Question

The Secretary of the U.S. Treasury commissioned you to estimate the effect of income on tax revenue by state. You estimate the following tax function using cross-sectional data for the 50 U.S. states and the District of Columbia:

Tax^=−0.221+0.142×Income(0.087)(<0.0001)           

with n=51, R2=0.997, and s=0.687 where Tax is total taxes paid and Income is total income, both measured in billions of dollars, and the number in parentheses are the corresponding p-values. Interpret the results for the Treasury Secretary. State the null and alternative hypotheses that the p-values, given above, test. Are the coefficients significant at the 5% level? Justify your answers.

Answer 1

Ho:   β1=   0
H1:   β1╪   0

p value<0.0001

decison :    p-value<α , reject Ho
Conclusion:   Reject Ho and conclude that slope is significantly different from zero

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Ho:   βo=   0
H1:   βo╪   0
p value=0.087

decison :    p-value>α , do not reject Ho
Conclusion: fail to Reject Ho and conclude that intercept  is not significantly different from zero

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for every billion dollar increase in total income,total taxes paid get increase by 0.142 billion dollars