Question

A social scientist would like to analyze the relationship between educational attainment and salary. He collects the following sample data, where Education refers to years of higher education and Salary is the individual’s annual salary (in $1,000s):

Education 3 4 6 2 5 4 8 0

Salary 40 53 80 42 70 50 110 38

Data is in the spreadsheet.

From the regression results, interpret the coefficient for Education. Remember that you are answering the question, "What happens to the predicted salary when a person obtains an additional year of education?"

a. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.

b. As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.

c. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $9,000.

d. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $9.380.

Answer 1

Solution:

Education	Salary (in $1000s)
3	40
4	53
6	80
2	42
5	70
4	50
8	110
0	38

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.921157
R Square	0.848531
Adjusted R Square	0.823286
Standard Error	10.48634
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3696.095	3696.095	33.61208	0.001154
Residual	6	659.7798	109.9633
Total	7	4355.875
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	22.85119	7.458967	3.063586	0.022123	4.599755	41.10263	4.599755	41.10263
Education	9.380952	1.618077	5.797593	0.001154	5.42166	13.34024	5.42166	13.34024

Here,

The coefficient of Education is 9.38095 which is positive.

Interpretation: When the education is increased or decreased by 1 unit, The resulting predicted salary will increased or decreased by 9.38095 units respectively.

#"What happens to the predicted salary when a person obtains an additional year of education?"

  As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $9,000. (C)

Note: Here the salary will increased by $9,381 and there is no such option. so I select option c for the rounded figure.

But as I notice that the question is typed by you. If you use decimal instead of comma in last option for $9.380 by mistake and If this figure is $9,380, then go for the option D. If not, then this type of option is given to test whether you read the question properly as the coefficient of Education is 9.380 but the salary is measured in $1,000s.