why can’t i afford a home?

Why Can’t I Afford a Why Can’t I Afford a Home?Home?

By:By:Philippe BonnanPhilippe BonnanEmelia BragadottirEmelia BragadottirTroy DewittTroy DewittAnders GrahamAnders GrahamS. Matthew ScottS. Matthew ScottLingli TangLingli Tang

OrganizationOrganization

Time Series RegressionTime Series Regression• United States: Ten year regression United States: Ten year regression

of explanatory variables against of explanatory variables against median price of a home median price of a home


Cross Section RegressionCross Section Regression• 14 Different Areas for 2 separate years: 2000 14 Different Areas for 2 separate years: 2000

and 2005and 2005Metropolitan Statistical Area

Santa Barbara, CA MSASan Diego, CA MSADallas-Fort Worth, TX MSAEl Paso, TX MSAColorado Springs, CO MSAWashington-Arlington-Alexandria DC-MD-VA-WV MSAChicago-Naperville-Joliet,IL MSABoston-Cambridge-Quincy, MA MSANY-Northern New Jersey-Long Island, NY MSAColumbus, OH MSAOmaha, NE MSAMiami-Fort Lauderdale-Miami Beach, FL MSACumberland, MD-VA MSASan Francisco, CA MSA

The VariablesThe Variables

Median Price of a Home (dependent Median Price of a Home (dependent variable)variable)

ββ11= Unemployment Rate= Unemployment Rate ββ22= Median Family Income= Median Family Income ββ33= Building Permits= Building Permits ββ44= Population= Population ββ55= Distance from the coast (Not = Distance from the coast (Not

applicable for Time-Series)applicable for Time-Series) ΒΒ66= Mortgage Rates (Not applicable = Mortgage Rates (Not applicable

for Cross-Section)for Cross-Section)

Graphical RelationshipsGraphical Relationships

The following graphs compare The following graphs compare the median price of a home with the median price of a home with each variable over a period of each variable over a period of ten yearsten years

Each variable uses 1996 as an Each variable uses 1996 as an index for comparison (For each index for comparison (For each variable, the value for 1996 is variable, the value for 1996 is set to 1)set to 1)

Unemployment RateUnemployment Rate

0.00

0.50

1.00

1.50

2.00

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Median Price Unemployment Rate

Median Family IncomeMedian Family Income

0.0

0.5

1.0

1.5

2.0

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Median Family Income Median Price

Building PermitsBuilding Permits

0.00

0.50

1.00

1.50

2.00

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Building Permits Median Price

PopulationPopulation

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Median Price Population

Mortgage RatesMortgage Rates

0.00

0.50

1.00

1.50

2.00

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Median Price Home Mortgage Rates

Our HypothesisOur Hypothesis

• Ho: The explanatory variables in Ho: The explanatory variables in the regression don’t explain the the regression don’t explain the median price of a homemedian price of a home

i.e. i.e. ββ11= = ββ22= … == … =ββnn=0=0

• Ha: At least one explanatory Ha: At least one explanatory variable explains the median variable explains the median price of a homeprice of a home

i.e. i.e. ββ11≠0 or ≠0 or ββ22≠0 … or ≠0 … or ββnn≠0 ≠0

Results for Time Series Results for Time Series Analysis (U.S.)Analysis (U.S.)

Time Series Analysis – Time Series Analysis – Correlation MatrixCorrelation Matrix

