Kbd47 Kushan Dave CRP 5450: Inferential Statistics for Planing and Public Policy Empirical Project
I.
Introduction The purpose of this research paper is to determine if there is a link between housing price
and occurrence of crime in the area where the house is located. Specifically, the research question underpinning this study is: With all other factors considered either equal or held constant, what is the impact of crime on housing price? Many factors are observed and recorded as possible attributes to housing prices in this research. The setting of this project is in Washington, District Columbia with all the observations recorded at the census tract level.
II. Motivation Housing prices are affected by several factors with crime, presumably, being one of them. One of the important findings of my GIS project in Fall 2013 was that between 2009 and 2011, 43.4% crime incidents happened around 0.5 miles of public housing located in Bedfordstuyvesant, Crown heights and Brownsville neighborhood in uptown Brooklyn, New York City. Incidentally, the median housing price in these census tracts are lower than the median housing price of Brooklyn1. However, since the conclusions of my study were based on spatial concentration of crime incidents and not on empirical analysis, we cannot establish correlation between crime and housing prices. The current paper, therefore, provides an opportunity to test the hypothesis that crime has negative impact on the housing prices. On a general note, crime affecting housing prices is of 1
Source: Homeownership and Housing cost 2009 and 2011, US Census Bureau. 1
interest not only to the new homebuyers but also to the policy makers since public safety accounts for a significant percentage of the local government budget.2 For instance, if the policy makers can infer that a 10% decrease in crime rates increases the median housing values by 20%, than they are more likely to allocate higher budget to control crime. Intuitively, the current research can also argue that the housing prices increase, as the neighborhood feels safer. Also, such information is very useful for real estate agencies and can potentially help them decide the price listing of a property in a high crime rate area. The main objective therefore, is to find whether crime has an impact on housing price, and if so, how much? The study also account for other relative variables affecting the housing price, such as square footage and poor housing characteristics. By accounting for these variables, if there exists a correlation between crime and housing prices, it should not be grossly overstated.
III. Literature review Literatures surrounding the impact of crime on housing prices are plentiful. As the crime statistics become increasingly available to researchers, so has the supporting literature establishing negative correlation between crime rate and housing prices. The 1980 study of central Boston by Naroff, Hellman and Skinner, shows that the variation in crime rate can negatively affect property values and thus reduce the property revenue. The study shows that an increase in crime rate by 1% reduces the housing price by a dollar amount of 1.67. In order to avoid multicollinearity, the violent and nonviolent crimes are combined to create a single variable of crime rate. At a policy level, the study effectively demonstrated the need for an 2 “$4.4 million of the total funds of $10.7 billion will be spent on public safety”. Source: Fiscal year 2015 Budget (as proposed by Mayor Gray), Executive Office of the Mayor, The District of Columbia.
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increase in public safety funding by showing the actual dollar value increase in property value because of 1%, 2% and 10% reduction in crime rate. An important aspect of the study is that it accounts for neighborhood characteristics which affect the median housing prices. However, the study does not account for important qualitative variables related to the housing unit, like the age and size of a housing unit. In this aspect, the study by Sirmans, MacDonald and Macpherson is important to understand because it determines which housing characteristics affect the housing value. At the top of their list are square foot, age and number of bedrooms and bathrooms with an average t statistic value of 28.50, 6.53 and 7.02 respectively3. Therefore, the current study will include variables defining housing characteristics, such as such as age, square footage and lack of facilities, which can potentially impact the median housing price in Washington D.C. Another study of impact of crime on property prices in London by Gibbons (2004) argues that, “low income houses attract lowincome residents, and if low income residents are prone to commit crimes in their own neighborhood we will find more crime in lowprice neighborhoods”. Similarly, the study of 71 neighborhood communities within the city of Chicago by Rizzo in 1979 demonstrates the dollar value effects of variables like unemployment rate, population density, proportion of households on the housing. His most important conclusions is that the crime rate affects the housing prices disproportionately and that poorer neighborhoods tend to suffer more. On an average, one increase in crime incident decreases the housing price by an average of $238 in poorer neighborhood as compared to an average $139 decrease in the rest of the neighborhoods. For the purpose of the current study, it is therefore imperative to include median household income as a key variable.
