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
35	4
71	1
84	3
52	3
70	7
80	5
107	9
55	0
23	4
33	6
102	6
40	4
67	2
68	5
163	9
55	0
83	8
56	3
125	11
31	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 $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $7,161.

• 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 $7,161.

c. What is the predicted salary for an individual who completed 6 years of higher education? (Round answer to the nearest whole number.)

SalaryˆSalary^               $

Answer 1

a)

using excel data analysis tool for regression,steps are: write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

Regression Statistics
Multiple R	0.6597
R Square	0.4352
Adjusted R Square	0.4038
Standard Error	26.7125
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	9896.0	9896.0	13.87	0.0016
Residual	18	12844.0	713.6
Total	19	22740.0
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	37.7772	10.5141	3.5930	0.0021	15.6879	59.8665
X	7.1606	1.9228	3.7240	0.0016	3.1210	11.2003

so, regression line is   Ŷ =   37.777 +   7.161 *x

b) As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $7,161.

c)

Ŷ =   37.777 +   7.161 *   6   =   80.741

predicted salary for an individual who completed 6 years of higher education = $80741