The Study on the Influencing Factors of Housing Price

Zhiyi Chen

School of Beijing Haidian KaiWen Academy, Beijing, 100000, China

Keywords: House Price, Multiple Linear Regression, House Sales.

Abstract: This paper aims to find out the factors that affect the housing price. Multiple Linear Regression method was

used to analyze the significant factors between May 2014 and May 2015 in King County. Through the graph

test, 13 of the 15 variables selected are related to house prices. In the model analysis, the p values and the VIF

values of these variables were compared, and the accuracy of the model was confirmed. The results showed

that the number of bedrooms, number of bathrooms, living area, waterfront, view level, overall condition,

building grade, above ground area, below ground area, year of renovation, there is a significant linear

relationship between the living area and lot size of neighbors and the housing price, and there is no

significance test between the number of floors of the building and the housing price. In general, the fluctuation

of home prices in King County can be considered by the extent to which these factors affect home prices.

1. INTRODUCTION

House is an important part of people's life, and its

price has always been a concern of people. Since

2002, house prices in the United States have

continued to rise, which have a significant impact on

people's lives. According to the research of Case and

Shiller, the real estate market has obvious

fluctuations, and the average house price will soar by

about 20% from 2000 to 2020 (Mian and Amir, 2024).

Nowadays, the house prices continue to change and

rise, according to the latest S&P Case-Shiller Index,

the average home price in the United States increased

by 1% year over year in July 2023, hit a record high.

Meanwhile, the cumulative 5.3% increase in the S&P

Case-Shiller average home price index from January

2023 has offset the cumulative 5% decline in home

prices from the peak last June to the slowdown in

January this year (Feng, 2023). The fluctuation of

housing price has a great impact on the consumption

structure of urban residents (Xu and Liu, 2024).

While choosing the house for a suitable price, it is

also important to consider the conditions of the house

that affect the price of the house. Therefore, this paper

will analyze the structural direct factors that have the

greatest impact on home prices and provides advice

on what to expect to buy, based on the home price

data of King County, Seattle.

The real estate market is a complex model with

many factors, in addition to the general condition of

the house and the grade of construction, there are

many factors related to the interior of the house. By

investigating the demand for housing in various

regions, the main influencing factors are found and

determined. Quitzau's study in 2008 showed that

people are very concerned about the number of

bedrooms and bathrooms in the house (Quitzau and

Røpke, 2008). Khajehzadeh et al. also showed that

since the concept of bedroom size may be different

from region to region, living area should also be a

priority for people (Khajehzadeh and Brenda, 2017).

Jim's research found that the number of floors, floor

height and window orientation (view level) of the

house also deeply affect people's purchase intention,

and thus affect the price (Jim and Chen, 2006). Water

source is the most commonly used and typical

housing characteristic. In North's research, the

availability of high-quality and available water

resources also plays a significant role in real estate

valuation (North and Griffin, 1993). In the study of

Zabel et al. and Cho et al., the effect of minimum lot

size restrictions (MLRs) in the housing price model is

also very large in the value of real estate, so this is

also considered to be one of the main influencing

factors of housing price (Jeffrey and Maurice, 2011 &

Cho et al., 2009).

As mentioned in the research of Liu Wenjing et

al., owners have the demand for the basement, thus,

the balance between basement and above-ground

floor area is also important for housing. This also

258

Chen, Z.

The Study on the Inﬂuencing Factors of Housing Price.

DOI: 10.5220/0013055900004601

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 1st International Conference on Innovations in Applied Mathematics, Physics and Astronomy (IAMPA 2024), pages 258-263

ISBN: 978-989-758-722-1

provides a new way of thinking about the factors of

housing prices, that is, the above-ground area and the

underground area (Liu et al., 2022). At the same time,

Cho's research model also showed that from the

perspective of low-carbon green buildings, there is

also a correlation between the property value caused

by renovation and the house price (Cho et al., 2020).