3
The high t‐stat values tell us that the variables have a significant impact on the dependent variable (of median housing price)
3
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The study by Lynch and Rasmussen (2001) in Jacksonville, Florida, in the 1990â€™s makes an important point about the severity of the crime. They claim that as the seriousness of the crime rises, the public safety declines and conclude that most house sales occurred in relatively safe neighborhoods. They found that houses located in the top two crime areas were discounted at a rate of about 39% relative to comparable dwelling. Furthermore they argue that the â€˜fear of crimeâ€™ is an important factor that can further reduce the price and therefore, nonviolent crime should be treated as a separate variable than violent crime. However, Gibbons study of London (2004) argues that although nonviolent crimes motivate the â€˜fear of crimeâ€™, there is no significant correlation between nonviolent crimes and property values. Moreover, since violent and nonviolent crime rates are highly collinear, with no research suggesting that one affects the property values significantly more than the other, the current study will combine both the crime rates (violent and nonviolent) as a single variable.
IV. Initial regression model Y = đ?œˇđ?&#x;Ž âˆ’ Â đ?œˇđ?&#x;? âˆ— đ?‘żđ?&#x;? + Â đ?œˇđ?&#x;? âˆ— đ?‘żđ?&#x;? âˆ’ Â đ?œˇđ?&#x;‘ âˆ— đ?‘żđ?&#x;‘ + Â đ?œˇđ?&#x;’ âˆ— đ?‘żđ?&#x;’ âˆ’ Â đ?œˇđ?&#x;“ âˆ— đ?‘ż5 Â Ââ€? Â đ?œˇđ?&#x;” âˆ— đ?‘ż6 Â + Îľ medhouprc = Î˛0  Î˛1 crper1000 + Î˛1 medsqft â€“ Î˛3 perhouprch + Î˛4 medhouinc â€“ Î˛5 houvacrate â€“ Î˛6 medagestr For the particular study, the dependent variable Y will be median housing price. From the literature review it is clear that the independent variables should be carefully selected to include qualitative aspects at the level of neighborhood as well as at the household level. The current empirical study therefore uses the following variables: a) Crime Rate per 1000 residents: X1 (positive) As suggested by literature review, crime rates are a better measure of crime than incidents themselves. This avoids the possibility of including another highly correlated variable of population.
Â
4 Â
Â
b) Median square footage: X2 (positive) The size of the house is the first thing a buyer/seller looks at. Furthermore from study by Sirmans, et al, we can conclude that square footage is an important variable. To avoid multicollinearity, the study will not include the number of bedrooms and bathrooms. c) Percentage of housing with poor characteristics: X3 (negative) Basic Characteristic accounting for the lack of plumbing facilities, kitchen, and telephone services will make the area less attractive for new homebuyers and therefore can potentially decrease the housing prices in the area.
d) Median Household Income: X4 (positive) The study by Naroff et al, leads us to believe that median household income is an important qualitative variable which further eliminates the need to include poverty and unemployment rate. e) Housing vacancy rate: X5 (negative) For the purpose of this study, the vacancy rate variable can be helpful in determining the characteristics of the census tract itself. For instance, a neighborhood with high vacancy rate might automatically drive down the median housing price in the area. f)
Median age of structure: X6 (negative) As suggested by Sirmans et al, the age of structure is an important variable affecting the housing price. The current study calculates the age of structure up to the year 2012
Â
5 Â
V. Data Variable
Assigned Unit
Formula Used
Name Median
medhoup
Y Housing
rc
Price*
Base
Data Source File in
Variables N/A
N/A
Dollars
Link US Census
N/A
Bureau
http://factfinder2.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=ACS_1
2_5YR_DP04&prodType=table
X1 Crime Rate per 1000 residents
‐
crper100
Percent
0
age
http://data.octo.dc.gov/
of housing
US Census
N/A
incidents *
n Census
Bureau
1000) / total
Tract
population of
No. of
Office of
Crime
census tract ]
Crime
City
Incident
incidents
Administrat
s ASAP
or
(2012)
ductview.xhtml?pid=ACS_12_5YR_DP05&prodType=table
Median
+
Populatio
http://factfinder2.census.gov/faces/tableservices/jsf/pages/pro
X2 Square Foot
[(no. of crime
medsqft
Square feet
(median
Median
US Census
N/A
housing price /
Housing
Bureau
median price
price
per sq ft)
Median
www.trulia.
