Analysis of Automated Valuation Models using Mulitiple Regression Modeling Techniques.

1. Multiple RegressionMultiple Regression
AnalysisAnalysis
TCADTCAD
2011 Reappraisal2011 Reappraisal

2. Part 1Part 1
Common Themes:Common Themes:
TCADTCAD
TARBTARB
Texas ConstitutionTexas Constitution
Property Value StudyProperty Value Study
Fair Market ValueFair Market Value
&&
Equality/UniformityEquality/Uniformity

3. TCADTCAD
Mission StatementMission Statement
 To provide market value appraisals of all taxableTo provide market value appraisals of all taxable
property in Travis County in aproperty in Travis County in a fair and equitablefair and equitable,,
and cost effective manner, and to provide servicesand cost effective manner, and to provide services
and assistance to the public and taxing jurisdictions.and assistance to the public and taxing jurisdictions.
 Fair (Market Value)Fair (Market Value)
 Equitable (Consistent Value Application)Equitable (Consistent Value Application)

4. TARBTARB
MissionMission
 Mission - To provide taxpayers with opportunity toMission - To provide taxpayers with opportunity to
resolve their conflicts with the appraisal district,resolve their conflicts with the appraisal district,
according to the Texas Property Tax Code.according to the Texas Property Tax Code.
 GoalsGoals
 ToTo LISTENLISTEN to taxpayer proteststo taxpayer protests
 WITHOUTWITHOUT prejudice.prejudice.
 Render aRender a fair and equitablefair and equitable decision,decision, based on testimonybased on testimony
presented.presented.

5. The Texas ConstitutionThe Texas Constitution
Article 8, Section 1Article 8, Section 1
 Tax in Proportion toTax in Proportion to
ValueValue
 Ad Valorem (Fair MarketAd Valorem (Fair Market
Value)Value)
 Equality andEquality and
UniformityUniformity
 Consistent ValueConsistent Value
ApplicationsApplications

6. Property Value Study (PVS)Property Value Study (PVS)
 Section 5.10 of the Texas Property Tax Code
 Comptroller must conduct a study every other year
to determine:
 Median level of appraisal (Market)
 Uniformity of appraisal (Equity)
 The PVS usesThe PVS uses ratio statisticsratio statistics to evaluate TCADto evaluate TCAD
appraisal performance.appraisal performance.
 Only one ratio is considered....Only one ratio is considered....

7. ““The Appraisal Ratio”The Appraisal Ratio”
Model ValueModel Value
Sale PriceSale Price

8. Ratio StatisticsRatio Statistics
 Other ConsiderationsOther Considerations
 Price Related DifferentialPrice Related Differential
 RangeRange
 Standard DeviationStandard Deviation
 Coefficient of VariationCoefficient of Variation
 The most importantThe most important
statistics used tostatistics used to
evaluate TCADevaluate TCAD
appraisal performance:appraisal performance:
1.1. Median Level of ValueMedian Level of Value
1.1. Market ValueMarket Value
2.2. Coefficient ofCoefficient of
DispersionDispersion
1.1. Uniformity of AppraisalUniformity of Appraisal

9. Ratio StatisticsRatio Statistics
 MedianMedian
LevelLevel
ofof
ValueValue
 98%98%
 C.O.D.C.O.D.
 6.9%6.9%

10. The ChallengeThe Challenge
 Can TCAD improve its appraisal performanceCan TCAD improve its appraisal performance
with the help of Multiple Regression Analysis?with the help of Multiple Regression Analysis?
 Produce a Fair Market Level of ValueProduce a Fair Market Level of Value
 Tighten the C.O.D.Tighten the C.O.D.
 Reduce the Standard ErrorReduce the Standard Error
 Reduce the Standard DeviationReduce the Standard Deviation
COMMON GOALS:COMMON GOALS:
Fair Market Value & Uniformity/EqualityFair Market Value & Uniformity/Equality

