1. SAN FRANCISCO STATE UNIVERSITY
Hedonic Regression Analysis In
The Chicago Housing Market
Econ 312: Modeling Project, Fall 2014
Dion Rosete, ID#911507147
12/15/2014

2. 1
I. Introduction
According to economist Kelvin Lancaster’ attributes theory of the consumer, it is not that
“goods are the direct objects of utility,” but “it is the properties or characteristics of a good from
which utility is derived” (Bluestone 2008) The housing market is marked by extreme
heterogeneity – no two homes are exactly alike. They vary widely along many useful dimensions
related to size, quality, and location. With hedonic pricing, the price of the good depends on this
bundle of attributes – if this bundle differs widely, then so will the price. All else equal, should
size, quality, or location increase, so will total price. Through hedonic regression analysis, one
can analyze how the individual attributes of a house contribute towards its price (Potepan 2014).
The housing market generates huge ripple effects. Historically, housing accounts for
17%-18% of GDP, approximately 5% in residential investment and 12%-13% in housing
services. In 2013, the housing market contributed to 15.6% of total GDP - 3.1% in residential
investment, and 12.5% in housing services (NAHB 2014). Additionally, in a 2012 Census
Bureau report, property taxes provide 65.27% of the revenue from local sources and 29.05%
from total sources to public school systems (Dixon 2014). There is an interplay - quality of local
schools drives home value, and the property tax on home values fund local schools. If the
housing supply within a metropolitan area does not expand to match demand, prices and rents
can rise high enough to dissuade economic expansion, particularly through slower employment
and population growth (Bluestone 2008). The attributes and price given to a house affect not
only the homeowners, but whole communities.
The sample data consists of 17 variables - 1 dependent, and 16 covariates - across 2000
observations of the housing market taken from Cook and DuPage Counties, two of the four
counties of the Chicago Primary Metropolitan Statistical Area (PMSA). The data measures

3. 2
attributes in the dwelling/housing itself, its neighborhood, local public goods, and city center
proximity, in their contribution to house contract sales price.
Variable Definition, Units, and Sources Natural
Logarithm
Expected
Signs
Dependent
SPRICE Contract sales price of the house in dollars. Does not include
any closing cost normally chargeable to the purchaser.
(Federal Housing Association 1989-1990)
LSPRICE
Covariates
NROOMS Total number of habitable rooms within the house. (FHA) LNROOMS positive
LVAREA Total living area in square feet. (FHA) LLVAREA positive
HAGEEFF Effective age of the house in years. (FHA) LHAGEFF negative
LSIZE Total area of lot in square feet. (FHA) LLSIZE positive
AIRCON Type of air-conditioning; If house possesses central air-
conditioning = 2, if window or wall air-conditioning = 1, and
if none = 0. (FHA)
(unlogged) positive
NBATH Total number of bathrooms within the dwelling unit; any room
containing “lavoratory or sink, water closet or toilet, and/ or a
tub or shower or both.” (FHA)
(unlogged) positive
GARAGE Type of parking garage; If house contains built-in garage = 4,
if carport (a simple roof or unwalled shed) = 3, if detached
garage = 2, if on-site parking = 1, and, if none = 0. (FHA)
(unlogged) positive
PTAXES Property tax rate in the township district in the year of
purchase, expressed as percentage. (Illinois Department of
Revenue)
LPTAXES negative
PCTWHT Percentage of white people within the local population,
according to the 1990 census tract. (US Census Bureau, 1990)
(unlogged) positive
MEDINC Local median income in dollars. (US Census Bureau, 1990) LMEDINC positive
DFCL Distance in tenths of a mile from the Loop area in downtown
Chicago. (Contemporary city maps)
LDFCL negative
DFNI Distance in tenths of a mile to the nearest expressway
entrance. (Contemporary city maps)
(unlogged) negative
SSPEND Operating expenses in dollars per student in the local school
district. (Illinois State Board of Education’s Annual Statistical
Reports, 1989 and 1990)
LSSPEND positive

