Question #121 - Reading 1 Multiple Regression

Reading: Reading 1 Multiple Regression

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of 139 Which of the following statements regarding heteroskedasticity is least accurate? A) When not related to independent variables, heteroskedasticity does not pose any major problems with the regression. B) Heteroskedasticity only occurs in cross-sectional regressions. C) Conditional heteroskedasticity can be detected using the Breusch-Pagan chi-square statistic. Binod Salve, CFA, is investigating the application of the Fama-French three-factor model (Model 1) for the Indian stock market for the period 2001–2011 (120 months). Using the dependent variable as annualized return (%), the results of the analysis are shown in Indian Equities—Fama-French Model Indian Equities—Fama-French Model Factor Coefficient P-Value VIF Intercept 1.22 <0.001 SMB 0.23 <0.001 3 HML 0.34 0.003 3 Rm-Rf 0.88 <0.001 2 R-squared 0.36 SSE 38.00 BG (lag 1) 2.11 BG (lag 2) 1.67 Partial F-Table (5% Level of Significance) Degrees of Freedom Denominator Degrees of Freedom Numerator 1 2 3 112 3.93 3.08 2.69 113 3.93 3.08 2.68 114 3.92 3.08 2.68 115 3.92 3.08 2.68 116 3.92 3.07 2.68 117 3.92 3.07 2.68 Partial Chi-Square Table (5% Level of Significance) Degrees of Freedom Critical Value 1 3.84 2 5.99 3 7.81 4 9.49 5 11.07 6 12.59

Question

Salve runs a regression using the squared residuals from the model using the original dependent variables. The coefficient of determination of this model is 6%. Which of the following is the most appropriate conclusion at a 5% level of significance?

Answer Choices:

A. Because the test statistic of 7.20 is higher than the critical value of 3.84, we reject the null hypothesis of no conditional heteroskedasticity in residuals

B. Because the test statistic of 7.20 is lower than the critical value of 7.81, we fail to reject the null hypothesis of no conditional heteroskedasticity in residuals

C. Because the test statistic of 3.60 is lower than the critical value of 3.84, we reject the null hypothesis of no conditional heteroskedasticity in residuals

Explanation

The chi-square test statistic = n × R2 = 120 × 0.06 = 7.20. The one-tailed critical value for a chi-square distribution with k = 3 degrees of freedom and α of 5% is 7.81. Therefore, we should not reject the null hypothesis and conclude that we don't have a problem with conditional heteroskedasticity.

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