Questions: Question 1 A statistician was interested in studying the determinants of the salaries of Chief Executive Officers (CEO) of companies. Data was collected from a sample of 209 firms. The model, the list of variables and the basic output are shown below. log(salary) = β₀ + β₁*log(sales) + β₂*roe + β₃*finance + ε List of variables: salary: the annual salary of the CEO in small dollars sales: the annual sales of the company in small dollars roe: return on equity finance: a dummy variable that equals one if the company is in the financial industry and zero for other sectors industrial: a dummy variable that equals one if the company is in industrial firm and zero for other firms Model output: [Table of regression output showing coefficients, standard errors, t-values, and p-values for the intercept, log(sales), roe, and finance variables] [Additional statistical output including R-squared, adjusted R-squared, F-statistic, and residual standard error] [Breusch-Pagan test results] [Variance Inflation Factors (VIF) results] [Cameron Trivedi's decomposition of IM-test results] Which statements are correct? (You may tick more than one of the tickboxes below, provided they are correct) □ At the significance level of 1%, the intercept is significant but the model suffers from heteroskedasticity □ At the significance level of 5%, the finance variable and intercept are the only statistically significant variables □ At the significance level of 1%, the White's test indicates that the model suffers from heteroskedasticity □ The White test shows there is heteroskedasticity at the significance level of 5%

To determine which statements are correct, we need to analyze the provided regression output and diagnostic test results. Since the actual numerical values and test results are not provided in the question, I will outline the steps you should take to evaluate each statement based on typical regression analysis procedures.

1. At the significance level of 1%, the intercept is significant but the model suffers from heteroskedasticity:

   • Intercept Significance: Check the p-value for the intercept. If the p-value is less than 0.01, the intercept is significant at the 1% level.
   • Heteroskedasticity: Check the results of the Breusch-Pagan test or White's test. If the p-value for these tests is less than 0.01, the model suffers from heteroskedasticity at the 1% significance level.

2. At the significance level of 5%, the finance variable and intercept are the only statistically significant variables:

   • Significance of Variables: Check the p-values for the finance variable and the intercept. If their p-values are less than 0.05, they are significant at the 5% level. Also, check the p-values for other variables (log(sales) and roe). If their p-values are greater than 0.05, they are not significant at the 5% level.

3. At the significance level of 1%, the White's test indicates that the model suffers from heteroskedasticity:

   • White's Test: Check the p-value for White's test. If the p-value is less than 0.01, the model suffers from heteroskedasticity at the 1% significance level.

4. The White test shows there is heteroskedasticity at the significance level of 5%:

   • White's Test: Check the p-value for White's test. If the p-value is less than 0.05, the model suffers from heteroskedasticity at the 5% significance level.

1. At the significance level of 1%, the intercept is significant but the model suffers from heteroskedasticity:

   • If the p-value for the intercept is less than 0.01, it is significant at the 1% level.
   • If the Breusch-Pagan test or White's test p-value is less than 0.01, the model suffers from heteroskedasticity at the 1% level.
   • Correct if both conditions are met.

2. At the significance level of 5%, the finance variable and intercept are the only statistically significant variables:

   • If the p-values for the finance variable and intercept are less than 0.05, they are significant at the 5% level.
   • If the p-values for log(sales) and roe are greater than 0.05, they are not significant at the 5% level.
   • Correct if all these conditions are met.

3. At the significance level of 1%, the White's test indicates that the model suffers from heteroskedasticity:

   • If the p-value for White's test is less than 0.01, the model suffers from heteroskedasticity at the 1% level.
   • Correct if this condition is met.

4. The White test shows there is heteroskedasticity at the significance level of 5%:

   • If the p-value for White's test is less than 0.05, the model suffers from heteroskedasticity at the 5% level.
   • Correct if this condition is met.

Without the actual numerical values, we cannot definitively determine which statements are correct. However, you can use the outlined steps to check the regression output and diagnostic test results to verify the correctness of each statement.