4. 3
MSPEND Municipal government expenditures per capita: primarily
measured to the nearest dollar, but a few instances to the
nearest cent. (Census of Government, 1987)
LMSPEND positive
COOK Dummy variable. If located in Cook County = 1; if located in
DuPage County = 0.
(unlogged) positive
OHARE Dummy variable. If located within 5-mile radius of O’Hare
business district = 1; if located outside = 0
(unlogged) positive
One could predict the coefficients attached to number of rooms, number of bathrooms,
living area, and lot size to be positive – one pays for larger quantities of property, and there is
obvious utility in spaciousness. With the natural deterioration of age, the house loses general
quality and function, costs of maintenance increase, and the house becomes less desirable,
resulting in a negative relationship with price. Air-conditioning’s and garage’s effect should be
positive; as the variable increases, the type used is upgraded.
The property tax rate is another extra cost to potential homeowners, so it should be
negative. Per capita municipal government spending is a proxy variable for quality and care of
city infrastructure, while per student school district spending is a proxy variable for the quality
and care of education offered nearby; both should be positive in relation to price. Median income
is a proxy variable for standard of living, so one would expect it to have a positive relationship as
well. With the controversial issues of upward filtering and gentrification, when upper income
households move into a dilapidated inner city neighborhood, they us their economic and political
privilege to help to improve the community, but in doing so, the neighborhood’s property values
rise (Bluestone 2014). Measuring percentage of white population plays into the racial prejudices
of society, which provide them with more opportunity; a product of gentrification is that
neighborhoods become less diverse. The socioeconomic issues of race and class spawn the
perception/issue of crime. They would have a positive relationship with home price.

5. 4
If the Alonso Bid-Rent Model’s tendencies hold true, then one should expect DFCL’s
coefficient to be negative, and OHARE’s to be positive; “willingness to bid” on parcels of land
decreases with distance from the central business district or city center, as potential land users
save in transportation costs by being closer (Bluestone 2014). By the same token, with increasing
distance from the expressway, there are increasing commute costs, so it should have a negative
relationship. Furthermore, though Chicago is located in between Cook and DuPage Counties, the
majority of it and its municipal government is in Cook County; the coefficient for COOK should
therefore be positive.
Proposed Population Model
log(𝑠𝑝𝑟𝑖𝑐𝑒) = 𝛽1 + 𝛽2 log(𝑛𝑟𝑜𝑜𝑚𝑠) + 𝛽3log(𝑙𝑣𝑎𝑟𝑒𝑎) + 𝛽4log(ℎ𝑎𝑔𝑒𝑒𝑓𝑓) + 𝛽5log(𝑙𝑠𝑖𝑧𝑒) +
𝛽6 𝑎𝑖𝑟𝑐𝑜𝑛 + 𝛽7 𝑛𝑏𝑎𝑡ℎ + 𝛽8 𝑔𝑎𝑟𝑎𝑔𝑒 + 𝛽9 log(𝑝𝑡𝑎𝑥𝑒𝑠) + 𝛽10 𝑝𝑐𝑡𝑤ℎ𝑡 + 𝛽11log(𝑚𝑒𝑑𝑖𝑛𝑐) +
𝛽12log(𝑑𝑓𝑐𝑙) + 𝛽13dfni + 𝛽14log(𝑠𝑠𝑝𝑒𝑛𝑑) + 𝛽15log(𝑚𝑠𝑝𝑒𝑛𝑑) + 𝛽16 𝑐𝑜𝑜𝑘 + 𝛽17 𝑜ℎ𝑎𝑟𝑒 + 𝑢𝑖
II. Regressions and Hypotheses Testing
Assuming the model is rendered linear in parameter, there does not exist an exact linear
relationship between regressors [for example, 𝑁𝐵𝐴𝑇𝐻 + 𝐿𝑁𝑅𝑂𝑂𝑀𝑆 ≠ 𝐿𝑉𝐴𝑅𝐸𝐴], expected
value of the error term is zero [as in, E(𝑢𝑖) = 0], variance of the error term is homoscedastic
[var(𝑢𝑖) = 𝜎 𝑢
2
], covariance between error terms is zero [cov(𝑢𝑖, 𝑢𝑗) = 0], and the error term
follows normal distribution [𝑢𝑖~𝑁(0, 𝜎 𝑢
2
)], OLS estimators are best least unbiased estimators.
First Run: Original Estimated Regression Equation
R2
= 0.5460; F(16,1983) = 149.02