Data
Price per
com
Request
Sq ft *
ed for 2012
http://www.trulia.com/home_prices/District_Of_Columbia/Washington‐heat_map/
* Median Price square feet is at Neighborhood level (Source: Trulia Real Estate). All the census tracts within the neighborhood have been assigned the same Median Price per square feet value.
6
total housing
Total
units with poor Housing X3
poor characterist
N/A
Bureau
characteristics / Units with
Percentage Houses with
US Census
perhouprc
Percen
h
tage
total housing units
Poor Characteri stics
ics ‐
Total
US Census
Housing
Bureau
N/A
Units http://factfinder2.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=ACS_12_5 YR_DP04&prodType=table
X4
Median Household
+
N/A
N/A
medhouinc Dollars
US Census
N/A
Bureau
Income
http://factfinder2.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=ACS_12_5 YR_DP03&prodType=table
X5 ‐
Housing Vacancy
houvacrate
Rate
Percen
N/A
N/A
US Census
N/A
Bureau
tage
http://factfinder2.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=ACS_12_5 YR_DP04&prodType=table
X6
Median Age of Structure
‐
medagestr
Year
2012 ‐ median
Median
Social
year structure
Year
Explorer
built
Structure Built
http://www.socialexplorer.com/tables/ACS2012_5yr/R10723971
N/A
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Unit of Observation: 174 (of 179) Census Tracts of Washing, DC (Observations from Census Tracts 2.01, 62.02, 68.04, 73.01, and 109 have been omitted because of missing data) Data type: Cross Sectional
VI. Descriptive statistic and correlation matrix a. Descriptive Statistic Summary Table
stats
medho~rc
crp~1000
houvac~e
perhou~h
medsqft
N mean p50 sd min max skewness
174 463096.6 402300 241527.5 169200 1525000 1.527724
174 63.65929 54.14552 50.90867 6.81074 432.1782 4.576446
174 12.3507 11.31513 6.713806 0 37.72242 .8475434
174 4.843333 3.075 4.955389 0 27.96 1.782582
174 1325.934 1172.377 656.9706 457.8498 6668.142 3.589053
medho~nc
medage~r
174 174 68785.68 60.73563 61583.5 63 38220.87 12.89483 13730 9 221771 73 1.123665 1.413178
b. Correlation Matrix . correlate medhouprc crper1000 (obs=174)
houvacrate perhouprch medsqft medhouinc medagestr
medho~rc crp~1000 houvac~e perhou~h medhouprc crper1000 houvacrate perhouprch medsqft medhouinc medagestr
1.0000 0.1042 0.3732 0.1530 0.2429 0.8177 0.3046
1.0000 0.2093 0.0538 0.0974 0.0265 0.2350
1.0000 0.1156 0.0300 0.3656 0.2723
1.0000 0.0232 0.1014 0.0179
medsqft medho~nc medage~r
1.0000 0.0320 0.1005
1.0000 0.2970
1.0000
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VII. Initial Regression . regress medhouprc crper1000 houvacrate perhouprch medsqft medhouinc medagestr Source
SS
MS
Model Residual
7.4230e+12 2.6691e+12
6 167
1.2372e+12 1.5983e+10
Total
1.0092e+13
173
5.8336e+10
medhouprc
Coef.
crper1000 houvacrate perhouprch medsqft medhouinc medagestr _cons
162.504 2436.968 3625.448 83.36555 4.770122 1412.127 3320.878
VIII.
df
Std. Err. 199.956 1600.308 1963.048 14.87879 .2799309 819.3438 65960.53
t 0.81 1.52 1.85 5.60 17.04 1.72 0.05
Number of obs F( 6, 167) Prob > F Rsquared Adj Rsquared Root MSE
P>t 0.418 0.130 0.067 0.000 0.000 0.087 0.960
= = = = = =
174 77.41 0.0000 0.7355 0.7260 1.3e+05
[95% Conf. Interval] 557.2714 5596.41 7501.036 53.99079 4.217463 205.4793 133544.8
232.2633 722.4749 250.1402 112.7403 5.322782 3029.734 126903.1
Regression Diagnostic Check
a. Ramsey Test
Ramsey RESET test using powers of the independent variables Ho: model has no omitted variables F(18, 149) = 0.96 Prob > F = 0.5112
Based on the ramsey test, the model shows that omitted variable bias does not exist.4 However, by looking at the scatter plot (included in the Appendix), we can infer that current functional forms are not the best to be used. For instance, median housing price and median square feet should definitely be logged for homoscedasticity. The median housing price vs 4
Considering that Prob>F value to be more than 0.2 or 0.3 is generally considered a good model.
