Question: Reducing the number of workers. To be competitive in global markets, many corporations are undertaking major reorganizations. Often these involve "downsizing" or a "reduction in force" (RIF), where 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                         7              41

No                         504           765

(a) Write the logistic regression model for this problem using the log odds of a RIF as the response variable and an indicator for over and under 40 years of age as the explanatory variable.

(b) Explain the assumptions concerning binomial distributions in terms of the variables in this exercise. To what extent do you think that these assumptions are reasonable?

(c) Software gives the estimated slope b1 = 1.3504 and its standard error SEb1 = 0.4130. Transform the results to the odds scale. Summarize the results and write a short conclusion.

(d) If additional explanatory variables were available (for example, a performance evaluation), how would you use this information to study the RIF?