6. 5
log(𝑠𝑝𝑟𝑖𝑐𝑒) = 4.9945 + . 1051⏟
(.0404)
log(𝑛𝑟𝑜𝑜𝑚𝑠) + . 3259⏟
(.0374)
log(𝑙𝑣𝑎𝑟𝑒𝑎) − . 0853⏟
(.0096)
log(ℎ𝑎𝑔𝑒𝑒𝑓𝑓)
+ . 0893⏟
(.0110)
log(𝑙𝑠𝑖𝑧𝑒) + . 0288⏟
(.0066)
𝑎𝑖𝑟𝑐𝑜𝑛 + . 0168⏟
(.0146)
𝑛𝑏𝑎𝑡ℎ + . 0131⏟
(.0042)
𝑔𝑎𝑟𝑎𝑔𝑒
− . 5917⏟
(.0575)
log(𝑝𝑡𝑎𝑥𝑒𝑠) + . 0029⏟
(.0003)
𝑝𝑐𝑡𝑤ℎ𝑡 + . 4753⏟
(.0279)
log(𝑚𝑒𝑑𝑖𝑛𝑐) − . 2148⏟
(.0160)
log(𝑑𝑓𝑐𝑙)
− . 0047⏟
(.0039)
dfni + . 0109⏟
(.0511)
log(𝑠𝑠𝑝𝑒𝑛𝑑) − . 0361⏟
(.0208)
log(𝑚𝑠𝑝𝑒𝑛𝑑) + . 0830⏟
(.0276)
𝑐𝑜𝑜𝑘
+ . 0652⏟
(.0311)
𝑜ℎ𝑎𝑟𝑒 + 𝑒 𝑖
R-squared signifies 54.60% of the variation is explained in the regression of the natural
logarithm of house contract sales price on all 16 covariates as measures of house attributes. At
the 5% significance level, there is enough sample information to conclude at least one of the
explanatory variables has a significant influence on home contract sales price (logged).
H0: 𝛽2 = 𝛽3 = 𝛽4 = 𝛽5 … = 𝛽17 = 0
Ha: 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 ≠ 0
Decision Rule: Reject 𝐻0 if 𝐹 > 𝐹(𝛼,𝑘−1,𝑛−𝑘); Reject 𝐻0 if 𝑃 𝑣𝑎𝑙𝑢𝑒 < 𝛼
𝐹(16,1983) =
𝑅2
(𝑘 − 1)⁄
(1 − 𝑅2)/(𝑛 − 𝑘)
=
. 5460 (17 − 1)⁄
(1 − .5460)/(2000 − 17)
= 149.0526 ≈ 149.02
𝐹(𝛼,𝑘−1,𝑛−𝑘) = 𝐹(.05,16,1983) = 𝐹. 𝐼𝑁𝑉. 𝑅𝑇(0.05,16,1983) = 1.6486
P value = F. DIST. RT(149.02,16,1983) = 0.0000
149.02 > 1.6486 → 𝑅𝑒𝑗𝑒𝑐𝑡; 0 < .05 → Reject
Through the t-test, at the 5% significance level, there is enough sample information to
conclude that the effective age of a house has a significant influence on contract home sales price
(logged).
𝐻0: 𝛽4 = 0
𝐻 𝑎: 𝛽4 < 0
Decision Rule: Reject 𝐻0 if 𝑡 < 𝑡(𝑛−2,𝛼) ; Reject 𝐻0 if 𝑃 𝑣𝑎𝑙𝑢𝑒 < 𝛼
𝑡 =
𝑏4 − 𝛽4
𝑆 𝑏4
=
𝑏4
𝑆 𝑏4
=
−.0852755
. 0095621
= −8.92
𝑡(𝑛−2,𝛼) = 𝑡(1998, .05) = 𝑇. 𝐼𝑁𝑉(0.05,1998) = −1.6456
𝑃 𝑣𝑎𝑙𝑢𝑒 = T. DIST(−8.92,1998, 𝑇𝑅𝑈𝐸) = 5.14292 ∗ 10−19
−8.92 < −1.65 → 𝑅𝑒𝑗𝑒𝑐𝑡; 5.14292 ∗ 10−19
< .05 → 𝑅𝑒𝑗𝑒𝑐𝑡

