Question

6. 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			1
	67			6
	⋮			⋮
	32			0

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

Salaryˆ=Salary^=    Not attempted+  Not attempted Education

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.)

SalaryˆSalary^               $

Salary	Education
35	1
67	6
79	2
46	1
69	7
78	5
111	6
62	0
20	4
25	5
100	6
47	5
64	3
66	9
154	7
61	0
87	1
60	3
123	7
32	0

Answer 1

	Education (X)	Salary (Y)	X * Y
	1	35	35	1	1225
	6	67	402	36	4489
	2	79	158	4	6241
	1	46	46	1	2116
	7	69	483	49	4761
	5	78	390	25	6084
	6	111	666	36	12321
	0	62	0	0	3844
	4	20	80	16	400
	5	25	125	25	625
	6	100	600	36	10000
	5	47	235	25	2209
	3	64	192	9	4096
	9	66	594	81	4356
	7	154	1078	49	23716
	0	61	0	0	3721
	1	87	87	1	7569
	3	60	180	9	3600
	7	123	861	49	15129
	0	32	0	0	1024
Total	78	1386	6212	452	117526

Equation of regression line is


b = 5.46

a =( \Sigma Y - ( b * \Sigma X) ) / n
a =( 1386 - ( 5.4574 * 78 ) ) / 20
a = 48.02
Equation of regression line becomes

When X = 5
= 48.016 + 5.457 X
= 48.016 + 5.457 * 5
= 75.3   75