This paper will mainly study and analyze the

impact of 15 variables (house condition (overall),

building grade, bedroom numbers, bathroom

numbers, living area, number of floors, view level,

whether there is water source, lot size, basement size,

living area above the ground, year of construction,

year of renovation, neighborhood living condition) on

the housing price, and build a suitable housing price

model to provide people with better purchase

suggestions, the variables may adjust with the dataset

selected.

2. METHODS

2.1 Data Source

The data used of this analysis is from a public data set

of Kaggle.com, the title of the dataset is “House Sales

in King County, USA”. This dataset contains house

sale prices for King County, which includes Seattle.

It includes homes sold between May 2014 and May

2015. The original dataset is in .csv format.

2.2 Variable Introduction

The dataset includes 21613 records, each of them

represent a sale of a house. There are 21 columns in

the dataset, as table 1 shows:

Table 1. List of variables.

Variable name meaning

Id The unique identifier for the house

Date the date when the house was sold

Price the final sale price of the house

Bedroom Number of bedrooms

Bathrooms Number of bathrooms

sqft_living Living area (in square feet)

sqft_lot Lot area (in square feet)

floors Number of floors

waterfront Whether there is water (0 means no, 1 means yes)

view The rate of view of the house

condition the living area (square feet) above ground level

grade The area of the basement (in square feet)

sqft_above year the house was built

sqft_basement The area of the basement (in square feet)

yr_built year the house was built

yr_renovated The year in which the house was last renovated

zipcode zipcode

lat Latitude coordinates of the house

long the longitude coordinates of the house

sqft_living15 Living area (square feet) of 15 neighbors in the vicinity of the house in 2015.

sqft_lot15 sqft_lot15: Lot size (square feet) of 15 neighbors near the house in 2015.

In the data set, abnormal values are identified and

found based on the box plot, in this scenario, the

author finds the data with extremely high price and

extremely low price. Figure 1 shows that there is

some extremely high price data recorded. Now this

paper back to the dataset and try to find the reason for

those abnormal value. By observing those abnormal

value, the author finds that extremely high housing

prices are generally accompanied by extremely high

building levels, living area, lot area, condition level,

or view level. These variables are considered in the

dataset, those are not outliers due to factors that are

not considered, so this paper chooses to keep these

data.

The Study on the Inﬂuencing Factors of Housing Price

259

Fig. 1 Box plot of the price of the data.

2.3 Method Introduction

A multiple linear regression model is used to analysis

and predict house price based on the selected

independent variables. The regression model

equation includes the intercept term and coefficients

of each variable. The multiple linear regression model

is a model with multiple explanatory variables, and it

can be used to explain the relationship between

dependent variable and multiple independent

variables. The principle is to apply least squares on

the data and minimize the sum of the squares of the

residuals between the dependent variables and the

independent variables.

3. RESULTS AND DISCUSSION

3.1 Descriptive Analysis

The dataset contains a large amount of data, which

there is some of the variables in of the column has no

effect, or not a direct effect, on the house prices that.

Using scatter diagram of each independent variable to

see how they related to the dependent variable.

Fig. 2 Scatter Digram of sqft_lot & price.

Figure 2 shows that there is no linear relationship

between the lot size and the housing price. In order to

obtain better model results, it has been decided to

remove this variable.

Fig. 3 Scatter Digram of yr_built & price.

Figure 3 shows that there is no linear relationship

between the year the house was built and the housing

price, it has been decided to remove this variable.

Fig. 4 Scatter Digram of zipcode & price.

Figure 4 shows that there is no linear relationship

between the zipcode of the house and the housing

price, it has been decided to remove this variable.

Fig. 5 Scatter Digram of lat & price.

Figure 5 shows that there is no linear relationship

between the latitude of the house and the housing

price, it has been decided to remove this variable.

IAMPA 2024 - International Conference on Innovations in Applied Mathematics, Physics and Astronomy

260

Fig. 6 Scatter Digram of long & price.

Figure 6 shows that there is no linear relationship

between the longitude of the house and the housing

price, it has been decided to remove this variable.

