Economics for Management: London House Price Regression Report

This report presents a multiple regression analysis of London house prices, exploring the relationships between house prices and various independent variables. The study utilizes data from the Office of National Statistics (UK) spanning from 2000 to 2018. The methodology involves a step-by-step regression analysis using Microsoft Excel's Data Analysis ToolPak, examining the influence of gross domestic product, population, average income of borrowers, and average mortgage advance on London house prices. The results indicate a strong model fit, with the model explaining 99% of the variation in the dependent variable, as evidenced by a high R-squared value and a low Significance F. Scatter charts are employed to visualize the correlations between house prices and individual independent variables, revealing strong positive relationships with average mortgage advance and average borrower income. The analysis concludes that population, average borrower income, and average mortgage advance are statistically significant predictors of London house prices, while gross domestic product is not. The report underscores the importance of regression analysis in economic decision-making and provides valuable insights into the dynamics of the London housing market. The report also includes tables and charts to illustrate the analysis.

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London House Market:
Multiple Regression Analysis of London House Prices
Economics for Management
Module Code: 7BUSS001W.2
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Table of Contents
1. Abstract……………………………………………………………………
…………………………………3
2. Introduction………………………………………………………………
………………………………..3
3. Methodology and
Results………………………………………………………………………
……3
3.1. Regression Analysis………………………………….….
…………………………………………4
3.2. Scatter
Charts………………………………………………………………………
…………………6
4. Conclusion…………………………………………………………………
……………………………….8
5. Appendix……………………………………………………………………
……………………………….8
6. Bibliography………………………………………………………………
……………………………..11
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1. Abstract
The London house market is a key feature of the UK economy development due
to it being an indicator of progress. Construction and building prices usually
depend on multiple factors and as such, this report investigates some of those
components that could be considered remarkable to it. The reader will be able to
familiarize themselves with the existing relationships between London house
prices and some variables that affect the same with the help of multiple
regression analysis and Microsoft Excel. The model researched in this report is
concluded to be a good one due to the value of the Significance F which is
minuscule. The squared correlation coefficient (R2) also indicates that the model
used is liable for 99% of the dependant variable’s variation. Scatter charts are
explored and presented as well in order to perceive the correlation between
London house prices and each of the different variables selected. The model can
be useful for further research in the London house market.
Keywords: Regression analysis, London house prices, Significance F, Scatter
charts, Squared correlation coefficient, London house market.
2. Introduction
In this report, we will look at regression analysis which is the relation between a
dependent variable and multiple independent variables. A standard multiple
regression was performed. It was done so for the purpose of assessing the ability
of gross domestic product, population, average income of borrowers and average
mortgage advance to predict London house prices. Below, a step-by-step
approach is shown on how to carry out a regression analysis and how to construe
the same. This report looks at the specific model of this analysis, assesses it and
provides explanation of the results. The method is helpful for evaluating the
strength of the dependencies between the gross domestic product, population,
average income of borrowers, average mortgage advance and London house
prices.
3. Methodology and Results
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Firstly, the data gathered from the Office of National Statistics (UK) for the years
2000 to 2018 is placed in separate columns in Excel starting from the dependant
variable, London house prices, and then followed by the four dependant
variables which were carefully selected in order to stem from the same source.
Table 1
3.1. Regression Analysis
Secondly, a regression analysis is carried out using the Data Analysis ToolPak.
When inserting the data for this, the dependant variable, which in this case is
London house prices, is selected for Y range. The value of Y is reliable on X which
represents the independent variable(s). The latter, which in this instance is gross
domestic product, population, average income of borrowers and average
mortgage advance, is chosen when inputting the X range. The independent
variables are used to define and/or forecast any changes that could affect the
dependant variable. The outcome of the analysis is as seen below:
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Table 2
After Excel calculates the regression analysis, each section is looked into
separately in order to explain the outcome. The breakdown is as follows:
1. Regression Statistics
2. ANOVA
3. Intercept and Variables
Table 3
The Regression Statistics gives us information about whether the model fits the
data. On this occasion, multiple R is being disregarded as it does not account for
regression in a standardised way. R square equals approximately 0.99 which
means that the model we use is responsible for 99% of the variation of the
dependant variable. It is always better to have a higher number for the R square
which has been achieved in this case. In order to do a comparison of regression
models with different values of independent variable, we need the adjusted R
square. Multiple regression analyses were done taking into consideration only
one independent variable, and then two, and then three, but the highest number
was achieved by selecting all four Xs and it is normally the one most favoured.
The standard error measures whether the regression model is wrong. The lower
the value, the better. Ours, in this case, is estimated to approximately 10650
which is considerably high.
