Question

You are asked to study the determinants of job satisfaction at your new company. After randomly selecting 40 employees to fill out a questionnaire you regress their job satisfactions score (JOBSAT) on the following variables: SCHOOL = years of schooling MALE = 1 if male Engr = 1 if employee is in the technical division Adv = 1 if employee is in the marketing division Sales = 1 if employee is in the sales division Exec = 1 if employee is in the corporate division Some regression output is attached following the questions below: a) Test whether any of the explanatory variables are related to job satisfaction b) Test the hypothesis that schooling affects job satisfaction c) Give a confidence interval for the coefficient for the MALE variable. What does the interval imply about male versus female job satisfaction? d) Test whether an employee’s job satisfaction depends on the department where they work 4 e) When explaining your results to your boss, she questions whether you performed your analysis correctly since there are four departments in your firm but you only included variables for three departments. How would you respond?

The regression equation is JOBSAT = 51.8 + 3.48 MALE + 0.504 SCHOOL + 6.06 Engr -0.37 Adv +2.99 Sales

Predictor Coef Stdev t-ratio

Constant 51.798 6.888 7.52

MALE 3.484 1.558 2.24

SCHOOL 0.504 0.478 1.05

Engr 6.055 2.219 2.73

Adv -0.370 2.308 -0.16

Sales 2.987 2.190 1.36

s = 4.869 R-sq = 35.3% R-sq(adj) = 25.8%

Analysis of Variance

SOURCE DF SS MS F p

Regression 5 440.18 88.04 3.71 0.009

Error 34 805.89 23.70

Total 39 1246.07

The regression equation is JOBSAT = 53.8 + 3.48 MALE + 0.517 SCHOOL

Predictor Coef Stdev t-ratio

Constant 51.794 6.677 8.06

MALE 3.477 1.723 2.02

SCHOOL 0.517 0.498 1.04 s = 5.390 R-sq = 13.7% R-sq(adj) = 9.1%

Analysis of Variance

SOURCE DF SS MS F p

Regression 2 171.18 85.50 2.94 0.065

Error 37 1075.08 29.06

Total 39 1246.07

Answer 1

a)

Hypothesis:

The null hypothesis is defined as no variable fits the regression model and the alternative hypothesis test the claim that at least one variable significantly fit the regression model, i.e

Let the significance level = 0.05

Test statistic and P-value:

From the regression model ANOVA table,

F-statistic = 3.71

P-value = 0.009

Decision and Conclusion:

Since the p-value = 0.009 is less than 0.05 at a 5% significance level, the null hypothesis is rejected. Hence we can conclude that at least one independent variables significantly fit the regression model.

b)

Hypothesis:

The null hypothesis is defined as the coefficient of variable years of schooling is zero and the alternative hypothesis test the claim that coefficient of variable years of schooling is not zero, i.e

Let the significance level = 0.05

Test statistic and P-value:

From the regression model,

t-statistic = 1.05

The p-value is obtained from the t distribution table for the degree of freedom = 34

P-value = 0.1506

Decision and Conclusion:

Since the p-value = 0.1506 is greater than 0.05 at a 5% significance level, the null hypothesis is not rejected. Hence we can conclude that the independent variable years of schooling don't fit the regression model.

c)

The confidence interval for the regression coefficient of the variable MALE is obtained using the following formula,

where

The t-critical value is obtained from t distribution table for the degree of freedom = 34 and significance level = 0.05 for a 95% confidence interval. (t-critical = 2.228)

Interpretation: Since the confidence interval doesn't include zero value, we can conclude that the mean job satisfaction score for the male is significantly more compared to the female.

d)

Hypothesis:

Let the significance level = 0.05

Test statistic and P-value:

.	t-ratio	p-value		Significance level	Whether significant?
Engr	2.73	0.0050	<	0.05	Yes
Adv	-0.16	0.4369	>	0.05	No
Sales	1.36	0.0914	>	0.05	No

Since the p-value for Engineering department is less than 0.05 at a 5% significance level, it is significant in the regression model while the Advertisement and the Sales department are not significant in the regression model.

e)

For the 4th department, the regression analysis takes the following independent values,

Engr = 0

Adv = 0

Sales = 0

Hence when all the department values are zeron, the regression model predicts the value for the the 4th department.