Question

The data file collegetown contains data on 500 single-family houses sold in Baton Rouge, Louisiana, during 2009-2013. The data include sale price in $1000 units, PRICE, and total interior area in hundreds of square feet, SQFT.

b. Using the quadratic regression model in part (a), test the hypothesis that the marginal effect on expected house price of increasing the size of a 4000 square foot house by 100 square feet is less than or equal to 13000 against the alternative that the marginal effect will be greater than 13000. Use the 5% level of significance. Clearly state the test statistic used, the rejection region, and the test p-value. What do you conclude?

Answer 1

Using the linear regression model PRICE = β₁ + β₂SQFT + e

The null hypothesis is

H_o: β₂ ≤13 versus H₁ :β₂ >13

This is a one-tail, right-tail test. For the 5% level of significance the critical value is t_{(0.95,N-2=498)} , thus we reject the null hypothesis if the calculated t=(b₂-13)/se(b₂) is greater than this value.

se(b₂)=0.4491 and b₂=13.40294

The calculated t = 0.8970, which is less than the critical value, so that we fail to reject the null hypothesis at the 5% level. The p-value is P[t₍₄₉₈₎≥0 .8971] =0.1851.

We are unable to conclude that a 100 square foot increase in living area will increase price by more than $13,000.