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
38   5
70   5
96   8
55   3
80   9
78   8
108   9
49   0
31   6
37   6
96   5
40   1
69   7
70   7
166   5
63   0
83   1
62   3
131   5
28   0

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 $4,070.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $4,070.

• 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.

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
	5	38	190	25	1444
	5	70	350	25	4900
	8	96	768	64	9216
	3	55	165	9	3025
	9	80	720	81	6400
	8	78	624	64	6084
	9	108	972	81	11664
	0	49	0	0	2401
	6	31	186	36	961
	6	37	222	36	1369
	5	96	480	25	9216
	1	40	40	1	1600
	7	69	483	49	4761
	7	70	490	49	4900
	5	166	830	25	27556
	0	63	0	0	3969
	1	83	83	1	6889
	3	62	186	9	3844
	5	131	655	25	17161
	0	28	0	0	784
Total	93	1450	7444	605	128144

Equation of regression line is


b = 4.07

a =( 1450 - ( 4.0655 * 93 ) ) / 20
a = 53.60
Equation of regression line becomes

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $4,070.

When X = 6
= 53.595 + 4.065 X
= 53.595 + 4.065 * 6
= 77.98

= 78