Question

# Hello, I have computed a regression model where the dependent variable is "earn" as in how...

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

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

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