11. Part 2Part 2
From Here to There:From Here to There:
AdjustedAdjusted
CostCost
ModelModel
(ACM)(ACM)
Vs.Vs.
MultipleMultiple
RegressionRegression
AnalysisAnalysis
(MRA)(MRA)

12. Adjusted Cost Model (ACM)Adjusted Cost Model (ACM)
 ACM Prediction EquationACM Prediction Equation
 Model Value = (Land * %Adj) + ((Variable * UnitModel Value = (Land * %Adj) + ((Variable * Unit
Value * Depreciation) + (VValue * Depreciation) + (V22 * U* U22 * D* D22) + (V) + (V33 * U* U33 **
DD33) ... ) * NAF)) ... ) * NAF)
 4 Categories of attributes4 Categories of attributes
1.1. LandLand
2.2. ImprovementsImprovements
3.3. DepreciationDepreciation
4.4. Neighborhood Adjustment Factor (NAF)Neighborhood Adjustment Factor (NAF)

13. ACM – LandACM – Land
 Bluff (B - 1)Bluff (B - 1)
 Golf Course (GC - 5)Golf Course (GC - 5)
 Lake View (LV - 33)Lake View (LV - 33)
 Size and Shape (N -393)Size and Shape (N -393)
 Terrain (P - 3)Terrain (P - 3)
 View (Q - 49)View (Q - 49)
 Size (SZ - 1)Size (SZ - 1)
 Drainage (W - 3)Drainage (W - 3)
 Greenbelt (Y - 85)Greenbelt (Y - 85)
 54 others... (0)54 others... (0)
 9 of 63 Land adjustments present (n = 1390)9 of 63 Land adjustments present (n = 1390)
 2 methods (Lot, FF)2 methods (Lot, FF)

14. ACM – Land AdjustmentsACM – Land Adjustments

15. ACM – ImprovementsACM – Improvements
 Baths (1390)*Baths (1390)*
 Porch (1385)*Porch (1385)*
 Garage (1380)*Garage (1380)*
 Fireplace (1355)*Fireplace (1355)*
 Terrace (436)*Terrace (436)*
 Deck (288)*Deck (288)*
 Pool (168)*Pool (168)*
 HVAC (1388)HVAC (1388)
 Carports (110)Carports (110)
 Marshall and Swift Cost Index = Unit Values*Marshall and Swift Cost Index = Unit Values*
 15 of 26 Improvement Attributes in the sales file15 of 26 Improvement Attributes in the sales file
 Spa (71)Spa (71)
 Hot Tub (8 = Spa)Hot Tub (8 = Spa)
 Sport Court (7)Sport Court (7)
 Fountain (3)Fountain (3)
 Courtyard (2)Courtyard (2)
 Outside Stair (2)Outside Stair (2)
 SolariumSolarium
 LoftLoft
 BoathouseBoathouse
 Boat DockBoat Dock
 SaunaSauna
 GreenhouseGreenhouse
 PenthousePenthouse
 StableStable
 Tennis CourtsTennis Courts
 BathhouseBathhouse
 *MRA Sample*MRA Sample
Size (n = 1390)Size (n = 1390)

16. ACM – DepreciationACM – Depreciation
 Straight-line (age-life)Straight-line (age-life)
 Grade/Condition floors:Grade/Condition floors:
 Excellent (90%); Good (85%); Average (75%)...Excellent (90%); Good (85%); Average (75%)...
 Physical, Functional, EconomicPhysical, Functional, Economic
 1 case each in Sales file (n = 1390)1 case each in Sales file (n = 1390)
 Each case was a 10% discountEach case was a 10% discount

17. ACM Straight-Line DepreciationACM Straight-Line Depreciation
Excellent 90%
Good 85%
Average 75%
Dep % Fair 65%
Poor 40%
Salvage 20%
10 20 30 40 50 60 70
Age

18. ACM – Neighborhood AdjustmentACM – Neighborhood Adjustment
Factor (NAF)Factor (NAF)
 Calibrated to a target median ratio (.98) duringCalibrated to a target median ratio (.98) during
valuation season for all NBHDs with sufficientvaluation season for all NBHDs with sufficient
sales to value.sales to value.

