Multiple Multiple RegressionRegression

AnalysisAnalysisTCADTCAD

2011 Reappraisal2011 Reappraisal

Part 1Part 1Common Themes:Common Themes:

TCAD TCAD TARB TARB

Texas ConstitutionTexas ConstitutionProperty Value Property Value

StudyStudy

Fair Market Fair Market ValueValue&&

Equality/Equality/UniformityUniformity

TCAD TCAD Mission StatementMission Statement

To provide market value appraisals of all To provide market value appraisals of all taxable property in Travis County in a taxable property in Travis County in a fair fair and equitableand equitable, and cost effective manner, , and cost effective manner, and to provide services and assistance to and to provide services and assistance to the public and taxing jurisdictions.the public and taxing jurisdictions. Fair (Market Value) Fair (Market Value) Equitable (Consistent Value Application) Equitable (Consistent Value Application)

TARB TARB MissionMission

Mission - To provide taxpayers with Mission - To provide taxpayers with opportunity to resolve their conflicts opportunity to resolve their conflicts with the appraisal district, according to with the appraisal district, according to the Texas Property Tax Code.the Texas Property Tax Code.

GoalsGoals To To LISTENLISTEN to taxpayer protests to taxpayer protests WITHOUTWITHOUT prejudice. prejudice. Render a Render a fair and equitablefair and equitable decision, decision,

based on testimony presented.based on testimony presented.

The Texas ConstitutionThe Texas ConstitutionArticle 8, Section 1Article 8, Section 1

Tax in Proportion Tax in Proportion to Valueto Value Ad Valorem (Fair Ad Valorem (Fair

Market Value) Market Value) Equality and Equality and

UniformityUniformity Consistent Value Consistent Value

ApplicationsApplications

Property Value Study Property Value Study (PVS)(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 uses The PVS uses ratio statisticsratio statistics to evaluate to evaluate TCAD appraisal performance.TCAD appraisal performance.

Only one ratio is considered....Only one ratio is considered....

““The Appraisal Ratio”The Appraisal Ratio”

Model ValueModel Value Sale PriceSale Price

Ratio StatisticsRatio Statistics Other Other

ConsiderationsConsiderations Price Related Price Related

Differential Differential RangeRange Standard DeviationStandard Deviation Coefficient of Coefficient of

VariationVariation

The most The most important important statistics used to statistics used to evaluate TCAD evaluate TCAD appraisal appraisal performance:performance:

1.1. Median Level of Median Level of ValueValue

1.1. Market ValueMarket Value2.2. Coefficient of Coefficient of

DispersionDispersion 1.1. Uniformity of Uniformity of

Appraisal Appraisal

Ratio StatisticsRatio Statistics MediMedi

an an Level Level of of ValueValue 98%98%

C.O.DC.O.D.. 6.96.9

%%

The ChallengeThe Challenge Can TCAD improve its appraisal Can TCAD improve its appraisal

performance with the help of performance with the help of Multiple Regression Analysis?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 Error Reduce the Standard Error Reduce the Standard DeviationReduce the Standard Deviation

COMMON GOALS:COMMON GOALS:Fair Market Value & Fair Market Value &

Uniformity/EqualityUniformity/Equality

Part 2Part 2From Here to There:From Here to There:

AdjustedAdjustedCostCost

ModelModel(ACM)(ACM)

Vs.Vs.MultipleMultiple

RegressionRegressionAnalysisAnalysis(MRA)(MRA)

Adjusted Cost Model Adjusted Cost Model (ACM)(ACM)

ACM Prediction EquationACM Prediction Equation Model Value = (Land * %Adj) + Model Value = (Land * %Adj) +

((Variable * Unit Value * Depreciation) + ((Variable * Unit Value * Depreciation) + (V(V22 * U * U22 * D * D22) + (V) + (V33 * U * U33 * D * D33) ... ) * NAF)) ... ) * NAF)

4 Categories of attributes4 Categories of attributes1.1. LandLand2.2. ImprovementsImprovements3.3. DepreciationDepreciation4.4. Neighborhood Adjustment Factor (NAF)Neighborhood Adjustment Factor (NAF)

ACM – Land ACM – Land

Bluff (B - 1)Bluff (B - 1) Golf Course (GC - Golf Course (GC -

5)5) Lake View (LV - 33)Lake View (LV - 33) Size and Shape (N -Size and Shape (N -