7. 6
In subsequent runs, LSSPEND (p-value = .831), NBATH (p-value = .251), and DFNI (p-
value = .222) were dropped one at a time, deemed insignificant at the 5% level. Through the
subset F test, at the 5% significance level, there is enough sample information to conclude that
the dropping of the three variables was justified.
𝐻0: 𝛽7 = 𝛽13 = 𝛽14 = 0
𝐻𝐴 : 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 ≠ 0
Decision Rule: Reject H0 if 𝐹 > 𝐹(𝛼,𝑞,𝑛−𝑘); Reject 𝐻0 if 𝑃 𝑣𝑎𝑙𝑢𝑒 < 𝛼
𝐹 =
(𝑅 𝑈𝑅
2
− 𝑅 𝑅
2
) 𝑞⁄
(1 − 𝑅 𝑈𝑅
2
)/(𝑛 − 𝑘)
=
(.5460 − .5453) 3⁄
(1 − .5460)/(2000 − 17)
=
(0.0007) 3⁄
(0.454)/(1983)
= 1.0192
𝐹(𝛼,𝑞,𝑛−𝑘) = 𝐹(.05,3,1983) = F. INV. RT(0.05,3,1983) = 2.6094
𝑃 𝑣𝑎𝑙𝑢𝑒 = F. DIST. RT(1.0192,3,1983) =0.3831
1.0192 < 2.6094 → Fail To Reject; 0.3831 > .05 → Fail to Reject
Fifth Run: Revised Regression Equation
𝑅 𝑅
2
= 0.5453; F(13,1986) = 183.21
log(𝑠𝑝𝑟𝑖𝑐𝑒) = 5.0151 + . 1163⏟
(.0388)
log(𝑛𝑟𝑜𝑜𝑚𝑠) + . 3410⏟
(.0350)
log(𝑙𝑣𝑎𝑟𝑒𝑎) − . 0849⏟
(.0094)
log(ℎ𝑎𝑔𝑒𝑒𝑓𝑓)
+ . 0883⏟
(.0108)
log(𝑙𝑠𝑖𝑧𝑒) + . 0290⏟
(.0066)
𝑎𝑖𝑟𝑐𝑜𝑛 + . 0125⏟
(.0042)
𝑔𝑎𝑟𝑎𝑔𝑒
− . 6059⏟
(.0495)
log(𝑝𝑡𝑎𝑥𝑒𝑠) + . 0028⏟
(.0003)
𝑝𝑐𝑡𝑤ℎ𝑡 + . 4762⏟
(.0279)
log(𝑚𝑒𝑑𝑖𝑛𝑐) − . 2156⏟
(.0158)
log(𝑑𝑓𝑐𝑙)
− . 0386⏟
(.0164)
log(𝑚𝑠𝑝𝑒𝑛𝑑) + . 0943⏟
(.0229)
𝑐𝑜𝑜𝑘 + . 0701⏟
(.0306)
𝑜ℎ𝑎𝑟𝑒 + 𝑒𝑖
III. Preliminary Interpretations
LPTAX, LMEDINC, and LDFCL were the most significant. All else equal, for every 1%
increase in property tax (t = -12.24), sales price decreases by .6059%; for every 1% increase in
median income (t = 17.10), sales price increases by .4762%; and for every 1% increase in
distance from the Loop area (t = -13.65), sales price decreases by .2156%, on average.

8. 7
With 95% confidence, the interval [.00224, .00336] contains the true population
parameter 𝛽10, the coefficient for PCTWHT, and the interval [.06709, .10953] contains the true
population parameter 𝛽5, the coefficient for LLSIZE. All of the remaining variables have
confidence intervals that do not contain zero, while the ones eliminated did.
Confidence Interval: 𝑏𝑗 ± 𝑀𝑂𝐸, where 𝑀𝑂𝐸 = 𝑡 𝑛−2,𝛼/2 ∗ 𝑆 𝑏 𝑗
𝑏𝑗 − 𝑡 𝑛−2,𝛼/2 ∗ 𝑆 𝑏 𝑗
< 𝛽𝑗 < 𝑏𝑗 + 𝑡 𝑛−2,𝛼/2 ∗ 𝑆 𝑏 𝑗
± 𝑡 𝑛−2,𝛼/2 = ± 𝑡1998 ,.05/2 = 𝑇. 𝐼𝑁𝑉. 2𝑇(0.05,1998) = ± 1.961152015
𝑏10 = .0028045; 𝑆 𝑏10
= .0002856
𝑡1998,.025 ∗ 𝑆 𝑏10
= 1.961152015 ∗ .0002856 = 0.000560105
𝑏10 − 𝑡 𝑛−2,𝛼/2 ∗ 𝑆 𝑏10
= .0028045 − 0.000560105 =0.002244395
𝑏10 + 𝑡 𝑛−2,𝛼/2 ∗ 𝑆 𝑏10
= .0028045 + 0.000560105 =0.003364605
.002244 < 𝛽10 < .00336
𝑏5 = .0883127; 𝑆 𝑏5
= .0108195
𝑡1998,.025 ∗ 𝑆 𝑏5
= 1.961152015 ∗ .0108195 =0.021218684
𝑏10 − 𝑡 𝑛−2,𝛼/2 ∗ 𝑆 𝑏10
= .0883127 − 0.021218684 =0.06709
𝑏10 + 𝑡 𝑛−2,𝛼/2 ∗ 𝑆 𝑏10
= .0883127 + 0.021218684 =0.109531
. 06709 < 𝛽5 < .10953
IV. Conclusions
According to the regression of house sales price, distance from nearest expressway, local
school spending per student, and number of bathrooms have no significant influence on home
price; but number of rooms, living area, lot size, effective age, property tax, local median
income, type of garage, air-conditioning, government spending, and proximity to places of
activity definitely do. All the variables’ coefficients had their expected signs, except for
LMSPEND, which turned out negative. Municipal spending may not be a measure of quality and

