Are rent rates influenced by the student population in a college town? Let rent be the average monthly rent paid on rental units in a college town in the United States. Let pop denote the total city population, avginc the average city income, and pctstu the student population as a percentage of the total population. One model to test for a relationship for a relationship is
log (rent) = ß0 + ß1 log (pop) + ß2 log (avginc) + ß3 pctstu + u.
(i) State the null hypothesis that the size of the student body relative to the population has no ceteris paribus effect on monthly rents. State the alternative that there is an effect.
(ii) What signs do you expect for ß1and ß2?
(iii) The equation estimated using 1990 data for 64 college towns is
log ( rent ) = 0.043 + 0.066 log (pop) + 0.507 log (avginc) + 0.0056 pctstu
(0.844) (0.039) (0.081) (0.0017)
n = 64, R2 = 0.458.
What is wrong with the statement: “A 10% increase in the population is associated with about 6.6% increase in rent”?
(iv) Test the hypothesis stated in part (i) at the 1% level.