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
34	2
63	3
79	5
49	5
72	6
79	6
110	11
58	0
24	2
30	5
96	7
50	6
69	6
62	7
156	10
56	0
91	3
61	9
123	8
37	0

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers to 2 decimal places.)Click here for the Excel Data File

Salaryˆ=Salary^=     +   Education

b. Interpret the coefficient for Education.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.

• 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 decrease by $6,700.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,700.

c. What is the predicted salary for an individual who completed 5 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)

SalaryˆSalary^               $

Answer 1

Output using excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.658543892
R Square	0.433680058
Adjusted R Square	0.402217839
Standard Error	25.43656739
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	8918.6087	8918.608708	13.78415356	0.001592951
Residual	18	11646.34129	647.0189607
Total	19	20564.95
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	36.13822568	10.73728923	3.365674977	0.003443449	13.58001809	58.69643328
X	6.695400854	1.803377024	3.712701652	0.001592951	2.906646319	10.48415539

a) Regression equation :   

Salarŷ = 36.14 + (6.70) Education

b) As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,700.

c) Predicted value of y at x =    5

ŷ = 36.1382 + (6.6954) * 5 = 70