Question

An economist was interested in modeling the relationship among annual income, level of education, and work experience. The level of education is the number of years of education beyond eighth grade, so 1 represents completing 1 year of high school, 8 means completing 4 years of college, and so on. Work experience is the number of years employed in the current profession.

From a random sample of 12 individuals, this economist obtained the following data:

Work Experience (Years)	Level of Education	Annual Income ($ Thousands)
12	6	34.7
14	3	17.9
4	8	22.7
16	8	63.1
12	4	33
20	4	41.4
25	1	20.7
8	3	14.6
24	12	97.3
28	9	72.1
15	4	52

(a) Please state the regression equation.

(b) Please conduct a regression analysis of these data. Be sure to include your relevant regression output as part of your response.

(c) What can you conclude regarding the relationship among annual income, level of education and work experience based on your regression analysis results? Be sure to cite relevant numeric indices or results of your regression analysis as part of your response.

Answer 1

(a) Please state the regression equation.

Annual Income = -15.8222 + 1.6164*Work Experience + 5.7392*Level of Education

(b) Please conduct a regression analysis of these data. Be sure to include your relevant regression output as part of your response.

The regression output is:

	R²	0.858
	Adjusted R²	0.822
	R	0.926
	Std. Error	10.987
	n	11
	k	2
	Dep. Var.	Annual Income ($ Thousands)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	5,830.9231	2	2,915.4615	24.15	.0004
Residual	965.6733	8	120.7092
Total	6,796.5964	10
Regression output					confidence interval
variables	coefficients	std. error	t (df=8)	p-value	95% lower	95% upper
Intercept	-15.8222
Work Experience (Years)	1.6164	0.4780	3.381	.0096	0.5141	2.7187
Level of Education	5.7392	1.0857	5.286	.0007	3.2355	8.2428

(c) What can you conclude regarding the relationship among annual income, level of education and work experience based on your regression analysis results? Be sure to cite relevant numeric indices or results of your regression analysis as part of your response.

The hypothesis being tested is:

H₀: β₁ = β₂ = 0

H₁: At least one β_i ≠ 0

The p-value from the output is 0.0004.

Since the p-value (0.0004) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a significant relationship among annual income, level of education and work experience based on the regression analysis results.