A manager of a product sales group believes the number of sa

A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). She decides to perform a multiple linear regression to test this belief and use the resulting information for predicting sales. A random sample of 8 employees provides the following data:

Employee        Y         X1       X2

1          100      10        7

2          90        3          10

3          80        8          9

4          70        5          4

5          60        5          8

6          50        7          5

7          40        1          4

8          30        1          1

a. What is the adjusted r² for this model?

b. What is the value for the three regression coefficients, b0, b1, and b2?

c. For each coefficient, determine whether it is significant at the 95% confidence level? Explain.

d. Using the regression model as estimated, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what does the model predict for his or her expected sales?

e. Prepare a residuals plot against the two independent variables and comment on your interpretation of the results.

Solution

a) Adjusted R² = 0.61954

b) b₀= 21.2931; b₁=3.103448; b₂=4.698276

c) p-value for b_0, b₁ and b₂ respectively are 0.166,0.178 and 0.078. i.e., each coefficient is significant at 0.05 level

d) the model is given by 21.2931+3.103448*X₁ +4.698276*X₂ hence for given values the predicted sales = 79

e) Here X is X₁ and Z = X₂