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	33.0
20	4	41.4
25	1	20.7
8	3	14.6
24	12	97.3
28	9	72.1
4	11	49.1
15	4	52.0

Required:

1. Please state the regression equation corresponding to the above scenario.

(b) Please conduct a regression analysis of these data. Be sure to include (e.g., copy and paste) 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 in part (b)? Be sure to cite relevant numeric indices or results of your regression analysis as part of your response.

Answer 1

A) The regression equation is

Annual income = B0+B1*WorkExperience+B2*LevelofEducation

B) The fitted equation is

Annual income = -16.3104+1.6896*WorkExperience+5.5730*LevelofEducation

Reference R lang Output:

lm(formula = Income ~ LevelOfEdu + WorkExp, data = data)

Residuals:
Min 1Q Median 3Q Max
-12.3315 -6.8851 -0.9876 6.3252 20.6753

Coefficients:
Estimate Std.Error t value Pr(>|t|)
(Intercept) -16.3104 8.8635 -1.840 0.098882 .
LevelOfEdu 5.5730 0.9050 6.158 0.000167 ***
WorkExp 1.6896 0.3984 4.240 0.002173 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 10.42 on 9 degrees of freedom
Multiple R-squared: 0.8569,   Adjusted R-squared: 0.8251
F-statistic: 26.94 on 2 and 9 DF, p-value: 0.0001587

C) Interpretation:

Both the independent variables are significant because the p value is less than 0.05 and conclude that there is association between the independent(Level of Education,Work Experience) and dependent variable(Annual Income)

If one unit increase in work experience there is 1.6896 unit increase in annual income

If one unit increase in LevelOfEdu there is 5.5730 unit increase in annual income

And there is 83% of variation in annual income is explained by both the independent variables(Level of Education,Work Experience)