Question

Hello, I have computed a regression model where the dependent variable is "earn" as in how much money the student will earn after college. My independent variables include "public" as in was this college public(1) or private(0), "academic ability" (a score calculated as the average score from SAT/ACT data of admitted students), "Average Cost" of tuition and  "population" (of the city the college is in). What is the impact on earnings of higher population of the college area/city?

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.649
R Square	0.421
Adjusted R Square	0.418
Standard Error	5188.8229
Observations	612
ANOVA
	df	SS	MS	F	Significance F
Regression	4	11900671012	2975167753	110.502922	0
Residual	607	16342797033	26923883.09
Total	611	28243468045
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95%
Intercept	13079.29751	1793.002809	7.294633031	9.40E-13	9558.055594	16600.53943	9558.055594
Public	5803.055751	692.3876623	8.381223506	3.65E-16	4443.289637	7162.821864	4443.289637
Academic Ability	30963.20394	3177.133618	9.745641091	6.01E-21	24723.69554	37202.71233	24723.69554
Average Cost of Tuition	0.234348603	0.037041991	6.32656614	4.87E-10	0.161602588	0.307094618	0.161602588
Population	0.000232352	7.84E-05	2.962605212	0.003169884	7.83E-05	0.000386376	7.83E-05

Answer 1

Sol:

From output

For popualtion coeffcient

=0.000232352

since coeffcient is positive

For unit increase in popualtion,earning increaases by 0.000232352 units,holding Public,Academic Ability ,

Average Cost of Tuition

and

Population

As popualtion increases,earning increaes and vice versa

Hypothesis tets for slope of popualtion

tstat= coeffcient/std error

=0.000232352/7.84E-05

=2.963673

p value=0.003169884

As nothing mentioned take alpha=0.05

p<alpha

Reject Ho

Accept Ha

Popualtion is a significant variable for predicting earn