 1)) 2 + ( . 8 - . 5) 2 + ( - 1 . 3 - . 8) 2 = 4 + 2 . 25 + . 09 + 4 . 41 = 10 . 75. The denominator is found by squaring each residual and adding them up: 1+1+0.25+0.64+1.69=4.58. The Durbin-Watson test statistic is then the numerator di- vided by the denominator: 10.75/4.58= 2.3472 11. C. With a Durbin-Waton test statistic greater than 2, you need to compute the upper tail critical values of 4 - d L and 4 - d U which equal 3.09 and 2.65 respectively. Since the test statistic is less than 4 - d U and greater than d U , the test indicates that no autocorrelation is present for this data.
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Fall09Midterm2BSols - Midterm 2 - Form B - Fall 2009...

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