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	1
52	4
83	2
56	5
75	1
60	3
121	7
52	0
30	2
43	3
93	5
50	6
60	7
58	8
147	10
56	0
81	2
74	6
136	5
25	0

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

Salary^=    +   Education

b. Interpret the coefficient for Education.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,530.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $6,530.

• 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.

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.)

Salaryˆ= $

Answer 1

	Education (X)	Salary (Y)	X * Y
	1	34	34	1
	4	52	208	16
	2	83	166	4
	5	56	280	25
	1	75	75	1
	3	60	180	9
	7	121	847	49
	0	52	0	0
	2	30	60	4
	3	43	129	9
	5	93	465	25
	6	50	300	36
	7	60	420	49
	8	58	464	64
	10	147	1470	100
	0	56	0	0
	2	81	162	4
	6	74	444	36
	5	136	680	25
	0	25	0	0
Total	77	1386	6384	457

Equation of regression line is


b = 6.5269

a =( 1386 - ( 6.5269 * 77 ) ) / 20
a = 44.1713
Equation of regression line becomes

b. Interpret the coefficient for Education.

As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,530.

c. What is the predicted salary for an individual who completed 7 years of higher education?