Question 17.31

17.31 Analysis of a reduction in force.

To meet competition or cope with economic slowdowns, corporations sometimes undertake a “reduction in force” (RIF), in which substantial numbers of employees are terminated. Federal and various state laws require that employees be treated equally regardless of their age. In particular, employees over the age of 40 years are in a “protected” class, and many allegations of discrimination focus on comparing employees over 40 with their younger coworkers. Here are the data for a recent RIF:

Over 40
Terminated No Yes
Yes 17 71
No 564 835
  1. Write the logistic regression model for this problem using the log odds of a termination as the response variable and an indicator for over and under 40 years of age as the explanatory variable.
  2. Explain the assumption concerning binomial distributions in terms of the variables in this exercise. To what extent do you think that these assumptions are reasonable?
  3. Software gives the estimated slope and its standard error . Transform the results to the odds scale. Summarize the results and write a short conclusion.
  4. If additional explanatory variables were available, for example, a performance evaluation, how would you use this information to study the RIF?

17.31

(a) . (b) The binomial distribution assumes that each employee's termination is independent from one another's and the probability of being terminated is the same for each employee. Certainly the latter is not true because an individual's performance is likely different and largely determines whether or not they are terminated. (c) , with 95% the confidence interval is (1.644, 4.840). Because the interval does not contain 1, the results are significant at the 5% level. Employees over 40 are 2.82 times more likely to be terminated than those under 40. (d) We could use the additional variables in the logistic regression model to account for their effects before assessing if age has an effect.