Are rent rates influenced by student population in a college town? Let rent be the average monthly rent paid on rental units in a college town in Canada. Let pctstu be the student population as a percentage of the total population. One model to test for a relationship is log(rent) = ?0 + ?3 pctstu + u (a) (3 marks) State the null hypothesis that size of the student body relative to the population has no effect on monthly rents. State the alternative that there is an effect. (b) (3 marks) What signs do you expect for ?3? (c) (5 marks) The equation estimated using 1990 data for 64 college towns is ln(r?ent) = 0.043 + 0.0056 pctstu (.844) (.0017) R^2 = 0.458 N = 64 What is wrong with the statement: "A 10% increase in student population is associated with about 0.56% increase in rent"? (d) (4 marks) Test the hypothesis stated in part (a) at 1% level.
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(a) The null hypothesis (H0) and alternative hypothesis (H1) are as follows: H0: Ba = 0 (The size of the student body relative to the population has no effect on monthly rents) H1: Ba ≠ 0 (The size of the student body relative to the population has an effect on Show more…
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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 $$\log (\text {rent})=\beta_{0}+\beta_{1} \log (p o p)+\beta_{2} \log (\text {avginc})+\beta_{3} p c t s t u+u$$ i. 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. ii. What signs do you expect for $\beta_{1}$ and $\beta_{2} ?$ iii. The equation estimated using 1990 data from RENTAL for 64 college towns is $$\begin{aligned} &\widehat{\log (\text {rent})}=.043+.066 \log (\text {pop})+.507 \log (\text {avginc})+.0056 \text { pctstu}\\ &\begin{aligned} (.844)(.039) &(.081) \\ n=64, R^{2}=.458 \end{aligned} \end{aligned}$$ What is wrong with the statement: "A 10\% increase in population is associated with about a $6.6 \%$ increase in rent"? iv. Test the hypothesis stated in part (i) at the $1 \%$ level.
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 ln(rent) = β0 + β1ln(pop) + β2ln(avginc) + β3pctstu + u. a. Use rental.dta to estimate the model by OLS using data for 1990 only and report the results. Use non-robust standard errors. b. Difference the equation by calculating the difference between 1990 and 1980 for each city and estimate by OLS. Report the estimates. Use non-robust standard errors. c. Interpret the estimate for β3. Does the relative size of the student population appear to affect rental prices? d. Estimate the model by fixed effects using city and time fixed effects and report your estimates. Use non-robust standard errors. Compare these results to those in question (b) and comment.
Sri K.
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(rent) = ̠₀ + ̠₁ log(pop) + ̠₂ log(avginc) + ̠₃ pctstu + u. (a) 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. (b) What signs do you expect for ̠₁ and ̠₂? (c) The equation estimated using 1990 data from RENTAL.RAW for 64 college towns is log(rent) = .043 + .066 log(pop) + .507 log(avginc) + .0056 pctstu. (.844) (.039) (.081) (.0017) n 64, R% .458. What is wrong with the statement: "A 10% increase in population is associated with about a 6.6% increase in rent"? Please note () are standard errors. (e) Is any explanatory variable individually significant? Test all explanatory at the 5% level. (f) Test whether the explanatory variables are jointly significant at the 5% level. Compute Overall significance.
Madhur L.
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