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
	40			4
	73			1
	⋮			⋮
	25			0

Salary	Education
40	4
73	1
99	7
57	1
83	8
76	4
109	6
49	0
31	4
32	4
91	2
40	4
65	6
71	2
166	5
61	0
88	1
59	4
132	9
25	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 $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,220.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $6,220.

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.)

Answer 1

Ans:

	Education,x	Salary,y
1	4	40
2	1	73
3	7	99
4	1	57
5	8	83
6	4	76
7	6	109
8	0	49
9	4	31
10	4	32
11	2	91
12	4	40
13	6	65
14	2	71
15	5	166
16	0	61
17	1	88
18	4	59
19	9	132
20	0	25
mean	3.600	72.350
std. deviation	2.703	35.481
r=	0.474
slope=	6.22
y-intercept=	49.95

a)

Salary=49.95+6.22*Education

b)

As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,220.

c)

Predicted =49.9460+6.2233*5=81.063 thousand dollars

=81063 dollars