After removing those variables, the features

remaining that might influence house prices as

explanatory variables including (Table 2):

3.2 Model Results

When applying multiple linear regression with the

tool, the author finds that some independent variables

have multicollinearity, which will adversely affect the

stability and interpretability of the model and may

lead to inaccurate coefficient estimation and

increased standard error. First of all, a collinearity

analysis of the data is carried out:

On the table 3 shown, the author found that the

absolute value of correlation coefficient between

variable sqft_above and sqft_living is very strong

(>0.8), this means there may multicollinearity

between them. Thus, this paper chooses to remove

sqft_living in the linear regression, since it has high

absolute value of correlation coefficient with some

other variables. Finally, the multiple linear regression

model is applied.

Table 2. Explanatory variables.

Variable name Meaning Range

Bedrooms Number of bedrooms no

Bathrooms Number of bathrooms no

sqft_living Living area no

Floors Number of floors no

Waterfront Whether there is water 1 or 0

View The rate of view of the house 0~4

Condition The overall rate of condition of the house 1~5

Grade The building grade of the house 1~13

Sqft_above The living area above ground level no

Sqft_basement The area of the basement no

yr_renovated The year the house was last renovated no

Sqft_living15 Living area (square feet) of 15 neighbors in the vicinity of the house in 2015 no

Spft_lot15 Lot size (square feet) of 15 neighbors near the house in 2015 no

Table 3. Correlation results of part of the variables.

bedroomsbathroomssqft_living floors waterfron

sqft_lot15 view conditio

grade

bedrooms 1

bathrooms 0.516** 1

sqft_living 0.577** 0.755** 1

floors 0.175** 0.501** 0.354** 1

waterfront -0.007 0.064** 0.104** 0.024** 1

sqft_lot15 0.029** 0.087** 0.183** -0.011 0.031** 1

view 0.080** 0.188** 0.285** 0.029** 0.402** 0.073** 1

condition 0.028** -0.125** -0.059** -0.264** 0.017* -0.003 0.046** 1

grade 0.357** 0.665** 0.763** 0.458** 0.083** 0.119** 0.251**-0.145** 1

3.3 Model Results

The table 4 shows the result of the linear regression.

The model formula is:

𝑝𝑟𝑖𝑐𝑒  717503.880  34136.190 ∗

𝑏𝑒𝑑𝑟𝑜𝑜𝑚𝑠  ⋯  565696.394 ∗

𝑤𝑎𝑡𝑒𝑟𝑓𝑟𝑜𝑛𝑡 (1)

Where 𝑅



of the model is 0.613. this means the

variables selected can be used to explain 61.3% of the

The Study on the Inﬂuencing Factors of Housing Price

261

house price variation. The VIF of the variables in this

model are all less than 5, means that there is no

collinearity problem.

The p value of the independent variables:

bedrooms, bathrooms, sqft_living, waterfront, view,

condition, grade, sqft_above, sqft_basement,

yr_renovated, sqft_living15, sqft_lot15 are 0.00, so it

can be considered that all variables except floors have

a significant effect on the dependent variable price.

Moreover, D-W value of the model is close to number

2, which indicates that there is no autocorrelation in

the model, and there is no correlation between the

sample data, and the model is good.

The result shows that sqft_above, yr_renovated,

sqft_basement, grade, condition, sqft_living15, view,

waterfront has a significant positive impact on price.

And bedrooms, bathrooms, sqft_lot15 have

significant negative influence on price. But floors

have no effect on price.

Table 4. Model results.

Unstandardized Coe. Standardized Coe.

