Suppose that you are interested in examining the relationship between executive compensation and three independent variables that you believe have an effect: Proficiency in a second language, education level, and work experience abroad. You want to be sure, however, that conditional heteroscedasticity is not present in your data. Therefore, you regress the squared residuals of the regression model onto the three independent variables, and you find that the R2 for the regression 0.181. Your sample size of executives is 36.a. What is the name of the test that is used to determine if conditional heteroscedasticity is present? b. Using the information provided, calculate the F-statistic that you would use to determine if there is conditional heteroskedasticity present. c. Using the information provided, calculate the χ2 test statistic (LM method) that you would use to determine if there is conditional heteroskedasticity present. d. What critical value would you use if you are testing at a 5% significance level using the F-test approach? e. What critical value would you use if you are testing at a 5% significance level using the χ2 test approach?

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Suppose that you are interested in examining the relationship between executive compensation and three independent variables that you believe have an effect: Proficiency in a second language, education level, and work experience abroad. You want to be sure, however, that conditional heteroscedasticity is not present in your data. Therefore, you regress the squared residuals of the regression model onto the three independent variables, and you find that the R2 for the regression 0.181. Your sample size of executives is 36.a. What is the name of the test that is used to determine if conditional heteroscedasticity is present? b. Using the information provided, calculate the F-statistic that you would use to determine if there is conditional heteroskedasticity present.  c. Using the information provided, calculate the χ2 test statistic (LM method) that you would use to determine if there is conditional heteroskedasticity present. d. What critical value would you use if you are testing at a 5% significance level using the F-test approach? e. What critical value would you use if you are testing at a 5% significance level using the χ2 test approach?

Lesly Fernandez · Accepted Answer

Introduction -F-staticF=R2(k−1)(1−R2)(n−k)F=χ2awhere a=degree of freedomExplanation -a)  The name of the test that is used to determine if conditional heteroscedasticity is present is chi-squared test .b) n=36k=3R2=0.181F=0.181(3−1)(1−0.181)(36−3)F=0.9050.273=0.331c) chi-squared test F-static=0.331Degree of freedom of chi-squared test =(n-k)=(36-3)=33Chi -squared =33(0.331)=10.939d) F-statistic p-value at 5% level of significance p-value =0.7205 (calculated by using p-value calculator for f-test)since p-value is less critical region therefore , null hypothesis is reject at 5% level of significance .So , the test is significant.Conclusion -a)The name of the test that is used to determine if conditional heteroscedasticity is present is chi-squared test .b) f-static =0.331c) chi squared test =10.939d)  F-test Test is significant at 5% level of significance.

German Ferguson · Accepted Answer

e) Chi-squared test p-value at 5% level of significance p-value =0.9998 (calculated by p-value calculator for chi-squared test )since , p- value is less than test static therefore null hypothesis is rejected at 5% level of significance so . the test is significant.So, e)  Chi-squared test test is significant at 5% level of significance

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