Question

18. 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
	33			4
	71			2
	⋮			⋮
	35			0

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers to 3 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 $5,991.

• 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 $5,991.

• 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 6 years of higher education? (Round answer to the nearest whole number.)

SalaryˆSalary^               $

Salary	Education
33	4
71	2
84	3
50	3
65	1
78	3
112	5
54	0
28	3
29	3
101	4
38	7
72	9
65	6
160	12
57	0
87	2
56	1
127	5
35	0

Answer 1

	Education X	Salary Y	X * Y
	4	33	132	16	1089
	2	71	142	4	5041
	3	84	252	9	7056
	3	50	150	9	2500
	1	65	65	1	4225
	3	78	234	9	6084
	5	112	560	25	12544
	0	54	0	0	2916
	3	28	84	9	784
	3	29	87	9	841
	4	101	404	16	10201
	7	38	266	49	1444
	9	72	648	81	5184
	6	65	390	36	4225
	12	160	1920	144	25600
	0	57	0	0	3249
	2	87	174	4	7569
	1	56	56	1	3136
	5	127	635	25	16129
	0	35	0	0	1225
Total	73	1402	6199	447	121042

Equation of regression line is


b = 5.991

a =( 1402 - ( 5.9911 * 73 ) ) / 20
a = 48.232

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 $5,991.

Part c)

When X = 6
= 48.232 + 5.991 X
= 48.232 + 5.991 * 6
= 84.18
= 84