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Table 4
The key point of the ANOVA table and the one that is most importance to this
analysis is the Significance F. It represents the p-value of the F-test of overall
significance. Through this method, we can check if our model with all of the four
independent variables (Xs) gives us a better understanding of the different types
of London house prices (Y) in comparison to looking at it without the gross
domestic product, population, average income of borrowers and average
mortgage advance. It is visible that the model we have used is a good model due
to its’ statistical significance. This can be explained by observing the p value of
the F- test which is 2.34E-15. ‘E-15’ means that the decimal point is being
pushed fifteen places to the left which indicates that the value of the
Significance F is exceptionally low. From this, we can draw in the conclusion that
we have a statistically significant regression model.
Table 5
The table which indicates the intercept and the X variables is the one that
showcases the numbers for the parameter of the independent variable in our
regression analysis. The intercept in our model is the point where the regression
line meets the y-axis. This is normally insignificant to our analysis. There are four
independent variables we have explored for this report - gross domestic product
(X Variable 1), population in London (X Variable 2), average income of borrowers
(X Variable 3) and average mortgage advance (X Variable 4). The coefficient of
our GDP (gross domestic product) is negative (-5.6) which indicates that the
relation of our Y and X1 is not a positive one. To conclude this, if this
independent variable goes up, the London house prices will drop by
approximately 5.6 degrees for each unit’s growth of X1. We can see, however,
the rest of the Xs’ coefficients are positive. The first one of those (X2), London
population, showcases that if its’ value rises, our Y will increase too by about 0.1
degrees for each constituent. X variable 3, which is the average borrowers’
income for London, has coefficient of approximately 1.24 making London house
prices multiply by that exact number for every one unit of the X3 going up. The
last independent variable presented, the average mortgage advance, also has a
positive value. This estimates to an increase in our dependant variable of about
1.11 degrees for one entity in the case of our X4’s growth. The column with the p
value of the independent variables gives the information about whether the Y
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(London house prices) is statistically significant or not. The aim is for the p value
of each X variable to be less than 0.05 (5%) in order for us to be able to dismiss
the null hypothesis (H0) which states that the coefficient is equal to zero. This
type of hypothesis is used when explaining that the independent variable and
dependent variable have no relationship between each other. The value of the
population in London (X2), average income of borrowers (X3) and average
mortgage advance (X4) are respectively ~0.004, ~0.03 and ~0.003 which
indicates that they are statistically significant whereas the gross domestic
product (X1) equals to approximately 0.2 and therefore is insignificant.
3.2. Scatter Charts
Thirdly, we explored scatter charts for the purpose of understanding the
correlation between the dependent variable and an independent one. Below are
illustrated two of the outcomes:
Chart 1
This chart looks at the relationship between London house prices (Y) and average
mortgage advance (X4). The first one is positioned along the Y-axis or the vertical
axis and the latter – along the X-axis or the horizontal axis. The correlation can
be described as strong positive one due to its’ date points being close together
and their upward movement from left to right. This can also be concluded from
the value of R2 which equals 0.981. R2 or squared correlation coefficient indicates
the strength of the relationship which can vary from 0 to 1 with 0 being
uncorrelated and 1 being strongly correlated.
In the same fashion, we looked at London house prices as our dependent
variable and average income of borrowers.
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Chart 2
As seen, the results are quite similar. The correlation is strong as per the
positioning of the data points and the value of the squared correlation coefficient
(R2= 0.9434).
4. Conclusion
In economics, regression analysis is important in order to foresee prospective
decisions, improve the process, remedy any miscalculations and acquire better
insights. This report provides information about the London house market
between 2000 and 2018. It is clear that there are many independent variables
which affect the dependant – house prices. The most important that can be
concluded are population, average income of borrowers and average mortgage
advance which are said to be statistically significant. These have a strong
relationship with the dependant variable as per the calculation of the p value and
the results of the scatter graphs. The only one which was marked as statistically
insignificant is the gross domestic product (GDP) with its’ value being above 0.05
(5%).
5. Appendix
TABLE 1
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TABLE 2
TABLE 3
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TABLE 4
TABLE 5
CHART 1
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CHART 2
6. Bibliography
Curwen, J. and Slater, R. 2002. Quantitative Methods for Business Decisions. 5th
ed. Thompson.
Frost, J. 2019. Regression Analysis: An Intuitive Guide for Using and Interpreting
Linear Models. Statistics By Jim Publishing.
Ons.gov.uk. 2019. Regional economic activity by gross domestic product, UK -
Office for National Statistics. [online] Available at:
<https://www.ons.gov.uk/economy/grossdomesticproductgdp/bulletins/
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