9
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median age of structure plot also shows a nonlinear relationship. This is a specific case and we will need to either use to correct functional form and/or add a quadratic variable. Furthermore, median age of structure has a positive sign, contrary to what was hypothesized. However, the remainder of the regression coefficients have the correct sign. Based on the high p values (< 0.05), we can also say that crime rate, housing vacancy rate and poor housing characteristics are statistically insignificant. b. Pagan / Cook test for heteroskedasticity BreuschPagan / CookWeisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of medhouprc chi2(1) Prob > chi2
= =
35.70 0.0000
As prob > chi2 = 0, we cannot reject the null and therefore the model does have heterscedasticity. Given that the data is cross sectional, and by looking at the scatter plots, this was expected. Therefore, this further proves the need to change the functional form of some of the variables to have a more robust model.
0 400000
200000
Residuals
200000
400000
c. Residual vs fitted plot
Â
0
500000
Fitted values
1000000
1500000
10 Â
The residual vs fitted plot shows a fairly homoscedastic model. However, owing to the clutter on the bottom left of the cluster, we cannot reasonably conclude that the variances of the error term are equal. A model without the problem of heteroscedasticity would be plotted more randomly around the zero line.
IX. Alternative Model Final Regression logmedhouprc = β0  β1 crper1000 + β2 logmedsqft  β3 perhouprch + β4 medhouinc – β5 houvacrate  β6 medagestr + β7 medagestr 2 Source
SS
df
MS
Model Residual
27.8382572 10.4847894
7 166
3.97689389 .063161382
Total
38.3230466
173
.221520501
logmedpr
Coef.
crper1000 houvacrate perhouprch logmedsqft medhouinc medagestr medagestrsq _cons
.000294 .0091788 .0105259 .1409707 8.13e06 .0213033 .0002424 11.91249
Std. Err. .0004082 .0031949 .003903 .0498471 5.94e07 .0082089 .0000793 .4104069
t 0.72 2.87 2.70 2.83 13.68 2.60 3.06 29.03
Number of obs F( 7, 166) Prob > F Rsquared Adj Rsquared Root MSE
P>t 0.472 0.005 0.008 0.005 0.000 0.010 0.003 0.000
= = = = = =
174 62.96 0.0000 0.7264 0.7149 .25132
[95% Conf. Interval] .0011 .0154868 .0182318 .0425546 6.96e06 .0375105 .0000858 11.1022
.000512 .0028709 .00282 .2393867 9.30e06 .005096 .000399 12.72278
Amendments from first regression: 1. Changed functional form for the following variables to make the model more homoscedastic: a. medhouprc to “logmedpr” b. medsqft to “logmedsqft”
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2. Since the relationship between age and housing price (based on scatter plot) is nonlinear, by adding a quadratic version “medagestrsq”, square of independent variable “medagestr”, the model can account for the nonlinearity. Together, both the variables describe a monotonic relationship with one inflection point. (If the relationship was even more complex, we would have possible added a cubic term). Furthermore, by using the quadratic prediction scatter plots (qfit) in stata, we get the following result that verifies the need to include a quadratic variable in the
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12.5
13
13.5
14
14.5
equation.
0
20
40 Median Age of Housing logmedpr
60
80
Fitted values
Quadratic Prediction Scatter Plot
. hettest BreuschPagan / CookWeisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of logmedpr chi2(1) Prob > chi2
= =
0.13 0.7163
12
.5
0
Residuals
.5
1
12
12.5
13 13.5 Fitted values
14
14.5
Residual vs Fitted Plot
Furthermore, with a high probability realized in the Pagan/Cook test, it can be said with certainty that the model is homoscedastic. The Residual vs fitted plot also shows a comparatively random plot around the zero line. However, owing to the fact that we have quadratic version of a variable, the Ramsey Reset test omits both the variables due to multicollinearity and shows that the model has OVB. However, since both the variables (medagestr and medagestr2) are statistically significant (with high tvalues and low pvalues) the issue of multicollinearity is not considered a problem.