PRICE HOMEMORTGAGE

RATE

INCOME PERMITS POPULATION

UNEMPLOYMENTRATE

PRICE 1 -0.908548 0.923769 0.978469 0.952524 0.436929

HOMEMORTGAGERATE -0.90855 1 -0.91219 -0.93725 -0.91575 -0.573675

INCOME 0.923769 -0.912188 1 0.905082 0.994486 0.413594

PERMITS 0.978469 -0.937248 0.905082 1 0.93711 0.385133

POPULATION 0.952524 -0.915753 0.994486 0.93711 1 0.382568

UNEMPLOYMENTRATE 0.436929 -0.573675 0.413594 0.385133 0.382568 1

Time Series RegressionTime Series Regression Dependent Variable: PRICEDependent Variable: PRICE Method: Least SquaresMethod: Least Squares Date: 12/06/06 Time: 09:38Date: 12/06/06 Time: 09:38 Sample: 1 10Sample: 1 10 Included observations: 10Included observations: 10 VariableVariable CoefficientCoefficient Std. ErrorStd. Error t-Statistict-Statistic Prob. Prob. HOMEMORTGAGERATE 632665.HOMEMORTGAGERATE 632665. 1151196. 1151196. 1.418234 1.418234 0.2291 0.2291 INCOMEINCOME -6.116375-6.116375 6.401278 6.401278 -0.955493-0.955493 0.3934 0.3934 PERMITSPERMITS 0.092208 0.092208 0.056354 0.056354 1.636246 1.636246 0.1771 0.1771 POPULATIONPOPULATION 0.006230 0.006230 0.004887 0.004887 1.274867 1.274867 0.2714 0.2714 UNEMPLOYMENTRATEUNEMPLOYMENTRATE 1033710. 1033710. 358705.7 358705.7 2.881777 2.881777 0.0449 0.0449 CC -1622644.-1622644. 933044.8 933044.8 -1.739085-1.739085 0.1570 0.1570 R-squaredR-squared 0.990920 0.990920 Mean dependent var Mean dependent var 153950.0 153950.0 Adjusted R-sq.Adjusted R-sq. 0.979571 0.979571 S.D. dependent var S.D. dependent var 34063.41 34063.41 S.E. of regressionS.E. of regression 4868.733 4868.733 Akaike info criterion Akaike info criterion 20.10276 20.10276 Sum squared residSum squared resid 94818259 94818259 Schwarz criterion Schwarz criterion 20.28432 20.28432 Log likelihoodLog likelihood -94.51382-94.51382 F-statistic F-statistic 87.30830 87.30830 Durbin-Watson sta 3.279181Durbin-Watson sta 3.279181 Prob(F-statistic) Prob(F-statistic) 0.000357 0.000357

Significant Test with 10 observations and Alpha = 0.05Significant Test with 10 observations and Alpha = 0.05Unemployment Rate is the only significant variableUnemployment Rate is the only significant variable

Therefore we reject the null hypothesis because unemployment is Therefore we reject the null hypothesis because unemployment is Significant.Significant.

Explanation of results for Explanation of results for time series analysis time series analysis

T-stats for coefficients of the explanatory variables T-stats for coefficients of the explanatory variables are not significant (except unemployment) but are not significant (except unemployment) but coefficient of determination, R-squared, is high. coefficient of determination, R-squared, is high.

This means that the explanatory variables are This means that the explanatory variables are highly correlated. highly correlated.

This is explained in the correlation matrix on a This is explained in the correlation matrix on a previous slide. previous slide.

This is an example of multicollinearity. This is an example of multicollinearity. Therefore we decided to drop out one of the Therefore we decided to drop out one of the

explanatory variables in order to erase the explanatory variables in order to erase the multicollinearity.multicollinearity.

Drop Mortgage RateDrop Mortgage Rate Dependent Variable: PRICEDependent Variable: PRICE Method: Least SquaresMethod: Least Squares Date: 12/06/06 Time: 19:25Date: 12/06/06 Time: 19:25 Sample: 1 10Sample: 1 10 Included observations: 10Included observations: 10 VariableVariable CoefficientCoefficient Std. ErrorStd. Error t-Statistict-Statistic Prob. Prob. INCOMEINCOME -12.22777-12.22777 5.190382 5.190382 -2.355851-2.355851 0.0651 0.0651 PERMITSPERMITS 0.027076 0.027076 0.035811 0.035811 0.756096 0.756096 0.4837 0.4837 POPULATIONPOPULATION 0.010664 0.010664 0.004118 0.004118 2.589475 2.589475 0.0489 0.0489 UNEMPLOYMENTRATEUNEMPLOYMENTRATE 824150.2 824150.2 358395.3 358395.3 2.299557 2.299557 0.0698 0.0698 CC -2334912.-2334912. 862220.4 862220.4 -2.708022-2.708022 0.0424 0.0424 R-squaredR-squared 0.986355 0.986355 Mean dependent var Mean dependent var 153950.0 153950.0 Adjusted R-squared0.975438Adjusted R-squared0.975438 S.D. dependent var S.D. dependent var 34063.41 34063.41 S.E. of regressionS.E. of regression 5338.490 5338.490 Akaike info criterion Akaike info criterion 20.31013 20.31013 Sum squared residSum squared resid 1.42E+08 1.42E+08 Schwarz criterion Schwarz criterion 20.46142 20.46142 Log likelihoodLog likelihood -96.55063-96.55063 F-statistic F-statistic 90.35561 90.35561 Durbin-Watson stat 2.343565Durbin-Watson stat 2.343565 Prob(F-statistic) Prob(F-statistic) 0.000075 0.000075

