Buyout Agreement

        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 Laurier   Company recently bought the Western Company and subsequently terminated 20 of Western’s employees. As part of the buyout agreement, it was promised that the severance packages offered to the former Western employees would be equivalent to those offered to Laurier employees who had been terminated in   the past year.

Thirty-six-year-old Bill Smith a Western employee for the past   10 years, earning $32,000 per year, was one of those let go. His severance   package included an offer of 5 weeks’ severance pay. Bill complained that   this offer was less than that offered to Laurier’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 Laurier ex-employees was taken. For each, the following   variables were recorded:

  Number   of weeks if severance pay    Age   of employee     Annual   pay (in thousands of dollars)          SP Weeks (y) Age (x1) Service (x2) Pay (x3)   13 37 16 46   13 53 19 48   11 36 8 35   14 44 16 33   3 28 4 40   10 43 9 31   4 29 3 33   7 31 2 43   12 45 15 40   7 44 15 32   8 42 13 42   11 41 10 38   9 32 5 25   10 45 13 36   18 48 19 40   17 52 20 34   13 42 11 33   14 42 19 38   5 27 2 25   11 50 15 36   10 46 14 36   8 28 6 22   15 44 16 32   7 40 6 27   9 37 8 37   11 44 12 35   10 33 13 32   8 41 14 42   5 33 7 37   6 27 4 35   14 39 12 36   12 50 17 30   10 43 11 29   14 49 14 29   12 48 17 36   12 41 17 37   8 39 8 36   12 49 16 28   10 37 10 35   11 37 13 37   15 44 19 33   5 31 6 37   8 42 9 36   11 40 11 32   15 35 15 30   11 46 13 40   6 25 5 33   6 40 7 33   13 40 14 48   9 38 10 37    

     A)   Determine the regression equation    

     B)Comment   on how well the model fits the data.    

     C) Do all   the independent variables belong in the equation? Explain    

     D) Perform   an analysis to determine whether Bill is correct in his assessment of the   severance package.