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
	⋮			⋮
	28			0

Click here for the Excel Data File

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

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 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 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

Solution

The independent variable isEducation, and the dependent variable is Salary. In order to compute the regression coefficients, the following table needs to be used:

	Education	Salary	Education*Salary	Education2	Salary2
	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
Sum =	93	1450	7444	605	128144

Therefore, we find that the regression equation is:

Salary=53.60+4.07Education

b. Interpret the coefficient for Education.

As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $4.065.

c)

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.)

Salary=53.60+4.07Education

Salary=53.60+4.07*6

Salary= $78