Significant Test with 10 observations and Alpha = 0.05Significant Test with 10 observations and Alpha = 0.05 Population is the only significant variablePopulation is the only significant variable Unemployment now becomes insignificantUnemployment now becomes insignificant

Drop PermitsDrop Permits Dependent Variable: PRICEDependent Variable: PRICE Method: Least SquaresMethod: Least Squares Date: 12/06/06 Time: 19:27Date: 12/06/06 Time: 19:27 Sample: 1 10Sample: 1 10 Included observations: 10Included observations: 10 VariableVariable CoefficientCoefficient Std. ErrorStd. Error t-Statistict-Statistic Prob. Prob. HOMEMORTGAGERATEHOMEMORTGAGERATE 97613.97 97613.97 770997.7 770997.7 0.126607 0.126607 0.9042 0.9042 INCOMEINCOME -15.51536-15.51536 3.264526 3.264526 -4.752713-4.752713 0.0051 0.0051 POPULATIONPOPULATION 0.013532 0.013532 0.002301 0.002301 5.880010 5.880010 0.0020 0.0020 UNEMPLOYMENTRATEUNEMPLOYMENTRATE 998640.4 998640.4 413787.3 413787.3 2.413415 2.413415 0.0606 0.0606 CC -2949376.-2949376. 533483.0 533483.0 -5.528529-5.528529 0.0027 0.0027 R-squaredR-squared 0.984843 0.984843 Mean dependent var Mean dependent var 153950.0 153950.0 Adjusted R-squared 0.972717Adjusted R-squared 0.972717 S.D. dependent var S.D. dependent var 34063.41 34063.41 S.E. of regressionS.E. of regression 5626.411 5626.411 Akaike info criterion Akaike info criterion 20.41518 20.41518 Sum squared residSum squared resid 1.58E+08 1.58E+08 Schwarz criterion Schwarz criterion 20.56648 20.56648 Log likelihoodLog likelihood -97.07592-97.07592 F-statistic F-statistic 81.21998 81.21998 Durbin-Watson sta 2.325004Durbin-Watson sta 2.325004 Prob(F-statistic) Prob(F-statistic) 0.000098 0.000098

Both Income and Population are now significant explanatory Both Income and Population are now significant explanatory variablesvariables

Drop PopulationDrop Population Dependent Variable: PRICEDependent Variable: PRICE Method: Least SquaresMethod: Least Squares Date: 12/06/06 Time: 19:28Date: 12/06/06 Time: 19:28 Sample: 1 10Sample: 1 10 Included observations: 10Included observations: 10 VariableVariable CoefficientCoefficient Std. ErrorStd. Error t-Statistict-Statistic Prob. Prob. HOMEMORTGAGERATEHOMEMORTGAGERATE 2571603. 2571603. 938466.0 938466.0 2.740220 2.740220 0.0408 0.0408 INCOMEINCOME 1.9929471.992947 0.761256 0.761256 2.617971 2.617971 0.0472 0.0472 PERMITSPERMITS 0.157815 0.157815 0.024359 0.024359 6.478855 6.478855 0.0013 0.0013 UNEMPLOYMENTRATEUNEMPLOYMENTRATE 967915.6 967915.6 376516.0 376516.0 2.570715 2.570715 0.0500 0.0500 CC -442695.1-442695.1 125212.2 125212.2 -3.535560-3.535560 0.0166 0.0166 R-squaredR-squared 0.987231 0.987231 Mean dependent var Mean dependent var 153950.0 153950.0 Adjusted R-squared0.977016Adjusted R-squared0.977016 S.D. dependent var S.D. dependent var 34063.41 34063.41 S.E. of regressionS.E. of regression 5164.203 5164.203 Akaike info criterion Akaike info criterion 20.24374 20.24374 Sum squared residSum squared resid 1.33E+08 1.33E+08 Schwarz criterion Schwarz criterion 20.39503 20.39503 Log likelihoodLog likelihood -96.21871-96.21871 F-statistic F-statistic 96.64315 96.64315 Durbin-Watson stat3.147208Durbin-Watson stat3.147208 Prob(F-statistic) Prob(F-statistic) 0.000064 0.000064