X. Discussion on Heteroscedasticity and NonLinear relationship The data used was crosssection, which is when heteroscedasticity most often occurs. This is problematic because it implies that the variance of the disturbance is not constant, meaning that it renders the variance of the estimated parameter biased. Therefore, the tvalue of our estimated coefficients cannot be trusted. The test used to diagnose the presence of heteroscedasticity in linear regression was the Breusch – Pagan / Cook Weisburg test for heteroscedasticity (hettest). The initial regression showed heteroscedasticity, however, after
13
Â
changing the functional forms of a few variables we can see that the final model becomes more homoscedastic. However, as mentioned in the previous section, the unique problem with the model is the presence of a nonlinear relationship between the dependent variable and the independent medagestr variable that produces a tipping point/inflection point. The model uses medagestrsq, the quadratic version of continuous variable medagestr, to represent a decreasing function of housing price until a turning point is reached, from which point the function starts to increase.
XI. Multicollinearity
Variable
VIF
1/VIF
medagestrsq medagestr medhouinc houvacrate crper1000 logmedsqft perhouprch
31.84 30.69 1.41 1.26 1.18 1.06 1.02
0.031410 0.032584 0.707635 0.793498 0.845327 0.941497 0.976007
Mean VIF
9.78
The test result shows high multicollinearity between medagestr and medagestrsq since the later has been derived from the former. However, as mentioned earlier, since both of the variables are statistically significant (with low pvalues) we can say with certainty that multicolliearity is not a problem in the current model.
Â
14 Â
XII. Overall goodness of fit of corrected model The model reports R2 = 0.7264 and adjusted R2 = 0.7149. So about 72% of the total variance of the dependent variable is explained by the 7 independent variables used. This is significantly high number, which means that the model is accurate enough to draw statistical inferences. Furthermore, the model indicates statistically significant predictors, meaning it is useful in drawing conclusion about how changes in the seven independent variables are associated with changes in housing prices. For instance, the model specifically suggests that 1% increase in median square footage increases the median housing price by 0.14%. Using the median housing value for the entire city, this means an increase in housing price by $563.22 which is quite significant.
XIII.
Significant of explanatory variables
Although our main variable of crime rate has expected negative sign, but the high pvalue suggests that it is statistically insignificant. The tstat value is also significantly low as compared to other variables. Therefore, we can reject the null hypothesis since we cannot say for sure that crime impacts the housing prices. The rest of the variables show a low pvalue suggesting a high linear correlation to housing price in Washington DC. Furthermore, since the t statistics for all the remainder of the variables, except crime rate, is higher than 2, we can conclude that these variables have a significant impact on the dependent variable. The signs of the coefficients of each independent variable are as hypothesized.
XIV.
Interpretation of coefficients
Based on the model, the following can be interpreted about the coefficient:5
5
The median value of a house is taken as $402,300 from the dataset. 15

An increase of single crime incident will decrease the housing price by 0.02%  An insignificant decrease in housing price by $80.46.

A one percent increase in housing vacancy rate will decrease the housing price by 0.91%. – A significant decrease in housing price by $3660.93.

A one percent increase of houses with poor characteristics will decrease the housing value by 1.05%  A significant decrease in housing price by $4224.15.

A one percent increase in the median square footage increases the median housing price by 0.14%  A moderately significant increase in housing price by $563.22.

A one dollar increase in median housing income increases the housing price by 0.000813% – An insignificant increase in housing price by $3.27.

Since we have used quadratic version of median housing age of structure, the two age coefficient, medagestr and medagestrsq, cannot be interpreted separately. The negative coefficient of medagestr and positive coefficient of medhoustrsq suggests a monotonic decreasing function of housing price by age of housing until a turning point is reached, after which the function starts to increase. The inflection point can be further calculated by ( β6 medagestr / 2* β7 medagestr 2). This shows that the housing price starts to increase once the house is ~ 44 (43.94) years or older.
XV. Summary of research results The original hypothesis was that there is a negative relationship between crime and housing price, and therefore crime impacts housing prices. Although crime does have a negative correlation, its impact on housing price is not substantial. The coefficient of the other variables in the model are more significant considered to the crime rate variable.
