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
35	4
71	1
84	3
52	3
70	7
80	5
107	9
55	0
23	4
33	6
102	6
40	4
67	2
68	5
163	9
55	0
83	8
56	3
125	11
31	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 increase by $7,160.

• 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 $7,160.

c. What is the predicted salary for an individual who completed 6 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)

SalaryˆSalary^ $_______

Answer 1

	Education X	Salary Y	X * Y
	4	35	140	16	1225
	1	71	71	1	5041
	3	84	252	9	7056
	3	52	156	9	2704
	7	70	490	49	4900
	5	80	400	25	6400
	9	107	963	81	11449
	0	55	0	0	3025
	4	23	92	16	529
	6	33	198	36	1089
	6	102	612	36	10404
	4	40	160	16	1600
	2	67	134	4	4489
	5	68	340	25	4624
	9	163	1467	81	26569
	0	55	0	0	3025
	8	83	664	64	6889
	3	56	168	9	3136
	11	125	1375	121	15625
	0	31	0	0	961
Total	90	1400	7682	598	120740

Part a)

Equation of regression line is


b = 7.16
a =( \Sigma Y - ( b * \Sigma X) ) / n
a =( 1400 - ( 7.1606 * 90 ) ) / 20
a = 37.78
Equation of regression line becomes

Part b)

As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $7,160.

part c)

When X = 6
= 37.777 + 7.161 X
= 37.777 + 7.161 * 6
= 80.74

= 81