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Housing Price Prediction Model Business Research Assignment

Full time MBA 2009 Utrecht

Date of submission: 17 th November 2009

Word count: 900 words (excluding Appendix)

FTMBA09, UB Number: 09028224


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Business Research Assignment, FTMBA09, UB Number: 09028224

Table of Contents

Executive Summary ................................................................................................................................. 1

Introduction ............................................................................................................................................ 1

Objective........................................................................................................................................... 1

Data and Methodology ..................................................................................................................... 1

Data Analysis ........................................................................................................................................... 1

Linear Multiple Regression Analysis ....................................................................................................... 2

Conclusion ............................................................................................................................................... 4

Recommendations .................................................................................................................................. 4

Appendix ................................................................................................................................................. 5

Table of illustrations

Tables

Table 1 : Descriptive statistics of each variable from district A and B .................................................... 1

Table 2 : Correlations table ..................................................................................................................... 2

Table 3 : Multiple Regression Analysis of Price, H_Size, Age, District, H_Dist and Age_Dist ................. 2

Charts

Chart 1 : Box plot of price in district A and B .......................................................................................... 1

Chart 2 : Histogram of residual value from regression model 3 ............................................................. 3

Chart 3 : Residual value plot against predicted value from regression model 3 .................................... 3

Chart 4 : Scatter plot, Y axis = Price, X axis = H_Size, Z axis = Age separated by district ....................... 4


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Housing Price Prediction Model November 17, 2009

Real Estate Association 1

Executives summary

This report has developed a reliable housing price

prediction model to forecast the selling price in District A

and B by using linear multiple regression technique. Our

model can explain 88.6% of total variation in price within

the relevant range of house size and age of house.

Introduction

Objective

To develop a regression model as a tool for predicting

the selling price of resident properties in both districts in

the city

Data and Methodology

Several real estate agents and property assessors were

interviewed in order to identify what the major

explanatory variables are that might affect the price of

properties. The following independent variables were

considered:

Quantitative variables: H_Size (House size in square feet), L_Size (Lot size in acres), Age (House age in years),

Attract (An attractiveness rating of the property ranging

from 0 to 100, the higher the better), P_Tax (Property

tax of the prior year in dollars), N_Rooms (Number of

bedrooms in the house)

Qualitative variable: District (The district in the city: 0

for district A, 1 for district B)

The data consists of 625 properties sold in the past 3

months. We used linear multiple regression by adding

the dummy variable (District ) and interaction terms

(H_Dist : H_Size*District, Age_Dist : Age*District)

technique to find out the forecasting model that give the

most suitable relationship between independent

variables and Price (dependent variable) in each district.

Data Analysis

Chart 1: Box plot of price in district A and B

The median of property price in district B is higher than

that of in district A and there are no outliers. This means

that the price data are reliable.

District A (District = 0)

District B (District = 1)

Table 1: Descriptive statistics of each variable from district A and B


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Real Estate Association

Table 1 shows that the average of the housing price in

district B (USD 453,980.94) is more expensive than that

in district A (USD 226,174.77). Consequently, average

property

tax

in

district

B

is

more

expensive

than

that

in

district A (USD 5,300.90 in district B and USD 1,655.65 in

district A). Additionally, average house size and lot size

in district B are 4,055.05 square feet and 1.4568 acres

respectively, bigger than those in district A, which are

2,032.47 square feet and 0.6608 acres respectively. The

average age of a house in district B is 47.28 years, older

than in district A, which is 12.57 years. Average

attractiveness and number of bedrooms in both districts

are not significantly different.

2

Prce 50215.092 94.322H_Size 1241.796Age

(0.000) (0.000) (0.000)

6.994H_Dist 1087.526Age_Dist

(0.023) (0.001)

Std. Error of the Estimate = 46669.901

Table 2: Correlations table

As shown in Table 2, Attract and N_rooms have no

significant relationship to Price. However, H_Size,

L_Size, Age and P_Tax have a significant relationship

between each other. This means that there is multi

collinearity between independent variables.

Linear Multiple Regression Analysis

Table 3: Multiple Regression Analysis of Price, H_Size, Age, District, H_Dist and Age_Dist

Model 1:

= 0.886, Adjusted = 0.885


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Real Estate Association 3

odel 2:

88.970 95.212H_Size 1211.297Age

(0.000) (0.000) (0.000)

8District

(0.004) (0.646)

= 0.886, Adjusted = 0.885

Model 3:

Prce 42025.525 98.102H_Size 1212.041Age

(0.000) (0.000) (0.000)

e_Dist 22962.084District

(0.004) (0.031)

= 0.886, Adjusted = 0.885


odel 1

has the least Std. Error of the Estimate. However, model

1 arginality. It is not practical

includes interaction

erms but eliminates the main effect from the dummy

variable. Model 2 dropped because H_Dist and District

District terms).

all of p values of coefficient show that all regressors

have significant effect on Price. Secondly, even though

VIFs of Age and Age_Dist are more than 10, which mean

Chart 2: Histogram of residual value from regression model 3

Chart 3: Residual value plot against predicted value from regression model 3

M

Prce 478

4.856H_Dist 1029.883Age_Dist 8885.61

(0.384)


1025.601Ag

All models have the same R2and adjusted R2. M

violates the principle of m

to stipulate and fit a model that

t

terms have 95% potential to have no linear relationship

with Price (evaluated from p values of coefficients of

H_Dist and Therefore, model 3 is the

most appropriate to be our forecasting model. Firstly,

there is collinearity between them, it is acceptable

because Age_Dist is interaction term of Age and District.

