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
40   4
73   1
99   7
57   1
83   8
76   4
109   6
49   0
31   4
32   4
91   2
40   4
65   6
71   2
166   5
61   0
88   1
59   4
132   9
25   0

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

Salaryˆ=

+ 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 $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $6,220.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,220.

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.)

Salaryˆ               $

Answer 1

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	0.4741
R Square	0.2248
Adjusted R Square	0.1817
Standard Error	32.0961
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5375.7	5375.7	5.22	0.0347
Residual	18	18542.8	1030.2
Total	19	23918.6
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	49.9460	12.1530	4.1098	0.0007	24.4135	75.4785
X	6.2233	2.7243	2.2844	0.0347	0.4998	11.9469

salary^ = 49.95 + 6.22*education

b)

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,220.

c)

salary^ = 49.95 + 6.22*education

salary^ = 49.95 + 6.22*5 = 81.063

salary^ = $81063