When we drop Population, all our explanatory variables now When we drop Population, all our explanatory variables now become significantbecome significant

Drop Unemployment RateDrop Unemployment Rate Dependent Variable: PRICEDependent Variable: PRICE Method: Least SquaresMethod: Least Squares Date: 12/06/06 Time: 19:29Date: 12/06/06 Time: 19:29 Sample: 1 10Sample: 1 10 Included observations: 10Included observations: 10 VariableVariable CoefficientCoefficient Std. ErrorStd. Error t-Statistict-Statistic Prob. Prob. HOMEMORTGAGERATEHOMEMORTGAGERATE 266099.7 266099.7 1645584. 1645584. 0.161705 0.161705 0.8779 0.8779 INCOMEINCOME -3.839510-3.839510 9.965120 9.965120 -0.385295-0.385295 0.7159 0.7159 PERMITSPERMITS 0.0825050.082505 0.088246 0.088246 0.934945 0.934945 0.3927 0.3927 POPULATIONPOPULATION 0.0042040.004204 0.007586 0.007586 0.554139 0.554139 0.6034 0.6034 CC -1002577.-1002577. 1424248. 1424248. -0.703935-0.703935 0.5129 0.5129 R-squaredR-squared 0.972069 0.972069 Mean dependent var Mean dependent var 153950.0 153950.0 Adjusted R-square 0.949725Adjusted R-square 0.949725 S.D. dependent var S.D. dependent var 34063.41 34063.41 S.E. of regressionS.E. of regression 7637.749 7637.749 Akaike info criterion Akaike info criterion 21.02645 21.02645 Sum squared residSum squared resid 2.92E+08 2.92E+08 Schwarz criterion Schwarz criterion 21.17774 21.17774 Log likelihoodLog likelihood -100.1322-100.1322 F-statistic F-statistic 43.50361 43.50361 Durbin-Watson stat1.359493Durbin-Watson stat1.359493 Prob(F-statistic) Prob(F-statistic) 0.000447 0.000447

We have no significant explanatory variables when we drop We have no significant explanatory variables when we drop Unemployment RateUnemployment Rate

DROP INCOMEDROP INCOME

Dependent Variable: PRICEDependent Variable: PRICE Method: Least SquaresMethod: Least Squares Date: 12/06/06 Time: 09:42Date: 12/06/06 Time: 09:42 Sample: 1 10Sample: 1 10 Included observations: 10Included observations: 10 VariableVariable CoefficientCoefficient Std. ErrorStd. Error t-Statistict-Statistic Prob. Prob. HOMEMORTGAGERATEHOMEMORTGAGERATE 2373126. 2373126. 843852.1 843852.1 2.812254 2.812254 0.0374 0.0374 PERMITSPERMITS 0.1405270.140527 0.024652 0.024652 5.700503 5.700503 0.0023 0.0023 POPULATIONPOPULATION 0.0015900.001590 0.000543 0.000543 2.927870 2.927870 0.0327 0.0327 UNEMPLOYMENTRATEUNEMPLOYMENTRATE 991406.2 991406.2 352851.3 352851.3 2.809700 2.809700 0.0376 0.0376 CC -749970.5-749970.5 189154.5 189154.5 -3.964858-3.964858 0.0107 0.0107 R-squaredR-squared 0.988848 0.988848 Mean dependent var Mean dependent var 153950.0 153950.0 Adjusted R-sq 0.979926Adjusted R-sq 0.979926 S.D. dependent var S.D. dependent var 34063.41 34063.41 S.E. of regressionS.E. of regression 4826.173 4826.173 Akaike info criterion Akaike info criterion 20.10835 20.10835 Sum squared residSum squared resid 1.16E+08 1.16E+08 Schwarz criterion Schwarz criterion 20.25964 20.25964 Log likelihoodLog likelihood -95.54174-95.54174 F-statistic F-statistic 110.8364 110.8364 Durbin-Watson sta 3.205994Durbin-Watson sta 3.205994 Prob(F-statistic) Prob(F-statistic) 0.000046 0.000046

All our explanatory variables are significant.All our explanatory variables are significant.