Lastly, residual pattern analysis of model 3 shows there

is

no

evidence

to

violate

normality,

constant

variance

and independence of errors assumptions.(See chart 2, 3)


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Appendix

1 Define objective

To develop a regression model as a tool for predicting the selling price of resident properties in both

districts in the city

2 Specify model

Using linear multiple regression model (1 dependent variable and many independent variables)

3 Collect data

The data consists of 625 properties sold in the past 3 months both in District A and District B.

3.1 Dependent variable

Price (House selling price in USD)

3.2 Initial independent variables

Quantitative

H_Size (House size in square feet)

L_Size (Lot size in acres)

Age (House age in years)

Attract (An attractiveness rating of the property ranging from 0 to 100, the higher the

better)

P_Tax (Property tax of the prior year in dollars)

N_Rooms (Number of bedrooms in the house)

Qualitative

District (The district in the city: 0 for district A, 1 for district B)

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4 Descriptive Data Analysis

Figure 1: Box plot of Price

There are no outliers data in Price. Median of price in District B is more expensive than that in

District A

H_Size

L_Size Age

Attract

P_Tax N_Rooms

Figure 2: Box plot of all quantitative variables

There are no outliers data in any of independent variables. H_Size, L_Size, Age and P_Tax have the

same pattern of box plot.

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District A (District = 0)

District B (District = 1)

Figure 3: Descriptive statistics of each variable from district A and B

The average of the housing price in district B (USD 453,980.94) is more expensive than that in district

A (USD 226,174.77). Consequently, average property tax in district B is more expensive than that in

district A (USD 5,300.90 in district A and USD1,655.65 in district B). Additionally, average house size

and lot size in district B are 4,055.05 square feet and 1.4568 acres respectively, bigger than those in

district A, which are 2,032.47 square feet and 0.6608 acres respectively. The average age of a house

in district B is 47.28 years, older than in district A, which is 12.57 years. Average attractiveness and

number of bedrooms in both districts are not significantly different.

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Figure 4: Correlation between each of variables in both districts

Attract and N_rooms have no significant relationship to Price. However, H_Size, L_Size, Age and

P_Tax have a significant relationship between each other. This means that there is multi collinearity

between independent variables.

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5 Estimate unknown parameter and Evaluate model

We have one independent quantitative variable that is District. Therefore, we add District as dummy

variable into linear multiple regression model, created 2 interaction terms (H_Dist : H_Size*District , Age_Dist : Age*District). Attract and N_Rooms are eliminated because they are no relationship to

Price (from correlation analysis). We decide to not adding P_Tax because it is necessary to know the

price before we pay the tax that means it is not suitable to add it in price prediction model.

Figure 5: Statistic results from SPSS

(

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R2 = 0.886, Adjusted R2 = 0.885 and Standard Error of the Estimate = 46733.169

F test (Overall test)

: 0

F = 799.862, p value = 0.000 which is less than 0.05 (95% confident interval)

tly linear relationship

etween independent variables and dependent variable.

We reject null hypothesis. We are 95% confident that there are significan

b

T test (Individual test)

We fail to reject 0 : 2 0 , t = 0.334, p value = 0.739 which is more than 0.05. We are 95%

no significantly linear relationship between L_Size and Price.

L_Size fro

confident that there is

Now, we eliminate m the initial model

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R2 = 0.886, Adjusted R2 = 0.885 and Standard Error of the Estimate = 46699.169


: 0


e reject null hypothesis. We are 95% confident that there are significantly linear relationship


Wbetween independent variables and dependent variable.

We fail to reject 0 : 4 0 , t = 0.872, p value = 0.384 which is more than 0.05. We are 95%

re is no sign

though we fail to reject 0 : 3 0 , t = 0.460, p value = 0.646 which is more than 0.05, we

keep it in our model because of it is dummy variable. It is not practical to stipulate and fit a model

but elimina

confident that the ificantly linear relationship between H_Dist and Price.

Even

that includes interaction terms tes the main effect from the dummy variable.

ow, we eliminate H_Dist from the model N

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R2 = 0.886, Adjusted R2 = 0.885 and tandard Error of the Estimate = 46690.584


S

: 0


We reject null hypothesis. We are 95% confident that there are significantly linear relationship

between independent variables and variable. dependent

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We reject all null hypotheses ( 0 : 0 0 , 0 : 1 0, 0 : 2 0, 0 : 3 0, 0 : 4 0 ).

p values are more than 0.05. We are 95% confident that there are significantly linear relationship

etween each independent variables and Price.

6 Prediction model

1Age 1025.601Age_Dist 22962.084District

A (District = 0):

42025.525 98.102 _ 1212.041

Prediction equation for District B (District = 1):

64987.609 98.102 _ 186.44

Allb

Prce 42025.525 98.102H_Size 1212.04

Prediction equation for District

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