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Therefore, our hypothesis does not stand true. In fact, housing vacancy rate and houses with poor characteristics have a larger impact on the housing prices. Intuitively, we can conclude that the government of Washington D.C, should devote higher attention to prevent foreclosure and improving conditions of the existing housing stock. An important revelation during the study was the impact of age of housing structure. The housing prices seems to increase once the age of housing crosses 43.94 years. The only logical explanation can be that houses constructed in 1960’s might be located in better neighborhoods, have bigger rooms and/or yards compared to new constructions and perhaps closer to the city center. However, this is an interesting topic for another empirical analysis. The model might have been more robust if the source of median price per square feet data was more legitimate. On comparing the data with other real estate data website (like Zillow), the price per square feet seemed to vary a little for certain neighborhoods. Secondly, the data was at neighborhood level and so each of the census tracts within the neighborhood were assigned the same median price per square feet. For future similar studies, the model could be made robust by using similar values but at census tract level. Lastly, It would also help to assess the impact of violent and nonviolent crimes separately since there is a possibility that nonviolent crime rates might be pulling down the overall significance of the crime rate variable. However, within the scope of this model, we can conclude that crime does not significantly impact the housing prices in Washington D.C.
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XVI.
Appendices
Scatter Plots of Initial Regression
1000000 500000 0
0
500000
1000000
1500000
Housing Price vs Vacancy rate
1500000
Housing Price vs Crime Rate
0
100
200 crper1000 medhouprc
300
400
0.00
Fitted values
20.00 houvacrate
medhouprc
30.00
40.00
Fitted values
Housing Price vs Median Square foot
0
0
500000
500000
1000000
1000000
1500000
1500000
Housing Price vs %Housing with poor charac.
0
10 20 %housing w poor characteristics Med Housing Price
30
0
2000
Fitted values
4000 medsqft
medhouprc
6000
8000
Fitted values
Housing Price vs Median age of structure
0
0
500000
500000
1000000
1000000
1500000
1500000
Housing Price vs Median Household Income
0
50000
100000 150000 medhouinc medhouprc
10.00
200000
Fitted values
250000
0
20
40 medagestr medhouprc
60
80
Fitted values
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Scatter Plots of Final Regression Log(Housing Price) vs Vacancy rate
12
12
12.5
12.5
13
13
13.5
13.5
14
14
14.5
14.5
Log(Housing Price) vs Crime Rate
0
100
200 Crime Rate per 1000 logmedpr
300
400
0.00
Fitted values
20.00 Housing Vacancy Rate
logmedpr
30.00
40.00
Fitted values
Log(Housing Price) vs Median Square foot
12
12
12.5
12.5
13
13
13.5
13.5
14
14
14.5
14.5
Log(Housing Price) vs %Housing with poor charac.
0
10 20 %housing w poor characteristics logmedpr
0
30
2000
4000 Median Sq fotoage logmedpr
Fitted values
6000
8000
Fitted values
Log(Housing Price) vs Median age of structure
12
12
12.5
12.5
13
13
13.5
13.5
14
14
14.5
14.5
Log(Housing Price) vs Median Household Income
0
50000
100000 150000 Median Housing Income logmedpr
10.00
Fitted values
200000
250000
0
20
40 Median Age of Housing logmedpr
60
80
Fitted values
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XVII. References De Veaux, R.D., P.F. Velleman and D.E. Bock (2014), “Intro Stats”, PearsonAddison Wesley, 2nd Edition. Gibbons, S. (2004), “The costs of urban property crime”, The economic Journal 114, 441463. Lynch, A. and Rasmussen, D. (2001), “Measuring the impact of crime on house prices”, Applied Economics 33, 19811989. Naroff, J., Hellman,D. and Skinner,D. (1980), “Estimates of the impact of crime on property Values”, Growth and Change 11 (4), 2430. Rizzo, M. (1979), “The cost of crime to victims: An empirical analysis”, Journal of Legal Studies 8, 177205. Sirmans, Stacy, Macpherson, David A., Zietz, Emily N. (2005), “The Composition of Hedonic Pricing Models”, Journal of Real Estate Literature, Vol 13 (1), 5578.
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