Regression Analysis in
Residential Real Estate Litigation
Speakers:
Jeffrey W. Spilker, JD, CPA/ABV
Helga A. Zauner, AB, CFE, CVA, MBA
Speakers
Jeffrey W. Spilker, JD, CPA/ABV
Jeff Spilker is an Owner of Hill Schwartz Spilker Keller LLC (“HSSK”), a business valuation and
litigation consulting firm in Houston, Texas. Jeff leads the HSSK’s real estate consulting and
construction advisory practice.
Previously, Jeff was with a national accounting and consulting firm. He has also served as the
CFO of an engineering/construction company and Vice President/General Manager of a
construction and real estate development firm. Jeff has provided a wide range of financial and
economic consulting and financial forensics services to attorneys in matters involving intellectual
property and patent infringement claims, health care and professional practices, oil & gas issues,
construction disputes, professional liability claims, partnership disputes, real estate and business
valuation issues, environmental issues, personal injury and employment claims, lost profits
analyzes, fraud investigations and lender liability claims. He has provided expert testimony in
over 100 of these matters.
Jeff is a Certified Public Accountant, licensed attorney in the Commonwealth of Virginia and a
Texas State Certified General Real Estate Appraiser.
Speakers
Helga A. Zauner, AB, CFE, CVA, MBA
Helga Zauner is a Director in the Litigation Consulting group of Hill Schwartz Spilker Keller LLC
(“HSSK”) in Houston. She is a testifying expert and has over 20 years of unique experience in
Financial Analysis and Statistical Modeling. She specializes in Financial Forensics, Forecasting
Techniques, Time Series Analysis and Econometrics and has extensive experience in Quantitative
and Data Analysis.
Helga's background includes serving as a Financial Advisor in banking and corporate credit and as
a partner and Financial Manager in the construction and automobile dealership businesses. She
was an Associate Professor for four years at Universidad de Guanajuato in Mexico, where she
taught courses in Finance, Econometrics and Statistics, and did Applied Research in: Financial
Analysis, Investments, Project Analysis, Time Series, Forecasting and Econometrics.
Helga is a Certified Fraud Examiner and a Certified Valuation Analyst. Helga has a B.S. in
Mathematics, an MBA and an ABD in Statistics.
Today’s Program
I.
-- Litigation
II. -- Simple Regression
III. -- Multiple Regression
IV. -- Binary Variables
V. -- Examples of regression used in real estate litigation
Objective
Objective
To show the use of the statistical methodology of
multivariate regression analysis for:
• Group appraisals
• Prove/disprove an allegation in appraisal
related litigation
• Measure of damages
Group Appraisals
Prove/Disprove allegations
How much did the slope change and how
does that affect my value?
The expert’s worst nightmare
The Daubert Challenge
Daubert Criteria
1. Has the theory or technique in question been tested or
can it be tested?
2. Has this methodology been subjected to peer review and
publication?
3. Is there a known or potential error rate?
4. Do maintenance of standards controlling its operation
exist?
5. Has it attracted widespread acceptance within a relevant
scientific community?
Simple Linear Regression Model
Building Size v. Sales Price
350,000
300,000
250,000
200,000
150,000
100,000
50,000
-
1,000
Source: Multiple Listing Services
2,000
3,000
4,000
5,000
6,000
Simple Linear Regression Model (cont.)
Lot size v. Sales Price
350,000
300,000
250,000
200,000
SalesPrice
Linear (SalesPrice)
150,000
100,000
50,000
-
2,000
4,000
Source: Multiple Listing Services
6,000
8,000
10,000
12,000
14,000
16,000
18,000
Other Possible Variables
•
•
•
•
•
•
Property type (condo / multifamily / single family…)
Year property was built
Number of bedrooms / bathrooms
New or recent construction?
Renovated – Has property been renovated?
Date property sold
Bedrooms / Bathrooms
Bedrooms v. Sales Price
Bathrooms v. Sales Price
350,000
350,000
300,000
300,000
250,000
250,000
200,000
200,000
150,000
150,000
100,000
100,000
50,000
50,000
0
1
2
3
Source: Multiple Listing Services
4
5
6
0
1
2
3
4
5
Effect of time
Year Built v. SalesPrice
Closing Date v Sales Price
350,000
350,000
300,000
300,000
250,000
250,000
200,000
200,000
150,000
150,000
100,000
100,000
50,000
50,000
-
1998
2000
2002
2004
2006
Source: Multiple Listing Services
2008
2010
2012
2014
09/2011 04/2012 10/2012 05/2013 11/2013 06/2014 12/2014
Qualitative variables
•
•
•
•
•
Architect/Design
Nice view
Better materials
Cleaner
Good real estate agent for the seller?
