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

2. How much variance is not explained by the model? Test the validity of the models that X predict Y (provide hypotheses, decision, conclusion and conclusion in the business context)

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.815223777
R Square	0.664589806
Adjusted R Square	0.636638957
Standard Error	2.03641213
Observations	40
ANOVA
	df	SS	MS	F	Significance F
Regression	3	295.8089229	98.60297429	23.77708797	1.16489E-08
Residual	36	149.2910771	4.146974365
Total	39	445.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	5.043869282	3.279448261	1.538023741	0.132786894	-1.607160062	11.69489863
Age	0.042709678	0.084498975	0.5054461	0.616326346	-0.128662187	0.214081542
Years	0.505635057	0.123366833	4.098630432	0.000225843	0.255435523	0.755834591
Pay	-0.067275395	0.062311694	-1.079659227	0.28747453	-0.193649368	0.059098577

2. How much variance is not explained by the model?

This is given by R-squared or coefficient of determination.

R Square

0.664589806

So 66.45 % variation in y is explained by the model and 33.54% variation is not explained by this model.

Hypothesis:

H_0: The regression is not significant.

H_1: The regression is significant.

The significance level of F-statistic = 1.16489*10^{-8} << 0.05

This probability is low enough to reject the null hypothesis using the common significance level of 0.05.

So We reject the null hypothesis that the regression is not significant.

We conclude that the regression is significant.