Question

The Postal Service is attempting to reduce the number of complaints made by the public against its workers. In order to facilitate this task, a staff analyst for the Service regresses the number of complaints lodged against an employee last year (Y) on the hourly wage of the employee for the year (X). She obtains the following results.

Ŷ = 10.2 – 1.9X

r2 = .73 Sy|x = 1.1 sb = .87 n = 348

Based on these results, answer the following questions:

(a) If wages were increased by $1.00, what is the expected effect on the number of complaints received per employee?

(b) What percent of the variation in complaints can be explained by wages?

(c) At what level of wages can the employee be expected to receive zero (0) complaints?

(d) Can the null hypothesis be rejected at the .05 level of statistical significance that wages have no effect on the number of complaints?

(e) Discuss a possible policy implication of the regression analysis.

Answer 1

Solution :

a)

If wages were increased by $1 what is the effect on the number of complaints received per employee?

The number of complaints received per employee will decrease by 1.9.

b)

What percent of the variation and complaints can be explained by wages?

R2 = 0.73 = 73%

c)

At what level of wages can the employee be expected to receive zero (0) complaints?

Y =10.2 - 1.9X

Put Y = 0

0 = 10.2 - 1.9X

X = 5.368421

e)

Discuss a possible policy implication of the regression analysis?

Decreasing the hourly wage of the employee for the year will result in an increase the number of complaints lodged against an employee last year.

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