The Model
Price = 44,912.22 + 43.85 x sqft
A 3,200sqft house in
Lakes of Savannah
costs an average of
$185,232
Coefficients:
(Intercept)
Estimate
Std. Error
t value
Pr(>|t|)
44912.223
9033.256
4.972
1.85e-06
SqFtBldg
43.846
3.521
12.454 < 2e-16
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 26600 on 145 degrees of freedom
Multiple R-squared: 0.5168, Adjusted R-squared: 0.5135
F-statistic: 155.1 on 1 and 145 DF, p-value: < 2.2e-16
***
***
Price = 44,912.22 + 43.84 x sqft
Building Size v. Sales Price
350,000
300,000
250,000
Slope
200,000
SalesPrice
Linear (SalesPrice)
150,000
100,000
50,000
Intercept
-
1,000
2,000
3,000
4,000
5,000
6,000
Remember Daubert Criteria?
1. Has the theory or technique in question been tested or
can it be tested?
2. Has this methodology been subjected to peer review and
publication?
3. Is there a known or potential error rate?
4. Do maintenance of standards controlling its operation
exist?
5. Has it attracted widespread acceptance within a relevant
scientific community?
Multiple Regression Analysis
• One variable explains only a certain percentage of the
variability in price
• Can we combine the effects of several variables?
• Can we separate the effect each variable has on the price,
isolating it from the effects of other variables?
• Can we measure how much of the price variability our
model has captured?
• Can we determine how “trustworthy” our model is?
The Answer
Statistical methods allow us to
• choose the variables that create the better model
• measure the effect each variable has on the prices
• determine how much of the price variability is captured
by our model
• measure the “trustworthiness” of the model
– Perfect compliance to Daubert! 
– Difficult to explain 
• All this if our data and model comply with the assumptions
of the Gauss-Markov theorem…
The Model
Price = -7,691,000 + 1.736 x (lot size) + 39.47 x sqft + 3,845 x (year built) + 57.60 x (days after 01/01/2012)
Coefficients:
Estimate
Std. Error
t value
Pr(>|t|)
(Intercept) -7,691,000 1.470e+06
-5.233
6.16e-07
LotSize
1.736
1.046e+00
1.659
0.0994
SqFtBldg 39.47
3.712e+00
10.635
< 2e-16
YearBuilt 3,845
7.342e+02
5.237
6.06e-07
Days
57.60
7.098e+00
8.114
2.58e-13
--Significance codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
***
.
***
***
***
Residual standard error: 20440 on 136 degrees of freedom (6 observations deleted due to missingness)
Multiple R-squared: 0.7278, Adjusted R-squared: 0.7198
F-statistic: 90.91 on 4 and 136 DF, p-value: < 2.2e-16
Forecast
Price = -7,691,000 + 1.736 x (lot size) + 39.47 x sqft + 3,845 x (year built) + 57.60 x (days after 01/01/2012)
Price = -7,691,000 + 1.736 x 5,000sqft + 39,47x 3,200sqft + 3,845 x 2011 + 57.60 x 365 =
$197,303
A house in Lakes of Savannah, on a 5,000 sqft lot, with 3,200sqft construction, built in
2011 and purchased on January 1, 2013 would have cost an average of $197,303
Quantitative v. Appraiser
• The expertise of the appraiser can’t be substituted by a
purely quantitative model
• A model will provide the average price for a property
with certain measurable characteristics
• Regression models are particularly useful for group
appraisals, and to price properties that are equivalent
except for one or two variables – hence usefulness in
litigation
Binary (Dummy) Variables
• Used for a yes/no characteristic:
–
–
–
–
–
–
Garage/no garage
Pool/no pool
Single glass windows/double glass windows
Renovated/not renovated
In “special” area/not in “special” area
Before/after certain event
• Variable set to “1” if Yes or “0” if No
Example
• Use of binary variables for litigation:
– Beach Condo High Rise
– Damage model based on the assumption that prices changed
after January 1, 2010
– Regression model used to determine whether prices were
affected by this event of 2010.