This is the best result because the probability of the F-statistic is This is the best result because the probability of the F-statistic is the lowest.the lowest.

Observations of Time-Observations of Time-Series Regression AnalysisSeries Regression Analysis

After the original regression, After the original regression, dropping the variables with the dropping the variables with the lowest t-statistic optimized the lowest t-statistic optimized the regression results.regression results.

Ex: Population and IncomeEx: Population and Income Dropping the variable with the Dropping the variable with the

highest t-stat made the highest t-stat made the regression analysis less optimalregression analysis less optimal

Ex: Unemployment RateEx: Unemployment Rate

Results for Cross Results for Cross Section AnalysisSection Analysis


Cross Section RegressionCross Section Regression• 14 Different Areas for 2 separate years: 2000 14 Different Areas for 2 separate years: 2000

and 2005and 2005Metropolitan Statistical Area

Santa Barbara, CA MSASan Diego, CA MSADallas-Fort Worth, TX MSAEl Paso, TX MSAColorado Springs, CO MSAWashington-Arlington-Alexandria DC-MD-VA-WV MSAChicago-Naperville-Joliet,IL MSABoston-Cambridge-Quincy, MA MSANY-Northern New Jersey-Long Island, NY MSAColumbus, OH MSAOmaha, NE MSAMiami-Fort Lauderdale-Miami Beach, FL MSACumberland, MD-VA MSASan Francisco, CA MSA

Relationship between Location, Relationship between Location, Income and House PriceIncome and House Price

House Price and Income

$64,700

$63,400

$65,100

$38,250

$63,400

$89,300

$69,700

$82,600

$54,400

$64,000$65,250

$52,725

$47,450

$95,000

$0

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$0 $10,000 $20,000 $30,000 $40,000 $50,000 $60,000 $70,000 $80,000 $90,000 $100,000

Income

Ho

use

Pri

ce

The VariablesThe Variables

Median Price of a Home (dependent Median Price of a Home (dependent variable)variable)

ββ11= Unemployment Rate= Unemployment Rate ββ22= Median Family Income= Median Family Income ββ33= Building Permits= Building Permits ββ44= Population= Population ββ55= Distance from the coast= Distance from the coast

2000 and 20052000 and 2005

COAST OR NOTCOAST OR NOT DUMMY VARIABLEDUMMY VARIABLE IF COAST 1IF COAST 1 IF NOT 0IF NOT 0

Relationship between Relationship between Location and House PriceLocation and House Price

Dummy Coast and House Price

y = 2E-06x - 0.2202R2 = 0.7681

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

$0 $100,000 $200,000 $300,000 $400,000 $500,000 $600,000 $700,000 $800,000

House Price

Du

mm

y

Explanation of RelationshipExplanation of Relationship

Two different trends explained Two different trends explained by dummy = 1 (coastal) and by dummy = 1 (coastal) and dummy = 0 (not coastal)dummy = 0 (not coastal)

Those cities close to the coast Those cities close to the coast experience a higher median experience a higher median house pricehouse price

Is this relationship significant?Is this relationship significant?

Results for Cross Section Results for Cross Section Analysis (14 Metropolitan Analysis (14 Metropolitan

Statistical Areas)Statistical Areas)

Cross Section Analysis Cross Section Analysis Correlation Matrix - 2005Correlation Matrix - 2005