9. 8
care, but instead, constant deterioration, inefficient spending, and high crime. The insignificance
of distance from nearest expressway intuitively makes sense – by being closer, the home owner
may cut commute costs, but also experience constant car noise and exhaust; the benefits are
negated by the costs. The insignificance of school district spending per student is a bit surprising
– it would seem that more spending attractively implies better education. But, it is only a proxy,
only implicit in quality of the school. There is the issue of how school spending is used
constructively. It was surprising number of bathrooms was deemed insignificant, let alone zero in
some observations. Perhaps bathrooms are taken for granted as a necessity, or it is superfluous to
have many for less house members. NBATH also was highly correlated with LLVAREA (r =
.7977) and LNROOMS (.7805).
On that note, both before and after the variables were dropped, none of the variables
exhibited high variable inflation factors – in the end, multi-collinearity did not seem severe, so
the data became sufficient. But, there are also high correlations between student spending and
municipal government spending (r = 0.6879), number of rooms and living area (0.8987),
percentage white population and median income (0.6827), property tax rate and being in Cook
County (0.6579), median income and distance from Loop area (0.7070). This may require further
study on causality, but these relationships are somewhat intuitive – education spending draws
from local government, white populations tend to be more privileged, bigger living area allows
for more rooms, property tax is levied on more valuable property in Cook County, and higher
median income often is in the suburbs, away from the Loop area.
In order to efficiently accommodate potential homeowners and “bid up” price, perhaps
one must not focus on constructing/selling closer to the expressway or with more bathrooms, but
instead on lowering property tax rate, or constructing/selling within higher-income

10. 9
neighborhoods, closer to The Loop, among other significant attributes. Through manipulating
these significant attributes, one can increase price in an effort to increase school revenue through
property tax, upward-filter/gentrify a neighborhood, or generate general economic growth. One
must find a happy medium in property tax rate in juggling homeowners’ desires, home sales
price, and tax revenue; to raise tax revenue, one can increase the property tax rate, but
compensate by providing more of these positive attributes. One can also cool down the housing
market for the sake of population and employment growth by providing less of these positive
significant attributes and more of the negative ones, like increasing tax rates or distance to
central business districts. The insignificant school spending proxy variable reminds us that data
can only take us so far – sometimes quality is immeasurable, and should be directly observed.
V: Appendix
References
Bluestone, Barry, Mary Huff Stevenson, and Russell Williams. 2008. The Urban Experience:
Economics, Society, and Public Policy. New York: Oxford University Press.
Chattopadhyay, Sudip. 1999. "Estimating the Demand for Air Quality: New Evidence Based on
the Chicago Housing Market." Land Economics, Vol. 75, no. No. 1: Pp. 22-38.
Accessed November 12, 2014. http://www.jstor.org/stable/3146991.
Dixon, Mark. 2014. "Public Education Finances: 2012." United States Census Bureau.
Accessed December 13, 2014. http://www2.census.gov/govs/school/12f33pub.pdf.
NAHB. “Housing's Contribution to Gross Domestic Product (GDP)." 2014. National Association
of Home Builders (NAHB). Accessed December 13, 2014.
http://www.nahb.org/generic.aspx?genericContentID=66226.

11. 10
Potepan, Michael. Fall 2014. “Chapter 12: Urban Housing Markets & Residential Location.”
Class lecture for Urban Economics at San Francisco State University, San Francisco, CA.