Question

1. Use Minitab to get the same type of output (including graphs) with the following Income/Education data as the little data set discussed in class. Do the regression of Income on Education. Interpret the meaning of the coefficient of Education. What do you predict income to be for a person with 17 years of education? Why do you think Income for 21 years of Education is lower than Income for 19 years of Education in the data set? Education in Years 7 10 Income (2015) Dollars 22587 Row 1 2 3 28305 40196 49483 12 13 4 54483 78073 99540 5 6 7 14 16 18 19 21 15564 6 8 125310 Use Minitab or Excel to estimate the desired function.

Answer 1

Using excel, the OLS regression of Income on Education is given by:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.919340592
R Square	0.845187123
Adjusted R Square	0.823070998
Standard Error	19279.48857
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	14204791052	14204791052	38.21587711	0.000453181
Residual	7	2601890755	371698679.3
Total	8	16806681808
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-62539.86301	22789.46683	-2.744244237	0.028741615	-116428.389	-8651.337059	-116428.389	-8651.337059
Education_in_Years	9357.552055	1513.70183	6.181899151	0.000453181	5778.215999	12936.88811	5778.215999	12936.88811

The regression equation is: Income_2015_Dollars = -62539.86301 + 9357.552055*Education_in_Years

Interpretation of coefficient of Education_in_Years: On an average, when the education-year increases by 1 year, the income in 2015 dollars increases by 9357.552055 dollars.

When Education_in_Years=17, the predicted Income_2015_Dollars is:

=-62539.86301 + 9357.552055*Education_in_Years

=-62539.86301 + 9357.552055*17

=96538.52192

The income for 21 years of education is lower to 19 years of education because, the jobs available for one with 21 years of educations are not comparatively better paying jobs than jobs for one with 19 years of education.