HOUSEPRICE

DUMMYCOAST

INCOME PERMITS POPULATION

UNEMPLOYMENTRATE

HOUSEPRICE 1 0.876392 0.537036 0.152616 0.240021 -0.005214

DUMMYCOAST 0.876392 1 0.426185 0.342507 0.382309 0.063996

INCOME 0.537036 0.426185 1 0.032389 0.058681 -0.637418

PERMITS 0.152616 0.342507 0.032389 1 0.883983 -0.034606

POPULATION 0.240021 0.382309 0.058681 0.883983 1 -0.001086

UNEMPLOYMENTRATE -0.00521 0.063996 -0.63742 -0.03461 -0.00109 1

0

100000

200000

300000

400000

500000

600000

700000

800000

HOUSEPRIC

E

0.0

0.2

0.4

0.6

0.8

1.0

DUM

MYCOAST

30000

40000

50000

60000

70000

80000

90000

100000

INCOM

E

0

10000

20000

30000

40000

50000

60000

70000

PERM

ITS

0.00E+00

4.00E+06

8.00E+06

1.20E+07

1.60E+07

2.00E+07

POPULA

TIO

N

.02

.03

.04

.05

.06

.07

.08

.09

.10

.11

0 200000 400000 600000 800000

HOUSEPRICE

UNEM

PLO

YM

ENTRATE

0.0 0.2 0.4 0.6 0.8 1.0

DUMMYCOAST

30000 50000 70000 90000

INCOME

0 10000 30000 50000 70000

PERMITS

0.00E+00 1.00E+07 2.00E+07

POPULATION

.02 .04 .06 .08 .10 .12

UNEMPLOYMENTRATE

Cross-Section Regression Cross-Section Regression 20052005

Dependent Variable: HOUSEPRICEDependent Variable: HOUSEPRICE Method: Least SquaresMethod: Least Squares Date: 12/06/06 Time: 00:11Date: 12/06/06 Time: 00:11 Sample: 1 14Sample: 1 14 Included observations: 14Included observations: 14

VariableVariable Coefficient Coefficient Std. ErrorStd. Error t-Statistict-Statistic Prob. Prob.

DUMMYCOASTDUMMYCOAST 323679.4323679.4 84887.5884887.58 3.8130363.813036 0.00510.0051 INCOMEINCOME 3.798266 3.798266 3.4367863.436786 1.1051801.105180 0.30120.3012 PERMITSPERMITS -2.459958-2.459958 3.1604093.160409 -0.778367-0.778367 0.45880.4588 POPULATIONPOPULATION 0.0063280.006328 0.0140420.014042 0.4506170.450617 0.66420.6642 UNEMPLOYMENTRATEUNEMPLOYMENTRATE 1141333.1141333. 2298304.2298304. 0.4965980.496598 0.63280.6328 CC -112592.2 -112592.2 321611.0321611.0 -0.350088-0.350088 0.73530.7353

R-squaredR-squared 0.8288960.828896 Mean dependent var Mean dependent var 339964.3339964.3 Adjusted R-squaredAdjusted R-squared 0.7219560.721956 S.D. dependent var S.D. dependent var 214654.6214654.6 S.E. of regressionS.E. of regression 113187.2113187.2 Akaike info criterion Akaike info criterion 26.4090026.40900 Sum squared residSum squared resid 1.02E+111.02E+11 Schwarz criterion Schwarz criterion 26.6828826.68288 Log likelihoodLog likelihood -178.8630-178.8630 F-statistic F-statistic 7.751030 7.751030 Durbin-Watson statDurbin-Watson stat 2.3775822.377582 Prob(F-statistic) Prob(F-statistic) 0.0062040.006204

DummyCoast only variable that is significantDummyCoast only variable that is significant

Drop all insignificant Drop all insignificant variables (2005)variables (2005)


VariableVariable CoefficientCoefficient Std. ErrorStd. Error t-Statistict-Statistic Prob. Prob.

DUMMYCOASTDUMMYCOAST 362557.1362557.1 57513.8057513.80 6.3038296.303829 0.00000.0000 C C 158685.7158685.7 40668.4040668.40 3.9019423.901942 0.00210.0021

R-squaredR-squared 0.7680630.768063 Mean dependent var Mean dependent var 339964.3339964.3 Adjusted R-squared0.748735Adjusted R-squared0.748735 S.D. dependent var S.D. dependent var 214654.6214654.6 S.E. of regressionS.E. of regression 107598.5107598.5 Akaike info criterion Akaike info criterion 26.1417626.14176 Sum squared residSum squared resid 1.39E+111.39E+11 Schwarz criterion Schwarz criterion 26.2330626.23306 Log likelihoodLog likelihood -180.9923-180.9923 F-statistic F-statistic 39.7382639.73826 Durbin-Watson stat1.652406Durbin-Watson stat1.652406 Prob(F-statistic) Prob(F-statistic) 0.0000390.000039

Cross Section Regression Cross Section Regression 20002000


VariableVariable Coefficient Coefficient Std. ErrorStd. Error t-Statistict-Statistic Prob. Prob.

