Question

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 of severance pay,Age of employee,Number of years with the company,Annual pay (in thousands of dollars),

A. Determine the regression equation.

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

***USE EXCEL, or xlstat***

Weeks SP	Age	Years	Pay
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

Answer 1

Solution:

Here, we have to predict the response variable or dependent variable severance based on three independent variables age, number of years with the company, and annual pay in thousands of dollars. The excel output for this regression model is given as below:

Regression Statistics
Multiple R	0.837840782
R Square	0.701977176
Adjusted R Square	0.682540905
Standard Error	1.921049084
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	3	399.8602392	133.2867464	36.11686484	3.75831E-12
Residual	46	169.7597608	3.690429582
Total	49	569.62
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	6.061146253	2.604023375	2.327608235	0.024387039	0.819519144	11.30277336
Age	-0.007806104	0.066413795	-0.117537395	0.906945933	-0.141490138	0.125877929
Years	0.603481938	0.096560144	6.249803606	1.22137E-07	0.409116451	0.797847424
Pay	-0.070245631	0.052370206	-1.341328141	0.186399135	-0.175661386	0.035170124

A. Determine the regression equation.

From above regression output, the regression output is given as below:

Severance Package = 6.061146253 - 0.007806104*Age + 0.603481938*Years - 0.070245631*Pay

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

The P-value for this regression model is given as 0.0000 which is less than alpha value 0.05, so we reject the null hypothesis that the given regression model is not statistically significant. So, there is sufficient evidence to conclude that the given regression model is statistically significant and we can use this regression model for the further prediction purpose.