Question

Suppose a researcher gathered survey data from 19 employees and asked the employees to rate their job satisfaction on a scale from 0 to 100 (with 100 being perfectly satisfied). Suppose the following data represent the results of this survey. Assume that relationship with their supervisor is rated on a scale from 0 to 50 (0 represents a poor relationship and 50 represents an excellent relationship); overall quality of the work environment is rated on a scale from 0 to 100 (0 represents poor work environment and 100 represents an excellent work environment); and opportunities for advancement is rated on a scale from 0 to 100 (0 represents no opportunities and 100 represents excellent opportunities). Answer the following questions: What is the regression formula based on the results from your regression? How reliable do you think the estimates will be based on this formula? Explain your answer by citing the relevant metrics. Are there any variables that do not appear to be good predictors of job satisfaction? How can you tell? If a new employee reports that her relationship with her supervisor is 40, rates her opportunities for advancement to be at 30, finds the quality of the work environment to be at 75, and works 60 hours per week, what would you expect her job satisfaction score to be?

Job satisfaction	Relationship with supervisor	Opportunities for advancement	Overall quality of work environment	Total hours worked per week
55	27	42	50	52
20	35	28	60	60
85	40	7	45	42
65	35	48	65	53
45	29	32	40	58
70	42	41	50	48
35	22	18	75	55
60	34	32	40	50
95	40	48	45	40
65	33	11	60	38
85	38	33	55	47
10	5	21	50	62
75	37	42	45	43
80	37	46	40	42
50	31	48	60	46
90	42	30	55	38
75	36	39	70	43
45	20	22	40	42
65	32	12	55	53

Answer 1

Suppose a researcher gathered survey data from 19 employees and asked the employees to rate their job satisfaction on a scale from 0 to 100 (with 100 being perfectly satisfied).

We take job satisfaction as the dependent variable and relationship with their supervisor, total hour worked per week, overall quality of work environment and opportunity in advancement are independent variables.

The multiple linear regression output using SPSS software is given below

Variables Entered/Removeda
Model	Variables Entered	Variables Removed	Method
1	Total hour worked per week, overall quality of work environment, opportunity in advancement, Relationship with supevisorb	.	Enter
a. Dependent Variable: Job satisfaction
b. All requested variables entered.

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.970a	.941	.925	6.35510
a. Predictors: (Constant), total hour worked per week, overall quality of work environment, opportunity in advancement, Relationship with supervisor

ANOVAa
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	9087.209	4	2271.802	56.250	.000b
Residual	565.423	14	40.387
Total	9652.632	18
a. Dependent Variable: Job satisfaction
b. Predictors: (Constant), total hour worked per week, overall quality of work environment, opportunity in advancement, Relationship with supervisor

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
B	Std. Error	Beta
1	(Constant)	4.359	10.251		.425	.677
Relationship with supervisor	2.052	.171	1.010	11.977	.000
opportunity in advancement	-.178	.120	-.103	-1.481	.161
the overall quality of the work environment	-.037	.145	-.017	-.252	.805
total hour worked per week	-.030	.133	-.018	-.223	.826
a. Dependent Variable: Job satisfaction

What is the regression formula?

From the coefficient table,

The canonical form of the regression line is

Where Y = job satisfaction( Dependent variable)

X1, X2, X3, and X 4 are independent variables.

B0 = Y intercept

B1, B2, B3, and B4 are the slope of the four predictors.

--------------------------1)

How reliable do you think the estimates will be based on this formula? Explain your answer by citing the relevant metrics.

The regression hypothesis is given by

The null hypothesis is

H0: There is no statistically significant relationship between the dependent variable and independent variables.

The alternative hypothesis is

Ha: There is a statistically significant relationship between the dependent variable and independent variables.

ANOVA table provides us with model fit or predictive power (estimate) of the independent variable on the dependent variable.

From the ANOVA table, we can observe p-value associated with the F test is less than 0.05( p=0.000). Hence we reject the null hypothesis and conclude that there is a statistically significant relationship between the dependent variable and independent variables.

Are there any variables that do not appear to be good predictors of job satisfaction? How can you tell?

Yes. There are two variables that do not appear to be good predictors of job satisfaction.

1) overall quality of work environment: t-test static value is -.252 and p-value associated with t-test is also very high (0.805).

2) total hour worked per week: t-test static value is -.22 and p-value associated with t-test is also very high (0.829).

If a new employee reports that her relationship with her supervisor is 40, rates her opportunities for advancement to be at 30, finds the quality of the work environment to be at 75, and works 60 hours per week, what would you expect her job satisfaction score to be?

Put X1= 40, X2=30, X3= 75 AND X4=60 in equation 1, we have the value of job satisfaction

Job satisfaction y= 77