Example (cont.) – Condo Prices
Sale Price
$2,500,000.00
$2,000,000.00
$1,500,000.00
$1,000,000.00
$500,000.00
$01/03/05
01/03/06
01/03/07
01/03/08
01/03/09
01/03/10
01/03/11
Example (cont.) – Condo Prices
Average Price per Sq Ft per Floor
500.00
450.00
Average Price per Sq Ft
400.00
350.00
300.00
250.00
200.00
150.00
100.00
50.00
1
2
3
4
5
6
7
8
9
10 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Floor
Example (cont.) – Condo Prices
Floor
35
30
25
20
15
10
5
0
01/14/04
05/28/05
10/10/06
02/22/08
07/06/09
11/18/10
04/01/12
Example (cont.) – Condo Prices
Relevant factors for condo prices were Size in Square Feet and Floor:
Price = -207,420.87 + 429.32 x sqft + 5,069.41 x floor
Coefficients:
Estimate
Std. Error t value
Pr(>|t|)
(Intercept) -207420.87 27479.71 -7.548
2.84e-12 ***
Size
429.32
15.46
27.775
< 2e-16 ***
Floor
5069.41
675.56
7.504
3.65e-12 ***
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 75230 on 165 degrees of freedom
Multiple R-squared: 0.8405, Adjusted R-squared: 0.8386
F-statistic: 434.9 on 2 and 165 DF, p-value: < 2.2e-16
Example(cont.) –
Was there a change in 2010?
Price = -184,106.69 + 422.84 x sqft + 5,315 x floor – 59,197.88 af2010
Coefficients:
Estimate
Std. Error t value
Pr(>|t|)
(Intercept) -184106.69 26319.65 -6.995
6.40e-11
Size
422.84
14.61
28.948
< 2e-16
Floor
5315.44
637.73
8.335
2.97e-14
af2010
-59197.88 12508.94 -4.732
4.76e-06
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 70780 on 164 degrees of freedom
Multiple R-squared: 0.8597, Adjusted R-squared: 0.8571
F-statistic: 335 on 3 and 164 DF, p-value: < 2.2e-16
***
***
***
*** Prices went down by an average of $59,198!
Notice that
• By adding the binary variable the intercept and coefficients for floor and square feet
changed.
• Previous model was biased!
• Is the theory wrong?????
• No… the model just didn’t fulfill the assumptions.
• The Gauss-Markov theorem states that regression models which
fulfill the classical linear regression model assumptions provide the
best, linear and unbiased estimators. With respect to ordinary least
squares, the relevant assumption of the classical linear regression
model is that the error term is uncorrelated with the regressors.
• The presence of omitted-variable bias violates this particular
assumption. The violation causes the OLS estimator to be biased
and inconsistent.
Regression as an aid to a
“traditional” appraiser
• The coefficients of the regression indicate the change in
the price as a result of a unit change in the variable.
• This can be used to give a magnitude to the adjustments
used in traditional appraisal techniques.
Notes of Caution
• Regardless of the true relationship between variables,
you can ALWAYS run a regression between them.
• Correlation does not imply causation.
• The validity of the results of a
regression model depend on the assumptions being true:
– Normality
– No auto-correlation
– No multicollinearity
Must perform tests to
validate the significance
of the model
Bunnies cause peace!
Examples
• Regression analysis used in litigation in:
–
–
–
–
–
–
–
–
–
Age discrimination
Antitrust
Appraisal of shares
Breach of contract
Copyright infringement
Gender/racial discrimination
Patent infringement
Securities Fraud
Real property tax assessment/valuation
Environmental/Property Damage
• Ponca Tribe of Indians of Oklahoma v. Continental
Carbon Co.
– Defendant’s expert reported results of neighborhood
comparison analysis and multi variate regression analysis (test
of property value diminution in test areas compared to control
areas).
– Plaintiff’s complained that defendant’s expert selectively used
data to reach conclusions that he would not have reached had
he used all the data. Expert did not do an analysis of the
percentage of outliers.
Source: Litigation Services Handbook, 5th edition
Property Tax Valuation
• Department of Revenue v Grant Western Lumber Co.
– The court believes that it is an error to make a conclusion
about the slope coefficient for the price of the subject mill
because only one variable was taken in to account. Other
important factors such as age, condition, location, etc. were
not included in the analysis.
