Linear Regression Model of House Price in Boston

Niu Yilin

doi:doi:10.11648/j.sd.20200803.12

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Linear Regression Model of House Price in Boston

Niu Yilin

Published in Science Discovery (Volume 8, Issue 3)

Received: 23 May 2020 Published: 29 June 2020

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Abstract

The change of house price is a common phenomenon. People are eager to grasp the law of house price to become the winner of real estate investment. This paper uses Boston house price data to explore the relationship between Boston house price and which independent variables. This paper uses linear regression model to construct the relationship between housing prices and crime rate in Boston. First, the classical linear model is adopted. Then we do the collinearity test, removing the lever point and other operations, the residual of the model still does not conform to the normal distribution, so the classical linear model cannot describe the data very well. Then, we add the quadratic term and the cross term, and use the method of stepwise regression to get the optimal regression autoregressive quantum set. After removing the leverage point and significance test, we found that the residual distribution was approximately normal. It shows that the improved model has well described the law of data. Finally, according to the data, the main conclusions are as follows: house price and tax rate, index close to the highway and index close to the city center are inversely correlated, which is positively correlated with the number of rooms, the proportion of teachers and students, and whether it is close to the Charles River. In addition, the concentration of nitric oxide, the proportion of low-end population and crime rate also have a certain relationship with housing prices.

Published in	Science Discovery (Volume 8, Issue 3)
DOI	10.11648/j.sd.20200803.12
Page(s)	52-63
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Changes in House Prices, Linear Regression, Stepwise Regression, Positive Correlation, Negative Correlation

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APA Style

Niu Yilin. (2020). Linear Regression Model of House Price in Boston. Science Discovery, 8(3), 52-63. https://doi.org/10.11648/j.sd.20200803.12

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ACS Style

Niu Yilin. Linear Regression Model of House Price in Boston. Sci. Discov. 2020, 8(3), 52-63. doi: 10.11648/j.sd.20200803.12

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AMA Style

Niu Yilin. Linear Regression Model of House Price in Boston. Sci Discov. 2020;8(3):52-63. doi: 10.11648/j.sd.20200803.12

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@article{10.11648/j.sd.20200803.12,
  author = {Niu Yilin},
  title = {Linear Regression Model of House Price in Boston},
  journal = {Science Discovery},
  volume = {8},
  number = {3},
  pages = {52-63},
  doi = {10.11648/j.sd.20200803.12},
  url = {https://doi.org/10.11648/j.sd.20200803.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sd.20200803.12},
  abstract = {The change of house price is a common phenomenon. People are eager to grasp the law of house price to become the winner of real estate investment. This paper uses Boston house price data to explore the relationship between Boston house price and which independent variables. This paper uses linear regression model to construct the relationship between housing prices and crime rate in Boston. First, the classical linear model is adopted. Then we do the collinearity test, removing the lever point and other operations, the residual of the model still does not conform to the normal distribution, so the classical linear model cannot describe the data very well. Then, we add the quadratic term and the cross term, and use the method of stepwise regression to get the optimal regression autoregressive quantum set. After removing the leverage point and significance test, we found that the residual distribution was approximately normal. It shows that the improved model has well described the law of data. Finally, according to the data, the main conclusions are as follows: house price and tax rate, index close to the highway and index close to the city center are inversely correlated, which is positively correlated with the number of rooms, the proportion of teachers and students, and whether it is close to the Charles River. In addition, the concentration of nitric oxide, the proportion of low-end population and crime rate also have a certain relationship with housing prices.},
 year = {2020}
}

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TY - JOUR
T1 - Linear Regression Model of House Price in Boston
AU - Niu Yilin
Y1 - 2020/06/29
PY - 2020
N1 - https://doi.org/10.11648/j.sd.20200803.12
DO - 10.11648/j.sd.20200803.12
T2 - Science Discovery
JF - Science Discovery
JO - Science Discovery
SP - 52
EP - 63
PB - Science Publishing Group
SN - 2331-0650
UR - https://doi.org/10.11648/j.sd.20200803.12
AB - The change of house price is a common phenomenon. People are eager to grasp the law of house price to become the winner of real estate investment. This paper uses Boston house price data to explore the relationship between Boston house price and which independent variables. This paper uses linear regression model to construct the relationship between housing prices and crime rate in Boston. First, the classical linear model is adopted. Then we do the collinearity test, removing the lever point and other operations, the residual of the model still does not conform to the normal distribution, so the classical linear model cannot describe the data very well. Then, we add the quadratic term and the cross term, and use the method of stepwise regression to get the optimal regression autoregressive quantum set. After removing the leverage point and significance test, we found that the residual distribution was approximately normal. It shows that the improved model has well described the law of data. Finally, according to the data, the main conclusions are as follows: house price and tax rate, index close to the highway and index close to the city center are inversely correlated, which is positively correlated with the number of rooms, the proportion of teachers and students, and whether it is close to the Charles River. In addition, the concentration of nitric oxide, the proportion of low-end population and crime rate also have a certain relationship with housing prices.
VL - 8
IS - 3
ER -

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Author Information

Niu Yilin

School of Mathematics and Statistics, Lanzhou University, Lanzhou, China

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Plain Text BibTeX RIS

APA Style

Niu Yilin. (2020). Linear Regression Model of House Price in Boston. Science Discovery, 8(3), 52-63. https://doi.org/10.11648/j.sd.20200803.12

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ACS Style

Niu Yilin. Linear Regression Model of House Price in Boston. Sci. Discov. 2020, 8(3), 52-63. doi: 10.11648/j.sd.20200803.12

Copy | Download

AMA Style

Niu Yilin. Linear Regression Model of House Price in Boston. Sci Discov. 2020;8(3):52-63. doi: 10.11648/j.sd.20200803.12

Copy | Download

@article{10.11648/j.sd.20200803.12,
  author = {Niu Yilin},
  title = {Linear Regression Model of House Price in Boston},
  journal = {Science Discovery},
  volume = {8},
  number = {3},
  pages = {52-63},
  doi = {10.11648/j.sd.20200803.12},
  url = {https://doi.org/10.11648/j.sd.20200803.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sd.20200803.12},
  abstract = {The change of house price is a common phenomenon. People are eager to grasp the law of house price to become the winner of real estate investment. This paper uses Boston house price data to explore the relationship between Boston house price and which independent variables. This paper uses linear regression model to construct the relationship between housing prices and crime rate in Boston. First, the classical linear model is adopted. Then we do the collinearity test, removing the lever point and other operations, the residual of the model still does not conform to the normal distribution, so the classical linear model cannot describe the data very well. Then, we add the quadratic term and the cross term, and use the method of stepwise regression to get the optimal regression autoregressive quantum set. After removing the leverage point and significance test, we found that the residual distribution was approximately normal. It shows that the improved model has well described the law of data. Finally, according to the data, the main conclusions are as follows: house price and tax rate, index close to the highway and index close to the city center are inversely correlated, which is positively correlated with the number of rooms, the proportion of teachers and students, and whether it is close to the Charles River. In addition, the concentration of nitric oxide, the proportion of low-end population and crime rate also have a certain relationship with housing prices.},
 year = {2020}
}

Copy | Download