Question

The board of directors at a large corporation wants to base their division managers' pay raises on the profit performance of their respective divisions. They have asked you to evaluate the performance and raises at other companies and propose a formula for calculating the percentage increase in base pay based on the percentage change in the division's profit. You collected information from 50 divisions at similar companies and performed a linear regression on the percentage change in the division profits vs. the percentage change in the manager’s salary.

Use what you have learned about linear regression to answer the following questions. Click here to download the output from the Excel ToolPak, Regression Tool.

Response Parameters

What is the regression equation from the Summary Output? Is this a useful model? How do you know?

Are the assumptions of regression satisfied? How did you verify them?

Does change in division profit appear to be a good predictor for the manager’s pay raise? Why do you think that?

One of your company’s divisions had a –0.51 percent change in profits last year, while another had a 20 percent increase. What is the predicted percentage change in salary for these two division managers?

Answer 1

Answers,

1)

General simple linear regression equation is,

,

b₀ = intercept parameter and b₁ = Slope parameter.

Then regression equation is,

managers salary =2.289 + 0.9513 * Increase in profits.

Yes, is this model is useful because the given R-Square value is 0.9321.

That means the calculated regression model explain the 93% variation and its predict good model.

2)

First assumption (linearity), linear regression needs the relationship between the independent and dependent variables to be linear.

This assumption can check by residual vs increase in profits plot, and this are scattered, then this model is linear.

Second assumption (Normality), the linear regression analysis requires all variables to be normal.

This assumption can check by Normal probability plot, and this are look line linear, then the data are normal.

3)

From all above the R square is good it explain 93% variation and assumptions also meat.

Then division profit appear to be a good predictor for the manager’s pay raise.

4)

One of company’s division had a –0.51 percent change in profits last year then percentage change in salary for managers is,

Calculate from above equation,

managers salary = 2.289 + 0.9513 * Increase in profits.

= 2.289 + 0.9513 * (-0.51)

= 1.8038%.

another divisions had a 20 percent increase

then percentage change in salary for managers is,

managers salary = 2.289 + 0.9513 * Increase in profits.

= 2.289 + 0.9513 * (20)

= 21.315%.