Question

26. (For this question use the data file Per Capita Link). A researcher interested in examining how a state's per capita income may be affected by the percent of the state's adult population that has not completed high school and the percent of the state's population that is foreign bom. part a: Write down an appropriate model for this researcher to estimate. Clearly identify what is the response variable and what are the explanatory variables. part b: Using regression analysis, determine how good of a fit the model is to the data. Explain (report the relevant statistic from the regression results). Also, are the explanatory variables jointly significant at the 5% level? Explain (report the relevant statistic from the regression). part c: Based on the regression analysis, which factors are individually significant at the 5% level? Which are insignificant? Explain (report the relevant statistics from the regression results). Also interpret the sign of the coefficients for the explanatory variables. Are any of the results surprising? part d: Use this model to predict what a state's per capita income would be if 15 percent of the population did not complete high school and 10 percent of the population are foreign born.

Answer 1

a)

Response Variable = Per Capita Income

Explanatory Variable = % of No High School & % of Foriegn Born

Model :-

Per Capita Income = 30640.21 - 567.576 X No High School + 472.0749 X Foreign Born

b)

The model is an Ok fit to the data, albeit not extremely great. As our R-Square and Adjusted R-Square are as shown below:

R Square	0.52269
Adjusted R Square	0.502802

Our explanatory variables are jointly significant at 5% level because of the F-value and F-significance value (way below 0.05) you see below:

	df	SS	MS	F	Significance F
Regression	2	4.9E+08	2.45E+08	26.28179	1.96E-08

c) All of the explantory variables are significant at the 5% level as p-values for each ae way below 0.05

	Coefficients	Standard Error	t Stat	P-value
Intercept	30640.21	1789.005	17.12696	4.41E-22
No High School	-567.576	127.1506	-4.46381	4.87E-05
Foreign Born	472.0749	74.89545	6.303119	8.62E-08

Also, we can see that No high school has a negative sign indicating that higher the % of adult population that has not completed high school, lowe will be the per capita income - which is inline with our thought process

Similarly, Foreign Born has a positive sign, indicating more % of foreign born in our country, more will be the per capita income, which is also inline with our belied that foreign born pouplation, which generally moves to US, is smarter and brings higher income to the state.

d)

If % of No high School = 15 and % Foreign Born =10

Putting these in the regression equation above, we get

Per Capita Income = 26847.32