Question

A large corporation is interested in predicting a measure of job satisfaction among it employees. They have collected data on 15 employees who each supplied information on job satisfaction, level of responsibility, number of people supervised, rating of working environment and year of service.

Please write out the regression equation of using all predictors and explain the equation.

Which predictor(s) is(are) very important predictor(s) to predict job satisfaction? Why do you select it (them)?

Use the important predictors to form a regression equation and compare this equation with the previous calculated one.

Report all relevant results.

												Employee
Satisfaction	2		2			3	3		5		5		6	6		6	7		8		8		8		9		9
Responsibility	4		2			3	6		2		8		4	5		8	8		9		6		3		7		9
No. supervised	5		3			4	7		4		8		6	5		9	8		9		3		6		9		9
Environment rating	1		1			7	3		5		8		5	5		6	4		7		2		8		7		9
Years of service	5		7			5	3		3		6		3	2		7	3		5		5		8		8		1

Answer 1

SOLUTION:

The solution to this question might be a bit tricky because of the possibility of multicollinearity in the dataset. However, simple analysis can prove to be significant and sufficient for the question.

Job Satisfaction is usually affected by a number of factors. The one's that are given here can be termed as the predictors of Job-Satisfaction.

The possible solution Regression Equation to this can be,

Job Satisfaction = β₀ + β₁ Responsibility + β₂ No. of Supervised + β₃ Environment Rating + β₄ Years of Service + u_i

Thus, what we see here is that Job Satisfaction is a function of the other variables.

We can provide an explanation as follows,

The first term β₀ indicates that if all the other variables are 0, and have no effect, what will be the possible Job Satisfaction.

The second term β₁ indicates that what changes will occur in Job Satisfaction with a unit change in Responsibility.

The second term β₂indicates that what changes will occur in Job Satisfaction with a unit change in No. of People supervised.

The second term β₃indicates that what changes will occur in Job Satisfaction with a unit change in Environment Rating.

The second term β₄indicates that what changes will occur in Job Satisfaction with a unit change in Years of Service.

The last term is u_i which is nothing but the residual term in the errors.

The first step of analysis will be to run a multiple linear regression and check the results.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.698994
R Square	0.488592
Adjusted R Square	0.284029
Standard Error	2.052803
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	4	40.26001	10.065	2.388468	0.120439
Residual	10	42.13999	4.213999
Total	14	82.4
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1.559141	1.999689	0.779692	0.45363	-2.89644	6.014727	-2.89644	6.014727
Responsibility	0.607573	0.415223	1.463246	0.17411	-0.3176	1.532748	-0.3176	1.532748
No. of People Supervised	-0.33061	0.502991	-0.6573	0.525829	-1.45135	0.79012	-1.45135	0.79012
Environment Rating	0.483079	0.269828	1.79032	0.103673	-0.11814	1.084293	-0.11814	1.084293
Years of Service	0.084146	0.266413	0.315847	0.758612	-0.50946	0.677751	-0.50946	0.677751

Thus, what we see is all of the independent variables are showing insignificant results.

Thus, we need to check if their is possible correlation in the model.

Thus, the Correlation Coefficients will be as follows,

	Satisfaction	Responsibility	No. of People Supervised	Environment Rating	Years of Service
Satisfaction	1
Responsibility	0.562616	1
No. of People Supervised	0.506503	0.822024	1
Environment Rating	0.579897	0.402365	0.591278	1
Years of Service	-0.01077	-0.13843	0.057422	0.035604	1

Thus, there exists a substantial correlation between the variables specially between satisfaction, responsibility, no supervised, and environment rating.

However, we know that Job-Satisfaction can never be affected by the Number of years of service in a firm.

Thus, we can ignore that variable can show our regression equation as follows,

Job Satisfaction = β₀ + β₁ Responsibility + β₂ No. of Supervised + β₃ Environment Rating + u_i

Thus, we see that removing Years of Service, this must be an appropriate model.

The presence of statistical errors such as multicollinearity may be a possible problem for the model giving insignificant results.