Zoning of vacant land. \"Zoning\" is defined as the distribution of vacant land
ID: 3264650 • Letter: Z
Question
Zoning of vacant land. "Zoning" is defined as the distribution of vacant land to residential and nonresidential uses via policy set by local governments. Although the negative effects of zoning have been studied (e.g., distorting urban property markets, creating barriers to residential mobility, and impeding economic and social integration), little empirical evidence exists identifying the factors that encourage restrictive zoning practices. A study, reported in the Journal of Urban Economics (Vol. 21, 1987), developed a series of multiple regression models that hypothesize several determinants of zoning. One of the models studied took the form E(y) = beta_0 + beta_1 x_1 + beta_2 x^2_1 + beta_3 x_2 where y = Percentage of vacant land zoned for residential use x_1 = Proportion of existing land in nonresidential use x_2 = Proportion of total tax base derived from nonresidential property The model was fit to data collected for n = 185 municipal communities in northeastern New Jersey, with the following results: a. Construct a 95% confidence interval for beta_3. Interpret the result. b. Test the hypothesis that a curvilinear relationship exists between percentage (y) of land zoned for residential use and proportion (x_1) of existing land in nonresidential use. C. Is the overall model statistically useful for predicting y? d. Interpret the adjusted R^2 value.Explanation / Answer
Here we have given two independent variables and dependent variable.
a) Here we have to find 95% confidence intrval for B3.
95% confidence interval for B3 is,
b3 - E < B3 < b3 + E
where b3 is sample slope for x2 = -75.51
E is margin of error.
E =tc*SEb
where tc is the critical value for t-distribution.
SEb is standard derror of the estimate = 13.35
tc we can find by using EXCEL.
syntax :
=TINV(1-c, n-2)
Here n = 185
c is confidence level = 95% = 0.95
tc = 1.973
E = 1.973*13.35 = 26.34
Lower limit = b3 - E = -75.51 - 26.34 = -101.85
Upper limit = b3 + E = -75.51 + 26.34 = -49.17
95% confidence interval for B3 is (-101.85, -49.17).
We are 95% confident that the population slope for x2 is lies between -101.85, -49.17
b) Now we have to test,
H0 : B = 0 Vs H1 : B not= 0
where B is population slope for x1.
Or we can test the hypothesis that,
H0 : Rho = 0 Vs H1 : Rho not= 0
where Rho is population correlation coefficient between y and x1
Assume alpha = level of significance = 0.05
Here test statistic follows t-distribution with n-2 degrees of freedom.
Test statistic = -2.07
And also given that p-value < 0.05 (alpha)
Reject H0 at 5% level of significance.
Conclusion : There is some relation between y and x1.
We get significant reult.
c) Here we have to test the hypothesis that,
H0 : Bj = 0 Vs H1 : Bj not= 0
where Bj is population slope for jth independent variable.
Assume alpha = 0.01
Test statistic follows F-dstribution.
Test statistic = 21.86
Reject H0 at 1% level of significance.
Conclusion : The population slope for jth independent variable is differ than 0.
We get significant result about overall significance.
d) Adjusted R-sq = 0.25
The adjusted R-squared compares the explanatory power of regression models that contain different numbers of predictors.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.