Multiple Regression Analysis

• This question paper consists of 20 mandatory questions, each worth 5 marks
• Answers should be input into the Brightspace quiz section via the ProctorFree student portal.
• A scientific calculator is allowed, but it cannot be programmable, have wireless capabilities, store textual information, or require a mains electricity supply.
• A formula sheet and present value tables are provided in the appendix.

Information for questions 1 to 10

• A multiple linear regression model was used to determine the average hourly earnings of workers.
• The variables include: ahe, bachelor, female, and age.
• ahe represents worker's average hourly earnings in US Dollars per hour.
• bachelor is a dummy variable (1 for bachelor, 0 for non-bachelor).
• female is a dummy variable (1 for female, 0 for male).
• age represents worker's age in years.

Question 1

• The standard error of the coefficient of the regressor age is 0.045.

Question 2

• The 95% confidence interval estimator for the coefficient of the regressor bachelor is [9.33, 10.36].

Question 3

• Heteroscedasticity can cause the usual OLS t statistics to be invalid.

Question 4

• The error term u having zero variance given any values of the explanatory variable is not a Gauss-Markov assumption of the multiple linear regression model.

Question 5

• The correct interpretation of the coefficient for the regressor bachelor is that an individual with a bachelor's degree is expected to earn US$ 9.84 more in average hourly earnings than individuals without a bachelor's degree.

Question 6

• To estimate the effect of age on a worker's average hourly earnings, run a regression with age as the independent variable and the log of average hourly earnings as the dependent variable to see how an increase in one year of age increases the average hourly earnings by a constant percentage.

Question 7

• A low regression R² implies that other important factors influence the dependent variable.

Question 8

• If multicollinearity is present in a model, remove highly correlated predictors from the model.

Question 9

• The Jarque-Bera test results suggest that the null hypothesis that the residuals are normally distributed can be rejected at a significance level of 5%.

Question 10

• For a male individual with 36 years of age and a bachelor's degree, the expected average hourly earnings are approximately $31.02.

Information for questions 11 to 20

• A multiple linear regression model was calculated to determine the logarithm of the median salary for new law school graduates.
• The variables featured include: log(salary), LSAT, GPA, log(libvol), log(cost), rank, and faculty.
• log(salary) represents the log of the median salary for new law school graduates (salary measured in $1000s).
• LSAT represents the median LSAT score for the graduating class.
• GPA represents the median college GPA for the class.
• log(livbol) is The Log of the number of volumes in the law school library
• log(cost) represents the log of the annual cost of attending law school (cost measured in $1000s).
• rank represents the law school ranking (1 is the best).
• faculty represents the number of faculty in the law school.

Question 11

• A 1% increase in the cost of a law school is predicted to increase in approximately 4.9% the median salary of new law school graduates.

Question 12

• Omitted variable bias is a potential problem because it prevents accurately estimating true marginal effects.

Question 13

• Based on the p-value for the F-Test in the Summary, reject the null hypothesis that none of the variables have an impact in lsalary if the p-value is less than 5%.

Question 14

• The variable is not significant at a 5% level since the t-statistic is 1.13.

Question 15

• If the adjusted R² of the regression is 0.823 whereas the adjusted R² of a regression which has faculty as an additional regressor is 0.849, then including an additional regressor has improved the fit of the regression; therefore, including an additional regressor has improved the fit of the regression.

Question 16

• The fan-shaped pattern of residuals suggest the presence of heteroskedasticity.

Question 17

• A normally distributed variable has a skewness of 0 and a kurtosis of 3.

Question 18

• The null hypothesis of homoskedasticity can be rejected at the 5% significance level.

Question 19

• Errors are homoscedastic if the conditional variance of the errors is constant.

Question 20

• The 95% confident set for multiple coefficients is the set of values not rejected at the 5% confidence level by the F-Statistic for a test of the joint hypothesis.

This question paper focuses on multiple linear regression, specifically determining the average hourly earnings of workers. The variables considered are average hourly earnings, bachelor's degree attainment, gender, and age. It includes calculating confidence intervals and regression analysis.