19. ACM – Neighborhood Adjustment FactorACM – Neighborhood Adjustment Factor

20. MRA ModelMRA Model
Listen to the market....Listen to the market....
...To Find Unit Values!...To Find Unit Values!

21. Time Adjustments (TASP3)Time Adjustments (TASP3)
 Time Adjusted Sales Price (TASP3)Time Adjusted Sales Price (TASP3)
 Section 23.01.a of the Texas Property Tax CodeSection 23.01.a of the Texas Property Tax Code
requiresrequires Appraisal Districts to appraise market value asAppraisal Districts to appraise market value as
ofof January 1stJanuary 1st. Furthermore, section 23.013.c of the. Furthermore, section 23.013.c of the
Texas Property Tax CodeTexas Property Tax Code requiresrequires the appraisal districtthe appraisal district
toto adjust all sales for any change in the marketadjust all sales for any change in the market
value from the date of sale to the date as of whichvalue from the date of sale to the date as of which
the market value is to be determinedthe market value is to be determined..

22. Steiner Ranch
Monthly Median Sales Ratio
0.8
0.9
1
1.1
1.2
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Month - Year
Median(SalePrice/2010Val)
January 1st, 2011
Monthly Median Sales RatioMonthly Median Sales Ratio

23. Steiner Ranch
5 Year Time Trend
0.8
0.9
1
1.1
1.2
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Month - Year
Median(SalePrice/2010Val)
January 1st, 2011
Linear Regression
Linear Regression (Time Trend)Linear Regression (Time Trend)

24. Visual Test (Zero Slope)Visual Test (Zero Slope)
Zero Slope Visual Test (Linear)
0.8
0.9
1
1.1
1.2
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Month-Year
AdjustedSalesRatio
January 1st, 2011

25. 66thth
Order PolynomialOrder Polynomial
5-Year Time Trend
0.80
0.90
1.00
1.10
1.20
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Month-Year
Median(SalePrice/2010Val)
January 1, 2011
4th, 5th, 6th polynomial trendlines

26. Zero Slope Achieved!Zero Slope Achieved!
TASP3TASP3
Zero Slope Visual Test (6th order)
0.95
1
1.05
1.1
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Month-Year
AdjustedSalesRatio

27. TASP3 EquationTASP3 Equation
 The 6th order polynomial equation adequatelyThe 6th order polynomial equation adequately
addresses changes in market value over time. Theaddresses changes in market value over time. The
following equation was be used to adjust sale prices tofollowing equation was be used to adjust sale prices to
the January 1, 2011 appraisal date.the January 1, 2011 appraisal date.
 TASP3 = SPRICE*(1.0183 /TASP3R).TASP3 = SPRICE*(1.0183 /TASP3R).
 TASP3R = 0.0000000000471*MONTH^6 -TASP3R = 0.0000000000471*MONTH^6 -
0.0000000199942*MONTH^5 +0.0000000199942*MONTH^5 +
0.0000021807069*MONTH^4 -0.0000021807069*MONTH^4 -
0.00008852402*MONTH^3 +0.00008852402*MONTH^3 +
0.0010720575848*MONTH^2 +0.0010720575848*MONTH^2 +
0.0057238812883*MONTH + 1.021465983192.0.0057238812883*MONTH + 1.021465983192.

