Question

When one company (A) buys another company(B), some workers of company B are terminated. Terminated workers get severance pay. To be fair, company A fixes the severance payment to company B workers as equivalent to company A workers who were terminated in the last one year. A 36-year-old Mohammed, worked for company B for the last 10 years earning 32000 per year, was terminated with a severance pay of 5 weeks of salary. Bill smith complained that this is unfair that someone with the same credentials worked in company A received more. You are called in to settle the dispute. You are told that severance is determined by three factors; age, length of service with the company and the pay. You have randomly taken a sample of 40 employees of company A terminated last year. You recorded

Number of weeks of severance pay

Age of employee

Number of years with the company

Annual pay in 1000s

Weeks SP	Age	Years	Pay	Weeks SP	Age	Years	Pay
13	37	16	46	11	44	12	35
13	53	19	48	10	33	13	32
11	36	8	35	8	41	14	42
14	44	16	33	5	33	7	37
3	28	4	40	6	27	4	35
10	43	9	31	14	39	12	36
4	29	3	33	12	50	17	30
7	31	2	43	10	43	11	29
12	45	15	40	14	49	14	29
7	44	15	32	12	48	17	36
8	42	13	42	12	41	17	37
11	41	10	38	8	39	8	36
9	32	5	25	12	49	16	28
10	45	13	36	10	37	10	35
18	48	19	40	11	37	13	37
10	46	14	36	17	52	20	34
8	28	6	22	13	42	11	33
15	44	16	32	14	42	19	38
7	40	6	27	5	27	2	25
9	37	8	37	11	50	15	36

Identify best subsets of variables based on Mallows Cp. What is the value of R-square to this “best” model? How many outliers are in the dataset? Use the criteria of your choice and mention it(them)

Answer 1

using excel , to estimate the number of weeks SP the regression analysis output is

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.815224
R Square	0.66459
Adjusted R Square	0.636639
Standard Error	2.036412
Observations	40
ANOVA
	df	SS	MS	F	Significance F
Regression	3	295.8089	98.60297	23.77709	1.16E-08
Residual	36	149.2911	4.146974
Total	39	445.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	5.043869	3.279448	1.538024	0.132787	-1.60716	11.6949	-1.60716	11.6949
Age	0.04271	0.084499	0.505446	0.616326	-0.12866	0.214082	-0.12866	0.214082
years	0.505635	0.123367	4.09863	0.000226	0.255436	0.755835	0.255436	0.755835
pay	-0.06728	0.062312	-1.07966	0.287475	-0.19365	0.059099	-0.19365	0.059099

the value of R square 0.66459

there are two outliers present in the independent variable pay which are 22 and 48