## Homework #3 (100 Points)

Instructions: Please answer all of the following questions as best as possible in

groups up to 3 students. If you have any questions please see me immediately. The point

value for each question is in parentheses. This assignment is due March 19th at the

beginning of the class.

1. Are rents 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. The model is:

log(rent) = β0 + β1log(pop) + β2log(avginc) + β3pctstu+ u. (1)

(a) (5) 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.

(b) (5) What signs do you expect for β1 and β2? Why?

The estimated equation is:

̂log(rent) = 0.043 (0.844)

+ 0.066 (0.039)

log(pop) + 0.507 (0.081)

log(avginc) + 0.0056 (0.0017)

pctstu

n = 64, R2 = 0.458

(c) (5) What is wrong with the statement: “A 10% increase in population is asso-

ciated with about a 6.6% increase in rent”?

(d) (5) Using the traditional approach, test the hypothesis stated in question (a) at

the 1% level.

(e) (5) Does pctstu have a statistically significant effect on rent?

(f) (10) Test the statistical significance of log(avginc) at the 5% significance level,

by constructing a 95% confidence interval. What do you conclude?

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2. Use the data set named DISCRIM to answer this question about discrimination.

There are ZIP-code level data on prices for various items at fast-food restaurants.

The idea is to see whether fast-food restaurants charge higher prices in areas with

larger concentration of blacks. psoda is the price of medium soda, prpblck is the

proportion black, income is the median family income, prppov is the proportion of

population in poverty.

(a) (10) Use OLS to estimate the model

log(psoda) = β0 + β1prpblck + β2log(income) + β3prppov + u, (2)

and report the results in the usual form.

(b) (10) Is β̂1 statistically different from zero at the 5% level against the two-sided

alternative?

(c) (5) What about at the 1% level?

(d) (10) What is the correlation between log(income) and prppov? Is each variable

statistically significant in any case? (use the p-value and compare it to the

significance level to answer this question). Report the two-sided p-values.

(e) (10) To the regression in part (a), add the variable log(hseval), median hous-

ing value. Interpret its coefficient and report the two-sided p-value for H0 :

βlog(hseval) = 0.

(f) (5) In the regression in part (e), what happens to the individual statistical

significance of log(income) and prppov?

(g) (15) In the regression estimated in part (e), are log(income) and prppov jointly

significant at any level, 1%, 5% or 10%? To answer this question, calculate

the F statistic using R2 for the unrestricted and restricted model and use the

rejection rule.

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