Multiple Regression Example 1 -
Discrimination in Layoffs
When one company buys another company, it is not unusual that
some workers are terminated. The severance benefits offered to the
laid-off workers are often the subject of dispute. Suppose that the
Floopy Enterprises recently bought the Western Company and
subsequently terminated 20 of Western's employees. As part of the
buyout agreement, it's promised that the severance packages offered
to the former western employees would be equivalent to those offered
to Floopy Enterprises employees who had been terminated in the past
Thirty-six-year-old Cheryl Smith, a Western employee for the past two
years, earning $32,000 per year, was one of those let go. her
severance package included an offer of 5 weeks of severance pay.
Cheryl complained that their offer was less than that offered to Floopy
Enterprises's employees when they were laid off, in contravention of
the buyout agreement.
A statistician was called in to settle the dispute. The statistician was
told that severance is determined by three factors: age, length of
service with the company, and pay. To determine how generous the
severance package had been, a random sample of 50 Floopy
Enterprises ex-employees was taken.
Number of weeks of severance pay
Age of employee
Number of years with the company
Annual pay (in thousands of dollars)
The Regression Equation
y = 6.061 - .00781(x1) + .603(x2) - .0702(x3)
y [Weeks_SP] = 6.061 - .00781(Age) + .603(Years) - .0702(Pay)
y = 6.061 - .00781(36) + .603(2) - .0702(32)
y = 6.061 - .2812 + 1.206 - 2.246
y = 4.7398
So, we conclude that Cheryl was treated fairly.
As for the other questions, the overall model
was significant, F(3, 46) = 36.11, p < .001, R2
= .702; Only "years of service" was of real use.
The other predictors were nonsignificant (i.e.,
ps > .05).