28. MRA Prediction EquationMRA Prediction Equation
 Identify TASP3 (Jan 1, 2011)Identify TASP3 (Jan 1, 2011)
 Achieved with Time Trend EquationAchieved with Time Trend Equation
 Predict TASP3Predict TASP3
 Solve for Prediction EquationSolve for Prediction Equation

29. Linear EquationLinear Equation
 Linear Regression - Single VariableLinear Regression - Single Variable
 Example: “Volume of Sales over time...”Example: “Volume of Sales over time...”
 Y = mX + bY = mX + b
 Y = Dependant Variable - Number of SalesY = Dependant Variable - Number of Sales
 X = Independent Variable - Time (in years)X = Independent Variable - Time (in years)
 b = Constant - (y-intercept or # of sales at timeb = Constant - (y-intercept or # of sales at time
zero)zero)
 m = Coefficient - Calculated rate of change in the #m = Coefficient - Calculated rate of change in the #
of sales over timeof sales over time

30. Linear RegressionLinear Regression
“Least Squares Analysis”“Least Squares Analysis”
“The Line of Best Fit”“The Line of Best Fit”

31. Multiple RegressionMultiple Regression
 Multiple Regression (More than one variable)Multiple Regression (More than one variable)
 ““Advanced Paired Sales”Advanced Paired Sales”
 Ceteris Paribus - “All else the same”Ceteris Paribus - “All else the same”
 Value = (Constant + (Variable * Unit Value) + (VValue = (Constant + (Variable * Unit Value) + (V22 **
UU22) + (V) + (V33 * U* U33)) * NAF)) * NAF
 Remember ACM equation???Remember ACM equation???
 Value = (Land * %Adj) + ((Variable * Unit Value *Value = (Land * %Adj) + ((Variable * Unit Value *
Depreciation) + (VDepreciation) + (V22 * U* U22 * D* D22) + (V) + (V33 * U* U33 * D* D33) ... ) *) ... ) *
NAF)NAF)

32. Multiple Regression (Visual)Multiple Regression (Visual)

33. MRA ModelMRA Model
(10 Variables)(10 Variables)
 Landcode/SizeLandcode/Size
 Square Foot/QualitySquare Foot/Quality
 Age (sqrt)Age (sqrt)
 BathsBaths
 Deck sfDeck sf
 Terrace sfTerrace sf
 FireplaceFireplace
 Garage SpaceGarage Space
 Porch sfPorch sf
 PoolPool

34. MRA Model (Thrown Out)MRA Model (Thrown Out)
 Percentage of sales with insignificant attributesPercentage of sales with insignificant attributes
 Land Adjustments – 100%Land Adjustments – 100%
 Replaced by LandcodingReplaced by Landcoding
 Carports – 8%Carports – 8%
 Spa – 5%Spa – 5%
 Others (<2%)Others (<2%)
 CourtyardCourtyard
 Outside StairOutside Stair

35. ACM – Land AdjustmentsACM – Land Adjustments

36. MRA – Land CodesMRA – Land Codes

37. The ResultsThe Results
Model Summary
.976a .952 .951 39698.34800
Model
1
R R Square
Adjusted
R Square
Std. Error of
the Estimate
Predictors: (Constant), TERRASFZ, B301100,
L303200, L303101, B301450, L302150, QUALLOW,
L301425, L302250, B301300, B302300, L301210,
L301400, L301800, B302200, B301350, L301600,
SQFT6M, L301750, DECKSFZ, SQFT5M, L302800,
L301455, SQFT5P, EFFSQRT, SQFT6P, QUALLOWP,
POOLZ, SQFT7M, PORCHZ, SQFT6, FIRPLZ, GARSPZ,
LSQFT, QUALHP, SQFT5, BATHSZ
a.

