Question

A social scientist would like to analyze the relationship between educational attainment in years of higher education) and annual salary in $1,000s). He collects data on 20 individuals. A portion of the data is as follows: Salary Education Click here for the Excel Data File a. Find the sample regression equation for the model: Salary = Bo + Education: (Round answers to 2 decimal places.) Salary = O O Education b. Interpret the coefficient for Education As Education increases by 1 unit, an individual's annual salary is predicted to increase by $8,590. As Education increases by 1 unit, an individual's annual salary is predicted to increase by $4,690. As Education increases by 1 unit, an individual's annual salary is predicted to decrease by $4,690, As Education increases by 1 unit, an individual's annual salary is predicted to decrease by $8,590 c. What is the predicted salary for an individual who completed 7 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.) Salary O Prey 17 of 30 Next

Answer 1

Solution:

Here, we have to develop the regression model for the prediction of dependent variable salary based on the independent variable years of education. The regression output by using excel is given as below:

Regression Statistics
Multiple R	0.395737029
R Square	0.156607796
Adjusted R Square	0.109752673
Standard Error	33.16421913
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3676.172249	3676.172249	3.342383665	0.08413922
Residual	18	19797.57775	1099.865431
Total	19	23473.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	52.93181818	12.24669954	4.32212924	0.000410462	27.20245724	78.66117912
Education	4.688995215	2.564788983	1.828218714	0.08413922	-0.699426479	10.07741691

Part a

The required sample regression equation for the model by using above regression output is given as below:

Salary = 52.93 + 4.69*Education

Part b

Interpretation:

As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $4,690.

Part c

We are given

Education = 7 years

Salary = 52.93 + 4.69*Education

Salary = 52.93 + 4.69*7

Salary = 85.76

Predicted Salary = $85.76*1000

Predicted Salary = $85,760