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			3
	66			1
	⋮			⋮
	33			0

Salary	Education
34	3
66	1
89	4
56	3
71	7
80	2
111	7
51	0
23	7
36	2
100	1
35	1
71	6
68	9
163	5
56	0
86	5
58	4
128	9
33	0

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

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 $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 increase 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.)

SalaryˆSalary^               $

Answer 1

Regression summary output as follows.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.40
R Square	0.16
Adjusted R Square	0.11
Standard Error	33.16
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3676.17	3676.17	3.34	0.08
Residual	18	19797.58	1099.87
Total	19	23473.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	52.9318	12.25	4.32	0.00	27.20	78.66
Education	4.6890	2.56	1.83	0.08	-0.70	10.08

(a)

Regression equation: Salary^= 52.93 + 4.69 x Education

(b) Option (2)

As education increases (decreases) by 1 unit, salary increases (decreases) by $4,690.

(c) Salary ($'000) = 52.9318 + (7 x 4.6890) = 52.9318 + 32.8230 = 85.755

Salary = $85,755