6.Stepp is concerned about the validity of Hays’ regression analysis and asks Hays if he can test for the presence of heteroskedasticity. Hays complies with Stepp’s request, and detects the presence of unconditional heteroskedasticity. Which of the following statements regarding heteroskedasticity is most correct? A) Unconditional heteroskedasticity usually causes no major problems with the regression. B) Unconditional heteroskedasticity does create significant problems for statistical inference. C) Heteroskedasticity occurs when the variance of the residuals in the same across all observations in the sample. D) Heteroskedasticity can be detected either by examining scatter plots of the residual or by using the Durbin-Watson test. The correct answer was A) Unconditional heteroskedasticity occurs when the heteroskedasticity is not related to the level of the independent variables. This means that it does not systematically increase or decrease with changes in the independent variable(s). Note that heteroskedasticity occurs when the variance of the residuals is different across all observations in the sample and can be detected either by examining scatter plots or using a Breusch-Pagen test. 7.Werner Baltz, CFA, has regressed 30 years of data to forecast future sales for National Motor Company based on the percent change in GDP and the change in price of a U.S. gallon of fuel at retail. The results are presented below. Note: results must be multiplied by $1,000,000: Coefficient Estimates | | | | | | Standard Error | Predictor | Coefficient | of the Coefficient | Intercept | 78 | 13.710 | ∆1 GDP | 30.22 | 12.120 | ∆2$ Fuel | -412.39 | 183.981 |
Analysis of Variance Table (ANOVA) | | | | | Source | Degrees of Freedom | Sum of Squares | Mean Square | Regression | 2 | 291.30 | 145.65 | Error | 27 | 132.12 | 4.89 | Total | 29 | 423.42 | |
In 2002, if GDP rises 2.2 percent and the price of fuels falls $0.15, Baltz’s model will predict Company sales in 2002 to be (in $ millions) closest to: A) 128. B) 82. C) 254. D) 206. The correct answer was D) Sales will be closest to $78 + ($30.22 * 2.2) + ((-412.39) * (-$0.15)) = $206.34 million. 8.Baltz proceeds to test the hypothesis that none of the independent variables has significant explanatory power. He concludes that, at a 5 percent level of significance: A) at least one of the independent variables has explanatory power, because the calculated F-statistic exceeds its critical value. B) all of the independent variables have explanatory power, because the calculated F-statistic exceeds its critical value. C) none of the independent variables has explanatory power, because the calculated F-statistic does not exceed its critical value. D) at least one of the independent variables has explanatory power, because the calculated F-statistic does not exceed its critical value. The correct answer was A) From the ANOVA table, the calculated F-statistic is (mean square regression / mean square error) = 145.65 / 4.89 = 29.7853. From the F distribution table (2 df numerator, 27 df denominator) the F-critical value may be interpolated to be 3.36. Because 29.7853 is greater than 3.36, Baltz rejects the null hypothesis and concludes that at least one of the independent variables has explanatory power. 9.Baltz then tests the individual variables, at a 5 percent level of significance, to determine whether sales are explained by individual changes in GDP and fuel prices. Baltz concludes that: A) both GDP and fuel price changes explain changes in sales. B) neither GDP nor fuel price changes explain changes in sales. C) only GDP changes explain changes in sales. D) only fuel price changes explain changes in sales. The correct answer was A) From the ANOVA table, the calculated t-statistics are (30.22/12.12) = 2.49 for GDP and (-412.39 /183.981) = -2.24 for fuel prices. These values are both outside the t-critical value at 27 degrees of freedom of ±2.052. Therefore, Baltz is able to reject the null hypothesis that these coefficients are equal to zero, and concludes that each variable is important in explaining sales. 10.In a recent analysis of salaries (in $1,000) of financial analysts, a regression of salaries on education, experience, and gender is run. Gender equals one for men and zero for women. The regression results from a sample of 230 financial analysts are presented below, with t-statistics in parenthesis. Salaries = 34.98 + 1.2 Education + 0.5 Experience + 6.3 Gender (29.11) (8.93) (2.98) (1.58) What is the expected salary (in $1,000) of a woman with 16 years of education and 10 years of experience? A) 54.98. B) 59.18. C) 61.28. D) 65.48. The correct answer was B) 34.98 + 1.2(16) + 0.5(10) = 59.18 | 
发表于 2008-4-8 16:31
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