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
32	1
55	1
85	5
55	1
76	8
69	7
114	12
54	0
25	5
36	3
97	5
45	2
62	1
58	9
146	12
58	0
84	2
70	5
129	12
32	0

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

a. Salary=? Salary= ------ + ------- Education

b. Interpret the coefficient for Education.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $5,850.

• 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 $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $5,850.

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

	X	Y	X * Y
	1	32	32	1	1024
	1	55	55	1	3025
	5	85	425	25	7225
	1	55	55	1	3025
	8	76	608	64	5776
	7	69	483	49	4761
	12	114	1368	144	12996
	0	54	0	0	2916
	5	25	125	25	625
	3	36	108	9	1296
	5	97	485	25	9409
	2	45	90	4	2025
	1	62	62	1	3844
	9	58	522	81	3364
	12	146	1752	144	21316
	0	58	0	0	3364
	2	84	168	4	7056
	5	70	350	25	4900
	12	129	1548	144	16641
	0	32	0	0	1024
Total	91	1382	8236	747	115612

Equation of regression line is


b = 5.85

a =( 1382 - ( 5.8504 * 91 ) ) / 20
a = 42.481
Equation of regression line becomes

Part b)

Since the value of coefficient of (Education ) is positive

As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $5,850.

When X = 7
= 42.481 + 5.85 X
= 42.481 + 5.85 * 7
= 83.43   83