[#3] Regression Analysis, part 2.

Suppose you work for a manufacturing company. A regression model for employee salaries is shown above. The variables included in this new regression model are:

Y = Salary = Current annual salary in dollars.

X1 = Years_Previous_Experience = Number of years of relevant experience prior to coming to the company.

X2 = Years_Employed = Number of years employed by the company.

X3 = Years_Education = Number of years of education beyond high school.

X4 = Number_Supervised = Number of employees supervised by this employee.

X5 = Female = Indicator variable equal to “1” if the employee is female (base category is male).

X6 = Department: Purchasing = Indicator variable equal to “1” if the employee works in the Purchasing department (base category is Sales department).

X7 = Department: Advertising = Indicator variable equal to “1” if the employee works in the Advertising department (base category is Sales department).

X8 = Department: Engineering = Indicator variable equal to “1” if the employee works in the Engineering department (base category is Sales department)

a. After adding additional independent variables, what happened to the value of the Rsquare? Does this indicate that the regression model has been improved or made worse? Explain.

b. Can you think of an omitted variable that could improve the explanatory fit of the model? Provide an example and explain your reasoning.

c. Using the test statistic method, do a hypothesis test for whether a linear relationship exists between Number_Supervised and Salary. Show all steps to your hypothesis test and use a significance level of 5%.

d. Using the p-value method, perform separate hypothesis tests for whether there is a statistically significant difference between salaries in each of the three departments compared to the Sales department.

e. Can you think of an omitted variable that, if added to the model, could introduce multicollinearity? Provide an example and explain your reasoning.