393)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 - Greenbelt (Y -

85)85)

54 others... (0)54 others... (0)

9 of 63 Land adjustments present (n = 9 of 63 Land adjustments present (n = 1390)1390)

2 methods (Lot, FF)2 methods (Lot, FF)

ACM – Land AdjustmentsACM – Land Adjustments

ACM – Improvements ACM – Improvements

Baths (1390)*Baths (1390)* Porch (1385)*Porch (1385)* Garage (1380)*Garage (1380)* Fireplace Fireplace

(1355)*(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 Marshall and Swift Cost Index = Unit Values*Values*

15 of 26 Improvement Attributes in the 15 of 26 Improvement Attributes in the sales filesales file Spa (71)Spa (71)

Hot Tub (8 = Hot Tub (8 = Spa)Spa)

Sport Court Sport Court (7)(7)

Fountain (3)Fountain (3) Courtyard (2)Courtyard (2) Outside Stair Outside Stair

(2)(2) SolariumSolarium LoftLoft BoathouseBoathouse

Boat DockBoat Dock SaunaSauna GreenhouseGreenhouse PenthousePenthouse StableStable Tennis CourtsTennis Courts BathhouseBathhouse

*MRA Sample *MRA Sample Size (n = Size (n = 1390)1390)

ACM – Depreciation ACM – Depreciation

Straight-line (age-life)Straight-line (age-life) Grade/Condition floors:Grade/Condition floors:

Excellent (90%); Good (85%); Average Excellent (90%); Good (85%); Average (75%)...(75%)...

Physical, Functional, Economic Physical, 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

ACM Straight-Line ACM Straight-Line DepreciationDepreciation

Excellent 90%Good 85%

Average 75%Dep % Fair 65%

Poor 40%

Salvage 20%

10 20 30 40 50 60 70Age

ACM – Neighborhood ACM – Neighborhood Adjustment Factor (NAF)Adjustment Factor (NAF)

Calibrated to a target median ratio Calibrated to a target median ratio (.98) during valuation season for all (.98) during valuation season for all NBHDs with sufficient sales to value.NBHDs with sufficient sales to value.

ACM – Neighborhood ACM – Neighborhood Adjustment Factor Adjustment Factor

MRA ModelMRA ModelListen to the market....Listen to the market....

...To Find Unit Values!...To Find Unit Values!

Time Adjustments Time Adjustments (TASP3)(TASP3)

Time Adjusted Sales Price (TASP3)Time Adjusted Sales Price (TASP3) Section 23.01.a of the Texas Property Tax Section 23.01.a of the Texas Property Tax

CodeCode requires requires Appraisal Districts to Appraisal Districts to appraise market value as of appraise market value as of January 1stJanuary 1st. . Furthermore, section 23.013.c of the Texas Furthermore, section 23.013.c of the Texas Property Tax Code Property Tax Code requiresrequires the appraisal the appraisal district to district to adjust all sales for any adjust all sales for any change in the market value from the change in the market value from the date of sale to the date as of which the date of sale to the date as of which the market value is to be determinedmarket value is to be determined. .

Steiner RanchMonthly Median Sales Ratio

0.8

0.9

1

1.1

1.2

Month - Year

Med

ian

(Sal

e Pr

ice/

2010

Val

)

January 1st, 2011

Monthly Median Sales Monthly Median Sales RatioRatio

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

Med

ian

(Sal

e Pr

ice/

2010

Val

)

January 1st, 2011

Linear Regression

Linear Regression (Time Linear Regression (Time Trend)Trend)

Visual Test (Zero Slope)Visual Test (Zero Slope)Zero Slope Visual Test (Linear)

0.8

0.9

1

1.1

1.2

Month-Year

Adju

sted

Sal

es R

atio

January 1st, 2011

66thth Order Polynomial Order Polynomial5-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

Med

ian

(Sal

e Pr

ice/

2010

Val

)

January 1, 2011

4th, 5th, 6th polynomial trendlines

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

Adju

sted

Sal

es R

atio

TASP3 EquationTASP3 Equation The 6th order polynomial equation adequately The 6th order polynomial equation adequately

addresses changes in market value over time. addresses changes in market value over time. The following equation was be used to adjust The following equation was be used to adjust sale prices to the January 1, 2011 appraisal sale prices to the January 1, 2011 appraisal date.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.

