A sample of 30 companies was randomly selected for a study investigating what factors affect the size of company bonuses. Data were collected on the number of employees at the company and whether or not the employees were unionized (1 = yes, 0 = no). Below are the multiple regression results. a. Write out the estimated regression equation.
b. Are all of the independent variables significant in this regression equation (using α = 0 .05)? Explain.
c. Interpret the coefficient of the Union.
d. Based on the scatterplot below, do you think using Union as an indicator variable in this model is appropriate? Explain. e. An alternative multiple regression model is fit to these data and the results are shown below. Which model is better? Explain. f. Using the better model, predict the annual average bonus for a company with 7500 employees that are not unionized.

Question

A sample of 30 companies was randomly selected for a study investigating what factors affect the size of company bonuses. Data were collected on the number of employees at the company and whether or not the employees were unionized (1 = yes, 0 = no). Below are the multiple regression results.  a. Write out the estimated regression equation.
b. Are all of the independent variables significant in this regression equation (using α = 0 .05)? Explain.
c. Interpret the coefficient of the Union.
d. Based on the scatterplot below, do you think using Union as an indicator variable in this model is appropriate? Explain.  e. An alternative multiple regression model is fit to these data and the results are shown below. Which model is better? Explain.  f. Using the better model, predict the annual average bonus for a company with 7500 employees that are not unionized.

Quizplus · Accepted Answer

The Answer is a. The regression equation is Average Annual Bonus = 347.9 + 0.6547 Employees + 1259.5 Union.
b. Yes, the P-value associated with each t-statistic for the regression coefficients of Employees and Union is less than 0.05, therefore in each case we reject the null hypothesis. We can conclude that the regression coefficients associated with these two independent variables are significantly different from zero.
c. The estimated regression coefficient for Union is 1259.5. This means that the annual average bonus is $1259.5 more for unionized companies compared to non-unionized companies of the same size (same number of employees).
d. The scatterplot shows that if we consider unionized and non-unionized companies separately, we see two different slopes (the lines are not parallel). This indicates that an interaction term Employees×Union rather than the indicator variable Union might be more appropriate.
e. This second model is better. All independent variables (including the interaction term) are significant. It has a higher R2 and R2Adj than the first model. It has a smaller S than the first model as well.
f. The predicted value is $5413.

A Sample of 30 Companies Was Randomly Selected for a Study