Are rent rates influenced by the student population in a college town?\" Let ren
ID: 3200267 • Letter: A
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, avgine 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) = beta_0 + beta_1 log(pop) + beta_2 log(avgine) + beta_3pctstu + u. a) 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) What signs do you expect for beta_1 and beta_2? c) The equation estimated using 1990 data for 64 college towns is log(rent) = 0.043 + 0.066 middot log(pop) + 0.507 middot log(avginc) + 0.0056 middot pctstu, (0.844) (0.039) (0.081) (0.0017) where the standard error of the parameter estimates arc provided in the parenthesis, n = 64 (assume it is small for unless mentioned explicitly otherwise) and R^2 = 0.458. Is the statement correct: "A 10% increase in population is associated with about a 6.6% increase in rent?" d) Then test beta_3 = 0.002 against the two-sided alternative with alpha = 0:05. What do you conclude? Is p-value for testing beta_3 = 0.002 against the two-sided alternative greater or less than 0.05? Why? e) Suppose you test beta_3 lessthanorequalto 0.002 against the one-sided alternative that beta_3 > 0.002, what are you going lo conclude and why?Explanation / Answer
Given that,
pop = total city population
avginc = average city income
petstu = student population as a percentage of the total population
a) Here we have to test the hypothesis that,
H0 : B = 0 Vs H1 : B not= 0
where B is population slope for petstu
b) The sign for B1 and B2 are positive because we know that population and income is positive and their logarithm is also positive.
c) This statement is correct.
The statement is write in another way as one unit change in log(pop) will be 0.066 unit change in log(rent).
d) Here we have to test the hypothesis that,
H0 : B3 = 0.002 Vs H1 : B3 not= 0.002
Assume alpha = level of significance = 0.05
The test statistic follow t-distribution.
The test statistic is,
t = b3 / SEb
where b3 is sample slope for pettstu.
SEb is standard error for the estimate.
t = 0.0056/0.0017 = 3.29
Now we have to find P-value for taking decision.
P-value we can find by using EXCEL.
syntax :
=TDIST(x, deg_freedom, tails)
where x is absolute value of test statistic.
deg_freedom = n-2
where n = 64
tails = 2
P-value = 0.002
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : There is sufficient evidence to say that population sloe for petstu is differ than 0.002.
e) Here we have to test the hypothesis that,
H0 : B3 <= 0.002 Vs H1 : B2 > 0.002
Here test statistic value is same but P-value will be change.
P-value will be change because the test is one tailed.
P-value we can find by using EXCEL.
syntax :
=TDIST(x, deg_freedom, tails)
where x is absolute value of test statistic.
deg_freedom = n-2
where n = 64
tails = 1
P-value = 0.001
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : There is sufficient evidence to say that population sloe for petstu is greator than 0.002.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.