INCOMEINCOME 2.993843 2.993843 2.8886532.888653 1.0364151.036415 0.32710.3271 DUMMYCOASTDUMMYCOAST 134588.0134588.0 47862.7747862.77 2.8119572.811957 0.02030.0203 POPULATIONPOPULATION -0.002972-0.002972 0.0051460.005146 -0.577589-0.577589 0.57770.5777 UNEMPLOYMENTRATEUNEMPLOYMENTRATE 400794.1400794.1 2795135.2795135. 0.1433900.143390 0.88910.8891 CC -47469.59 -47469.59 248491.1248491.1 -0.191031-0.191031 0.85270.8527

R-squaredR-squared 0.6237540.623754 Mean dependent var Mean dependent var 195085.7195085.7 Adjusted R-squaredAdjusted R-squared 0.4565340.456534 S.D. dependent var S.D. dependent var 108047.6108047.6 S.E. of regressionS.E. of regression 79652.9279652.92 Akaike info criterion Akaike info criterion 25.6812025.68120 Sum squared residSum squared resid 5.71E+105.71E+10 Schwarz criterion Schwarz criterion 25.9094325.90943 Log likelihoodLog likelihood -174.7684-174.7684 F-statistic F-statistic 3.730130 3.730130 Durbin-Watson statDurbin-Watson stat 1.8666771.866677 Prob(F-statistic) Prob(F-statistic) 0.0467940.046794

DummyCoast variable is very significant but not as significant as in DummyCoast variable is very significant but not as significant as in 20052005

Drop all insignificant Drop all insignificant variables (2000)variables (2000)


VariableVariable CoefficientCoefficient Std. ErrorStd. Error t-Statistict-Statistic Prob. Prob.

DUMMYCOASTDUMMYCOAST 152342.9152342.9 40981.0140981.01 3.7174013.717401 0.00290.0029 CC 118914.3 118914.3 28977.9528977.95 4.1036134.103613 0.00150.0015

R-squaredR-squared 0.5352270.535227 Mean dependent var Mean dependent var 195085.7195085.7 Adjusted R-squared0.496496Adjusted R-squared0.496496 S.D. dependent var S.D. dependent var 108047.6108047.6 S.E. of regressionS.E. of regression 76668.4576668.45 Akaike info criterion Akaike info criterion 25.4639325.46393 Sum squared residSum squared resid 7.05E+107.05E+10 Schwarz criterion Schwarz criterion 25.5552325.55523 Log likelihoodLog likelihood -176.2475-176.2475 F-statistic F-statistic 13.8190713.81907 Durbin-Watson stat1.843468Durbin-Watson stat1.843468 Prob(F-statistic) Prob(F-statistic) 0.0029410.002941

ConclusionConclusion With time series we ran into multicollinearity issues, With time series we ran into multicollinearity issues,

and as a result of this we were forced to drop one and as a result of this we were forced to drop one explanatory variableexplanatory variable By dropping one explanatory variable we erased the By dropping one explanatory variable we erased the

multicollinearity issue and found that all of our multicollinearity issue and found that all of our variables can be significant (best results by dropping variables can be significant (best results by dropping median family income)median family income)

In the cross section analysis, none of these same In the cross section analysis, none of these same variables were significantvariables were significant

So we introduced one more variable (DummyCoast) So we introduced one more variable (DummyCoast) and found it to be very significantand found it to be very significant

Conc - Due to the variability of the housing market, Conc - Due to the variability of the housing market, it is difficult to predict housing price over a period of it is difficult to predict housing price over a period of time (difficult to determine the most significant time (difficult to determine the most significant explanatory variable when there is explanatory variable when there is multicollinearity). multicollinearity).

Since that is the case with all our explanatory Since that is the case with all our explanatory variables, the best is the variable that does not variables, the best is the variable that does not change with time (i.e. location)change with time (i.e. location)

ReferencesReferences US Census BureauUS Census Bureau US Department of Housing and US Department of Housing and

Urban DevelopmentUrban Development Real Estate Center at Texas A&M Real Estate Center at Texas A&M

UniversityUniversity www.mapquest.comwww.mapquest.com National Association of RealtorsNational Association of Realtors Keller – Statistics for Management Keller – Statistics for Management

and Economicsand Economics US Council of Economic AdvisorsUS Council of Economic Advisors Bureau of Labor StatisticsBureau of Labor Statistics Maryland Association of RealtorsMaryland Association of Realtors

why can’t i afford a home?

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