Source: Litigation Services Handbook, 5th edition
ASHBY HIGH-RISE
ASHBY HIGH-RISE
The Question
• Has the imminent threat of the construction of the high
rise already affected market prices?
• What area has been affected by the threat of the high
rise?
Ashby area is “different”
•
•
•
•
•
Traditional Houston neighborhood
Renovated historical homes more valuable than new homes
Size of home not as important as lot size
Many “special” homes
Typical variables are not the most important to determine
prices
Use price per square foot instead of price
2Q2013
1Q2013
4Q2012
3Q2012
2Q2012
1Q2012
4Q2011
3Q2011
2Q2011
1Q2011
4Q2010
3Q2010
2Q2010
1Q2010
4Q2009
3Q2009
2Q2009
1Q2009
4Q2008
3Q2008
2Q2008
1Q2008
4Q2007
3Q2007
2Q2007
1Q2007
4Q2006
3Q2006
2Q2006
1Q2006
Average
Price per Sq Ft
Ashby – Historical sales data
Ashby Area Average Price per Square Foot
450
400
350
300
250
200
Outside
150
Inside
100
50
0
2Q2013
1Q2013
4Q2012
3Q2012
2Q2012
1Q2012
4Q2011
3Q2011
2Q2011
1Q2011
4Q2010
3Q2010
2Q2010
1Q2010
4Q2009
3Q2009
2Q2009
1Q2009
4Q2008
3Q2008
2Q2008
1Q2008
4Q2007
3Q2007
2Q2007
1Q2007
4Q2006
3Q2006
2Q2006
1Q2006
Average
Price per Sq Ft
Ashby – Perhaps “smoothing” the data
Ashby Area Average Price per Square Foot
450
400
350
300
250
Outside
200
Inside
150
Poly. (Outside)
Poly. (Inside)
100
50
0
Ashby – “Larger lot size = Higher price”
Lot Size v PRSF
1000
900
800
700
600
PRSF
500
Linear (PRSF)
400
300
200
100
0
0
10000
20000
30000
40000
50000
60000
70000
80000
Ashby – Newer houses have lower prices?
Year Built v PRSF
1000
900
800
700
600
PRSF
500
Linear (PRSF)
400
300
200
100
0
1880
1900
1920
1940
1960
1980
2000
2020
Variables
• Dependent Variable:
–
PRSF – Price Per Square Foot
• Independent Variables:
–
–
–
–
–
–
–
–
–
Days – Number of Days after March 1, 2012
Townhome – Is property a Townhome (Yes = 1, 0=No)
Multifamily – Is Property a Multifamily Home (Yes = 1, 0=No)
Bldg – Square Feet of Construction
HR – Is Property In High Rise Affected Area? (Yes = 1, 0=No)
Year – Year Property was built
Lot – Lot Size in Square Feet
Historic – Is property located in the historic district? (Yes = 1, 0=No)
Renovated – Has Property been renovated? (Yes = 1, 0=No)
The Model and Result
Coefficients:
Estimate
-1,695
.09405
-47.35
-80.87
-.022170
.9890
.01327
53.33
31.42
-46.30
Std. Error
5.351e+02
3.146e-02
1.725e+01
2.347e+01
6.211e-03
2.748e-01
1.982e-03
1.851e+01
1.349e+01
1.439e+01
(Intercept)
Days
Townhome
Multifamily
Bldg
Year
Lot
Historic
Renovated
HR
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
t value
-3.168
2.989
-2.744
-3.445
-3.494
3.599
6.698
2.881
2.329
-3.219
Residual standard error: 60.8 on 135 degrees of freedom
Multiple R-squared: 0.5492, Adjusted R-squared: 0.5192
F-statistic: 18.28 on 9 and 135 DF, p-value: < 2.2e-16
Pr(>|t|)
0.001901 **
0.003326 **
0.006888 **
0.000760 ***
0.000644 ***
0.000448 ***
5.21e-10 ***
0.004616 **
0.021343 *
0.001613 **
Conclusions
• Regression analysis complies with Daubert criteria.
• However…
– Easy to “lie” with statistics – careful with the interpretation of the
model!
– Correlation does not imply causation
– Must perform reliability tests on model
– Can’t necessarily extrapolate
– Courts can be skeptical
Thank you!
Questions?
Helga Zauner
hzauner@hssk.com
Jeff Spilker
jspilker@hssk.com