Question

Suppose the following data were collected from a sample of 15 CEOs relating annual salary to years of experience and the economic sector their company belongs to. Use statistical software to find the following regression equation:

SALARYi=b0+b1EXPERIENCEi+b2SERVICEi+b3INDUSTRIALi+ei

Is there enough evidence to support the claim that on average, CEOs in the service sector have lower salaries than CEOs in the financial sector at the 0.01 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."

Copy Data

CEO Salaries

Salary	Experience	Service (1 if service sector, 0 otherwise)	Industrial (1 if industrial sector, 0 otherwise)	Financial (1 if financial sector, 0 otherwise)
144225	10	1	00	00
187765	20	00	00	1
142500	6	1	00	00
169650	28	1	00	00
167250	31	00	1	00
189145	20	00	00	1
175000	16	00	00	1
147925	14	00	1	00
142800	00	00	00	1
156200	20	1	00	00
147750	14	00	1	00
127600	2	00	1	00
140887	7	00	1	00
163875	31	1	00	00
186730	19	00	00	1

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.963722812
R Square	0.928761658
Adjusted R Square	0.909333019
Standard Error	5852.693459
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	3	4912411252	1.64E+09	47.80374	1.33964E-06
Residual	11	376794228	34254021
Total	14	5289205480
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	154891.50	3608.389733	42.92538	1.34E-13	146949.4844	162833.5089
Experience	1426.43	165.5921673	8.614137	3.21E-06	1061.967655	1790.89946
Service	-26703.73	3760.364416	-7.10137	1.99E-05	-34980.24051	-18427.22795
Industrial	-28008.59	3708.820971	-7.55189	1.13E-05	-36171.65294	-19845.5331

The p-value for the test of the significance of slope for Service independent variable is less than 0.01. Hence, we can conclude that Service has a significant effect on the Salary at the 0.01 significance level.

The coefficient of slope corresponding to Service is -26703.73. Hence, when service=0, the mean of the salary is increased by 26703.73. Therefore, CEOs in the service sector have lower salaries than CEOs in the financial sector at 0.01 level of significance.

The regression equation is
Salary = 154891.50+ 1426.43 Experience - 26703.73 Service -28008.59 Industrial