41．Consider a study of 100 university endowment funds that was conducted to determine if the funds’ annual risk-adjusted returns could be explained by the size of the fund and the percentage of fund assets that are managed to an indexing strategy. The equation used to model this relationship is: ARARi = b0 + b1Sizei + b2Indexi + ei
Where ARARi
| = | the average annual risk-adjusted percent returns for the fund i over the 1998-2002 time period. | Sizei | = | the natural logarithm of the average assets under management for fund i. | Indexi | = | the percentage of assets in fund i that were managed to an indexing strategy. |
The table below contains a portion of the regression results from the study. Partial Results from Regression ARAR on Size and Extent of Indexing |
| Coefficients | Standard Error | t-Statistic | Intercept | ??? | 0.55 | −5.2 | Size | 0.6 | 0.18 | ??? | Index | 1.1 | ??? | 2.1 |
Which of the following is the most accurate interpretation of the slope coefficient for Size? ARAR: A) will change by 1.0 percent when the natural logarithm of assets under management changes by 0.6, holding Index constant. B) and Index will change by 1.1 percent when the natural logarithm of assets under management changes by 1.0. C) will change by 0.6 percent when the natural logarithm of assets under management changes by 1.0, holding Index constant. D) will change by 1.1 percent when the natural logarithm of assets under management changes by 1.0 and Index changes by 0.6. The correct answer was C) A slope coefficient in a multiple linear regression model measures how much the dependent variable changes for a one-unit change in the independent variable, holding all other independent variables constant. In this case, the independent variable Size (= ln average assets under management) has a slope coefficient of 0.6, indicating that the dependent variable ARAR will change by 0.6 percent return for a one-unit change in Size, assuming nothing else changes. Pay attention to the units on the dependent variable. 42．Which of the following is the estimated standard error of the regression coefficient for Index? A) 1.91. B) 2.31. C) 0.52. D) 1.00. The correct answer was C) The t-statistic for testing the null hypothesis H0: βi = 0 is t = (bi – 0)/σi, where βi is the population parameter for independent variable i, bi is the estimated coefficient, and σi is the coefficient standard error. Using the information provided, the estimated coefficient standard error can be computed as bIndex/t = σIndex = 1.1/2.1 = 0.5238. 43．Which of the following is the t-Statistic for Size? A) 0.30. B) −0.12. C) 0.70. D) 3.33. The correct answer was D) The t-statistic for testing the null hypothesis H0: βi = 0 is t = (bi – 0)/σi, where βi is the population parameter for independent variable i, bi is the estimated coefficient, and σi is the coefficient standard error. Using the information provided, the t-statistic for Size can be computed as t = bSize/σSize = 0.6/0.18 = 3.3333. 44.Which of the following is the estimated intercept for the regression? A) −0.11. B) −2.86. C) −9.45. D) −4.65. The correct answer was B) The t-statistic for testing the null hypothesis H0: βi = 0 is t = (bi – 0)/σi, where βi is the population parameter for independent variable i, bi is the estimated parameter, and σi is the parameter’s standard error. Using the information provided, the estimated intercept can be computed as b0 = t x σ0 = −5.2 x 0.55 = −2.86. 45.Which of the following statements is TRUE regarding the significance of the regression parameters at a 5 percent level of significance? A) The parameter estimates for the intercept are significantly different than zero. The slope coefficients for Index and Size are not significant. B) The parameter estimates for the intercept and the independent variable Size are significantly different than zero. The coefficient for Index is not significant. C) All of the parameter estimates are significantly different than zero at the 5 percent level of significance. D) None of the regression parameters are significantly different than zero at the 5 percent level of significance. The correct answer was C) At 5-percent significance and 97 degrees of freedom (100 – 3), the critical t-value is slightly greater than, but very close to, 1.984. The t-statistic for the intercept and Index are provided as −5.2 and 2.1, respectively, and the t-statistic for Size is computed as 0.6/0.18 = 3.33. The absolute value of the all of the regression intercepts is greater than tcritical = 1.984. Thus, it can be concluded that all of the parameter estimates are significantly different than zero at the 5 percent level of significance. | 
发表于 2008-4-8 18:23
|