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
43	7
54	4
77	4
53	2
67	5
53	6
114	8
48	0
29	5
50	1
91	9
52	3
59	2
55	5
149	10
51	0
80	9
73	8
135	8
28	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 decrease by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,890.

• 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 $6,890.

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.)

Salaryˆ + _____ $

Answer 1

Salary	Education		SUMMARY OUTPUT
43	7
54	4		Regression Statistics
77	4		Multiple R	0.697062871
53	2		R Square	0.485896645
67	5		Adjusted R Square	0.457335348
53	6		Standard Error	23.81470671
114	8		Observations	20
48	0
29	5		ANOVA
50	1			df	SS	MS	F	Significance F
91	9		Regression	1	9648.425394	9648.425	17.01241	0.000636409
52	3		Residual	18	10208.52461	567.1403
59	2		Total	19	19856.95
55	5
149	10			Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
51	0		Intercept	34.97440945	9.626145626	3.633272	0.001901	14.75062794	55.19819096
80	9		X Variable 1	6.890748031	1.670641962	4.124611	0.000636	3.380859511	10.40063655
73	8
135	8
28	0