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 $R}^{2$ 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 $\chi}^{2$ 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 $\chi}^{2$ test approach?