38. PREDICTION EQUATIONPREDICTION EQUATION
CONSTANT 93,030$
+ 21,785$ * B301100 + 1$ * L302250
+ 85,537$ * B301300 + 2$ * L302800
+ 254,354$ * B301350 + 22$ * L303101
+ 98,006$ * B301450 + 20$ * L303200
+ 42,460$ * B302200 + 1$ * LSQFT
+ 76,286$ * B302300 + 29,107$ * POOLZ
+ 3,776$ * BATHSZ + 38$ * PORCHZ
+ 32$ * DECKSFZ + 468,124$ * QUALHP
+ (10,637)$ * EFFSQRT + 61,818$ * QUALLOW
+ 7,847$ * FIRPLZ + 99,676$ * QUALLOWP
+ 9,330$ * GARSPZ + 62$ * SQFT5
+ 8$ * L301210 + 60$ * SQFT5M
+ 3$ * L301400 + 66$ * SQFT5P
+ 2$ * L301425 + 76$ * SQFT6
+ 1$ * L301455 + 78$ * SQFT6M
+ 7$ * L301600 + 79$ * SQFT6P
+ 8$ * L301750 + 64$ * SQFT7M
+ 3$ * L301800 + 15$ * TERRASFZ.
+ 2$ * L302150

39. ACM vs MRAACM vs MRA

40. Ratio Study StandardsRatio Study Standards
 IAAOIAAO
 All Single Family ResidenceAll Single Family Residence
 C.O.D. < 15%C.O.D. < 15%
 ‘‘Fairly’ Homogeneous Areas (SFR)Fairly’ Homogeneous Areas (SFR)
 C.O.D. < 10%C.O.D. < 10%
 PVSPVS
 5 – 10% (Homogeneous)5 – 10% (Homogeneous)
 Appraisal UniformityAppraisal Uniformity
 MRA – 20% improvement over ACMMRA – 20% improvement over ACM

41. Standard Deviation and ProbabilityStandard Deviation and Probability
 StandardStandard
Deviation = .Deviation = .
09 rd.09 rd.
 Mean = .98Mean = .98
 68% from .68% from .
89 to 1.0789 to 1.07
 SE = 39KSE = 39K
 Avg Val =Avg Val =
438K438K
 68% from68% from
399K to399K to
477K477K
68.2%68.2%
95.5%95.5%
99.7%99.7%
FrequencyFrequency
-3s-3s -2s-2s -1s-1s MeanMean +1s+1s +2s+2s +3s+3s
X

42. Ratio StatisticsRatio Statistics
 MedianMedian
LevelLevel
ofof
ValueValue
 98%98%
 C.O.D.C.O.D.
 6.9%6.9%

43. ACM vs MRAACM vs MRA

44. Defense GridsDefense Grids
 EquityEquity
 41.43.b.3 - An ‘appropriately41.43.b.3 - An ‘appropriately
adjusted’ equity grid should useadjusted’ equity grid should use
the same values for adjustmentthe same values for adjustment
as used in the mass model.as used in the mass model.
 Its a ‘Non-Model Test’. TheIts a ‘Non-Model Test’. The
adjusted value is the same asadjusted value is the same as
notice valuenotice value if everyone wasif everyone was
treated fairly.treated fairly.
 MarketMarket
 Adjustments come solely fromAdjustments come solely from
the market.the market.
 Proven quantifiable evidenceProven quantifiable evidence
Quality
Living Area (sf)
Size x Quality
Landcode
Land Difference
Class
Age
Age Factor
Land Size (sf)
Bath
Deck (sf)
Terrace (sf)
Fireplace
Garage Space
Porch (sf)
Pool
Boat Docks
Sport Court
Additional Detail
Mkt Level Adjustment

45. ConclusionConclusion
 The two models are similar but different...The two models are similar but different...
 Value = (Variable * Unit Price)Value = (Variable * Unit Price)
 ACM – Marshall and SwiftACM – Marshall and Swift
 MRA – Immediate MarketMRA – Immediate Market
 The quality of any model will mirror the qualityThe quality of any model will mirror the quality
of the data.of the data.
 Improve and Expand – MRA valuation in 2012.Improve and Expand – MRA valuation in 2012.

46. Thank You!!Thank You!!