20.19. The human resources manager of a telemarketing firm is concerned about the rapid turnover of the firm’s telemarketers. It appears that many telemarketers do not work very long before quitting. There may be a number of reasons, including relatively low pay, personal unsuitability for the work, and the low probability of advancement. Because of the high cost of hiring and training new workers, the manager decided to examine the factors that influence the workers to quite. He reviewed the work history of a random sample of workers who have quit in the last year and recorded the number of weeks on the job before quitting, the age of each worker when originally hired and the gender of each worker (1=female, 0=male). These

(a)  Use regression analysis to describe how work period is related to age and gender.

(b)  Discuss what the coefficients tell you.

(c)  Can we infer that among female telemarketers and male telemarketers of the same age, female telemarketers stay at their jobs longer than male telemarketers.

Let Y=Work period (Job), and

= 1 if gender is female

= 0 if gender is male

We consider the following regression model:

Response Job

Whole Model

Actual by Predicted Plot

Summary of Fit

RSquare / 0.228437
RSquare Adj / 0.208396
Root Mean Square Error / 1.779302
Mean of Response / 26.275
Observations (or Sum Wgts) / 80

Analysis of Variance

Source / DF / Sum of Squares / Mean Square / F Ratio /
Model / 2 / 72.17452 / 36.0873 / 11.3987
Error / 77 / 243.77548 / 3.1659 / Prob > F
C. Total / 79 / 315.95000 / <.0001

Parameter Estimates

Term / Estimate / Std Error / t Ratio / Prob>|t| /
Intercept / 29.495446 / 1.171994 / 25.17 / <.0001
Age / -0.096953 / 0.028755 / -3.37 / 0.0012
Gender / 0.8507287 / 0.425459 / 2.00 / 0.0491

Effect Tests

Source / Nparm / DF / Sum of Squares / F Ratio / Prob > F /
Age / 1 / 1 / 35.991963 / 11.3686 / 0.0012
Gender / 1 / 1 / 12.658013 / 3.9982 / 0.0491

Residual by Predicted Plot

For both men and women, the decrease in expected job period for an increase of one year in age is 0.097 weeks. For a man and woman of the same age, women work an average of 0.851 weeks longer on average. We can infer that among male and female telemarketers of the same age, female telemarketers stay on their jobs longer on average at the 5% significance level (the p-value for this test is 0.0491).

Note: The above regression model assumes that there is no interaction between gender and age and also that a first-order model is appropriate for age. A second order model would be: