21.Damon Washburn, CFA, is currently enrolled as a part-time graduate student at State
University. One of his recent assignments for his course on Quantitative Analysis is to perform a regression analysis utilizing the concepts covered during the semester. He must interpret the results of the regression as well as the test statistics. Washburn is confident in his ability to calculate the statistics because the class is allowed to use statistical software. However, he realizes that the interpretation of the statistics will be the true test of his knowledge of regression analysis. His professor has given to the students a list of questions that must be answered by the results of the analysis. Washburn has estimated a regression equation in which 160 quarterly returns on the S& 500 are explained by three macroeconomic variables: employment growth (EMP) as measured by nonfarm payrolls, gross domestic product (GDP) growth, and private investment (INV). The results of the regression analysis are as follows: Coefficient Estimates | Parameter
| Coefficient
| Standard Error
of Coefficient | Intercept | 9.50 | 3.40 | EMP | -4.50 | 1.25 | GDP | 4.20 | 0.76 | INV | -0.30 | 0.16 |
Other Data: §
Regression sum of squares (RSS) = 126.00 §
Sum of squared errors (SSE) = 267.00 §
Durbin-Watson statistic (DW) = 1.34 Abbreviated Table of the Student’s t-distribution (One-Tailed Probabilities) | df
| p = 0.10
| p = 0.05
| p = 0.025
| p = 0.01
| p = 0.005 | 3 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 | 10 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 | 50 | 1.299 | 1.676 | 2.009 | 2.403 | 2.678 | 100 | 1.290 | 1.660 | 1.984 | 2.364 | 2.626 | 120 | 1.289 | 1.658 | 1.980 | 2.358 | 2.617 | 200 | 1.286 | 1.653 | 1.972 | 2.345 | 2.601 |
Critical Values for Durbin-Watson Statistic (α = 0.05) |
| K=1 | K=2 | K=3 | K=4 | K=5 | n | dl | du | dl | du | dl | du
| dl
| du
| dl
| du | 20 | 1.20 | 1.41 | 1.10 | 1.54 | 1.00 | 1.68 | 0.90 | 1.83 | 0.79 | 1.99 | 50 | 1.50 | 1.59 | 1.46 | 1.63 | 1.42 | 1.67 | 1.38 | 1.72 | 1.34 | 1.77 | >100 | 1.65 | 1.69 | 1.63 | 1.72 | 1.61 | 1.74 | 1.59 | 1.76 | 1.57 | 1.78 |
How many of the three independent variables (not including the intercept term) are statistically significant in explaining quarterly stock returns at the 5.0 percent level? A) One of the three is statistically significant. B) Two of the three are statistically significant. C) None of the three are statistically significant. D) All three are statistically significant. The correct answer was B) To determine whether the independent variables are statistically significant, we use the student’s t-statistic, where t equals the coefficient estimate divided by the standard error of the coefficient. This is a two-tailed test. The critical value for a 5.0% significance level and 156 degrees of freedom (160-3-1) is about 1.980, according to the table. The t-statistic for employment growth = -4.50/1.25 = -3.60. The t-statistic for GDP growth = 4.20/0.76 = 5.53. The t-statistic for investment growth = -0.30/0.16 = -1.88. Therefore, employment growth and GDP growth are statistically significant, because the absolute values of their t-statistics are larger than the critical value, which means two of the three independent variables are statistically significantly different from zero. 22.Can the null hypothesis that the GDP growth coefficient is equal to 3.50 be rejected at the 1.0 percent confidence level versus the alternative that it is not equal to 3.50? The null hypothesis is: A) accepted because the t-statistic is less than 2.617. B) rejected because the t-statistic is greater than 0.92. C) not rejected because the t-statistic is equal to 0.92. D) rejected because the t-statistic is less than 2.617. The correct answer was C) The hypothesis is: H0: bGDP = 3.50
Ha: bGDP ≠ 3.50 This is a two-tailed test. The critical value for the 1.0% significance level and 156 degrees of freedom (160-3-1) is about 2.617. The t-statistic is (4.20 – 3.50)/0.76 = 0.92. Because the t-statistic is less than the critical value, we cannot reject the null hypothesis. Notice we cannot say that the null hypothesis is accepted; only that it is not rejected. 23.The percentage of the total variation in quarterly stock returns explained by the independent variables is closest to: A) 42%. B) 25%. C) 32%. D) 47%. The correct answer was C) The R2 is the percentage of variation in the dependent variable explained by the independent variables. The R2 is equal to the SSRegession/SSTotal, where the SSTotal is equal to SSRegression + SSError. R2 = 126.00/(126.00+267.00) = 32%. 24.According to the Durbin-Watson statistic, there is: A) significant positive serial correlation in the residuals. B) no significant positive serial correlation in the residuals. C) no significant heteroskedasticity in the residuals. D) significant heteroskedasticity in the residuals. The correct answer was A) The Durbin-Watson statistic tests for serial correlation in the residuals. According to the table, dl = 1.61 and du = 1.74 for three independent variables and 160 degrees of freedom. Because the DW (1.34) is less than the lower value (1.61), the null hypothesis of no significant positive serial correlation can be rejected. This means there is a problem with serial correlation in the regression, which affects the interpretation of the results. 25.What is the predicted quarterly stock return, given the following forecasts? §
Employment growth = 2.0% §
GDP growth = 1.0% §
Private investment growth = -1.0% A) 5.0%. B) 4.4%. C) -4.5%. D) 23.0%. The correct answer was A) Predicted quarterly stock return is 9.50% + (-4.50)(2.0%) + (4.20)(1.0%) + (-0.30)(-1.0%) = 5.0%. | 
发表于 2008-4-8 16:53
| 