Math Solutions

(Steps Shown) 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

Question: 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 is

\[\log (\text { rent })=\beta_{0}+\beta_{1} \log (p o p)+\beta_{2} \log (\text { avginc })+\beta_{3} p c t s t u+u\]
  1. State the null hypothesis that 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.
  2. What signs do you expect for \(\beta_{1}\) and \(\beta_{2}\) ?
  3. The equation estimated using 1990 data from RENTAL.RAW for 64 college towns is
    \[\begin{aligned} & \widehat{\log (rent)}=.043+.066\log (\text{ pop })+.507\log (\text{ avginc })+.0056\text{ pctstu } \\ & (.844)(.039)\qquad \\ & n=64,{{R}^{2}}=.458 \\ \end{aligned}\]
    What is wrong with the statement: "A \(10 \%\) increase in population is associated with about a \(6.6 \%\) increase in rent"?
  4. Test the hypothesis stated in part (i) at the \(1 \%\) level.

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