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

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 b = Constant - (y-intercept or # of sales at

time zero)time zero) m = Coefficient - Calculated rate of change m = Coefficient - Calculated rate of change

in the # of sales over timein the # of sales over time

Linear RegressionLinear Regression“Least Squares Analysis” “Least Squares Analysis”

“The Line of Best Fit”“The Line of Best Fit”

Multiple RegressionMultiple Regression Multiple Regression (More than one Multiple Regression (More than one

variable)variable) ““Advanced Paired Sales” Advanced Paired Sales” Ceteris Paribus - “All else the same”Ceteris Paribus - “All else the same” Value = (Constant + (Variable * Unit Value) + Value = (Constant + (Variable * Unit Value) +

(V(V22 * U * U22) + (V) + (V33 * U * U33)) * NAF)) * NAF Remember ACM equation???Remember ACM equation???

Value = (Land * %Adj) + ((Variable * Unit Value = (Land * %Adj) + ((Variable * Unit Value * Depreciation) + (VValue * Depreciation) + (V22 * U * U22 * D * D22) + (V) + (V33 * * UU33 * D * D33) ... ) * NAF)) ... ) * NAF)

Multiple Regression Multiple Regression (Visual)(Visual)

MRA Model MRA Model (10 Variables)(10 Variables)

Landcode/SizeLandcode/Size Square Square

Foot/QualityFoot/Quality Age (sqrt)Age (sqrt) BathsBaths Deck sfDeck sf

Terrace sfTerrace sf FireplaceFireplace Garage SpaceGarage Space Porch sfPorch sf PoolPool

MRA Model (Thrown MRA Model (Thrown Out)Out)

Percentage of sales with insignificant Percentage of sales with insignificant attributesattributes 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

ACM – Land AdjustmentsACM – Land Adjustments

MRA – Land CodesMRA – Land Codes

The ResultsThe ResultsModel Summary

.976a .952 .951 39698.34800Model1

R R SquareAdjustedR Square

Std. Error ofthe 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.

PREDICTION EQUATIONPREDICTION EQUATIONCONSTANT 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

ACM vs MRAACM vs MRA

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

Standard Deviation and Standard Deviation and ProbabilityProbability

Standard Standard Deviation Deviation = .09 rd.= .09 rd.

Mean = .98Mean = .98 68% 68%

from .89 to from .89 to 1.071.07

SE = 39KSE = 39K Avg Val = Avg Val =

438K438K 68% from 68% from

399K to 399K to 477K477K

68.2%68.2%

95.5%95.5%99.7%99.7%

Freq

uenc

yFr

eque

ncy

-3s-3s -2s-2s -1s-1s MeanMean +1s+1s +2s+2s +3s+3s

X

Ratio StatisticsRatio Statistics MediMedi

an an Level Level of of ValueValue

98%98%

C.O.DC.O.D..

6.9%6.9%

ACM vs MRAACM vs MRA

Defense GridsDefense Grids EquityEquity

41.43.b.3 - An 41.43.b.3 - An ‘appropriately adjusted’ ‘appropriately adjusted’ equity grid should use the equity grid should use the same values for adjustment same values for adjustment as used in the mass model.as used in the mass model.

Its a ‘Non-Model Test’. The Its a ‘Non-Model Test’. The adjusted value is the same adjusted value is the same as notice valueas notice value if everyone if everyone was treated fairly.was treated fairly.

MarketMarket Adjustments come solely Adjustments come solely

from the market.from the market. Proven quantifiable Proven quantifiable

evidence evidence

QualityLiving Area (sf)Size x Quality

LandcodeLand Difference

ClassAge

Age FactorLand Size (sf)

BathDeck (sf)

Terrace (sf)Fireplace

Garage SpacePorch (sf)

PoolBoat DocksSport Court

Additional DetailMkt Level Adjustment

ConclusionConclusion The two models are similar but The two models are similar but

different... 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 quality of any model will mirror the quality of the data.the quality of the data.

Improve and Expand – MRA valuation Improve and Expand – MRA valuation in 2012.in 2012.

Thank You!!Thank You!!