t p

collinearity diagnostics

B SE Beta VIF tolerability

Constant -717503.88017314.851 - -41.4390.000** - -

bedrooms -34136.190 2138.522 -0.086 -15.9630.000** 1.639 0.610

bathrooms -16254.218 3453.362 -0.034 -4.707 0.000** 2.931 0.341

floors -2324.943 3948.933 -0.003 -0.589 0.556 1.884 0.531

sqft_above 182.790 4.086 0.412 44.740 0.000** 4.742 0.211

yr_renovated 72.552 3.923 0.079 18.494 0.000** 1.029 0.972

sqft_basement 210.271 4.848 0.253 43.370 0.000** 1.907 0.524

grade 102110.393 2348.118 0.327 43.486 0.000** 3.156 0.317

condition 57357.875 2515.927 0.102 22.798 0.000** 1.111 0.900

sqft_lot15 -0.722 0.059 -0.054 -12.2450.000** 1.073 0.932

sqft_living15 15.315 3.795 0.029 4.036 0.000** 2.802 0.357

view 56802.133 2384.400 0.119 23.822 0.000** 1.383 0.723

waterfront 565696.394 19691.576 0.133 28.728 0.000** 1.202 0.832

R2 0.613

Adj R2 0.613

F F (12,21600)=2853.269,p=0.000

D-W value 1.983

Dependent Variable: price

* p<0.05 ** p<0.01

4. CONCLUSION

This study selected the dataset of home prices sold in

King County which between May 2014 and May

2015. The study focused on 15 variables, two of

which were not linearly related to the dependent

variables in the selected data set and were removed

from the analysis for better modeling. The Multiple

Linear Regression accurately and effectively analyzes

the correlation coefficient of multiple factors to the

dependent variable.

This study analyzes the how the selected 13

variables related to housing price through the method

of multiple linear regression and finds that the main

factors affecting housing price are waterfront,

building grade, overall condition, and view level. The

number of floors in the variable has little effect on

prices. Above and below ground living area, year of

renovation, building grade, overall condition,

neighbors living area, view level, waterfront has a

significant positive impact on price, and then the

number of bedrooms, the number of bathrooms, the

lot size of the neighbors have significant negative

influence on price.

This research can provide reference value for

people are considering buying a house and help them

to determine the initial budget from different factors

IAMPA 2024 - International Conference on Innovations in Applied Mathematics, Physics and Astronomy

262

perspective. However, this model still has

shortcomings, such as other variables that are not

considered, the relationship between some variables

may not be represented, and the analysis sample

scope is limited, and so on. To improve these

problems, a larger range of data and a more optimized

approach are needed.

REFERENCES

Mian Atif, Amir Sufi. HOUSE PRICE GAINS AND U.S.

HOUSEHOLD SPENDIN. Working Paper, 2024, 2.

Feng Difan. American House Prices Have Hit Record

Highs. China Academic Journal Electronic Publishing

House, 2023, 1.

Xu Miao, Liu Xiaoying. The Impact of Housing Price

Fluctuation on the Upgrading of Consumption

Structure of Urban Residents: An Analysis Based on

the Central Region. School of Management, Zhengzhou

University, 2024, 44.

Quitzau M B, Røpke I. The construction of normal

expectations: Consumption drivers for the Danish

bathroom boom. Journal of Industrial Ecology, 2008,

186-206.

Khajehzadeh Iman, Brenda Vale. Estimating the Floor Area

of a House Knowing Its Number of Rooms and How

These Are Named, 2017, 315-323.

Jim C Y, Wendy Y. Chen, Impacts of urban environmental

elements on residential housing prices in Guangzhou

(China), Landscape and Urban Planning, 2006, 78: 422-

434.

North J H, Griffin C. Water Sources as a Housing

Charactersitic: Hedonic Valuation and Willingness to

Pay for Water. Water Resources Research, 1993, 29:

1923-1929.

Jeffrey Zabel, Maurice Dalton, The impact of minimum lot

size regulations on house prices in Eastern

Massachusetts, Regional Science and Urban

Economics, 2011, 41: 571-583.

Cho Seong Hoon, et al. Spatial and temporal variation in

the housing market values of lot size and open space.

Land Economics, 2009, 51-73.

Liu Wenjing, et al. The Above-Ground and Underground

Areas of Residential EPC Projects Whose Unit Price

Exceeds the Limit Are Balanced, 2022. Urban

Architecture Space. 2022,29 (S2): 780-782.

Cho K, et al. Model for predicting price change patterns in

multi-family houses post renovation work in South

Korea. Journal of Asian Architecture and Building

Engineering, 2020, 19(3): 230-241.

The Study on the Inﬂuencing Factors of Housing Price

263