Final Analytics Project Housing Neka

Running head: RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS

Comparative Analysis of the Relationship between Home Prices in the City of Ottawa and Key

Economic Indicators: CPI, Mortgage Rate, Overnight Rate and Hourly Income rate

for

Ahmad Teymouri, Professor

MGT4701_300, Algonquin College

by

Ifeoma Okafo Eke

REG#: 040572047

Group 2

Sunday, April 9, 2016

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RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS

Contents

Abstract......................................................................................................................................... 1

Introduction................................................................................................................................... 2

Background................................................................................................................................2

Buying a Home and the Debt Burden........................................................................................3

Research Approach........................................................................................................................5

Selection of Variables for Study................................................................................................5

Data and Variables under Consideration....................................................................................5

Dependent Variables..............................................................................................................5

Independent Variables........................................................................................................... 5

Sources of Data..........................................................................................................................7

Statistical Analysis.........................................................................................................................7

Statistical Tools Used................................................................................................................ 7

Data Used.................................................................................................................................. 7

Period under Review..................................................................................................................8

Results of analysis......................................................................................................................... 8

Descriptive Statistics..................................................................................................................8

Results................................................................................................................................... 8

Graphical Representation and Analysis of Results.................................................................9

Hypothesis Testing.................................................................................................................. 13

Description...........................................................................................................................13

Hypothesis testing –............................................................................................................14

Chi Test of Independence........................................................................................................21

Regression Analysis..................................................................................................................23

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Scatter Plot...........................................................................................................................23

Regression Results...............................................................................................................25

Interpretation of the Regression Summary Output.............................................................25

Conclusion................................................................................................................................... 30

Summary..................................................................................................................................30

Limitations of the Study...........................................................................................................30

Areas for Future Study.............................................................................................................31

REFERENES...................................................................................................................................32

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Abstract

A house is probably the single largest investment that most Canadians will ever make in

their lifetime and yet anecdotal evidence would suggest that many first-time home buyers are ill

prepared to take this first step (First-Time Home, 2015) and have no idea about the factors

influence home prices.

The initial Project proposal was focused on a study of income and factors that impact

house prices in different Canadian cities with a view of developing a model to determine the best

city to live in, in Canada based on annual income. It was believed that this subject would be of

great interest to final year students since many would soon be graduating and facing the decision

of where to work as well as whether to rent or buy. However, due to the limitations of time and

available data, this project has been limited to a study of some of the factors that may influence

house prices in the city of Ottawa and an examination of the relationship between these factors

(also referred to as independent variables) and home prices (the dependent variable).

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Introduction

Background

According to Statistics Canada, the Canadian construction industry, made up of residential, non-

residential and engineering, repair and other construction services accounts for 6% of the gross

domestic product (GDP). This represented a contribution of $73.8 billion to the Canadian

economy in 2010 (Construction, n.d.). Of this figure, $23.4 billion is attributed to residential

construction which represents almost 2% of GDP. The chart in the figure below shows the past

trend in the value of the different sectors of the construction industry (Construction, n.d.).

Figure1: GDP by Construction Industry

This figure while substantial does not include the value of existing homes which could not be

obtained at the time of creating this report.

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Buying a Home and the Debt Burden

While the place to buy might be influenced by such mundane factors as the desired amount of

square footage, the proximity to work and family and a social life or the border lines of a

particular school district as well as the need to stay away from areas with high crime rate

statistics, many a home buyer has come to discover that the price of a home depends on much

more than square footage. Real-estate brokers are fond of echoing the mantra “location- location-

location”, as being the driver of home prices. However recent data on home prices in such hot-

spots as Vancouver and Toronto point to a more fundamental factor – forces of demand and

supply ( due to speculation as well as other strong fundamentals) as being the reason for the

unusually high priced real-estate in these cities (Sturgeon, J., 2015).

Figure 2: World Ranking of Housing Affordability in Major Markets

Figure 2 above shows Vancouver ranks third in terms of affordability when compared to

other major cities in the world (Demographia.,n.d.). A rank of 85 and a median multiple of 10.8

would means that a family with a median income would require 10.8 times their income in order

to afford to buy a home based on regular mortgage terms in Vancouver.

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Also of importance in purchasing real estate is the amount of debt incurred by Canadians either

to purchase a home or as part of credit card debt. Statistics Canada reports that in 2012, while the

interest paid on debt as a proportion of disposable income declined to 6.9% in the first half of the

year, consumer debt rose by 1.3% in the same period (Parkinson, D., 2014).

Fig 3: A comparison of debt service ratio to credit debt

Figure 3 shows the trend in these ratios from 1990 to the third quarter of 2012. Since

most Canadians will buy a home with the assistance of a mortgage, these numbers are

significant. When considering the housing market, the ratio of credit debt to disposable income is

a key consideration in measuring the household debt burden as well as the ability of the average

Canadian to buy a home.

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Research Approach

Selection of Variables for Study

We observed that real estate and construction in particular represent a significant portion

of the GDP. In addition, Inflation is a major determinant of prices within an economy. Monetary

and Fiscal policy are also tools the government uses to try to control economic performance.

Given the forgoing, our research study is focused on the some of the economic indicators that

affect the price of goods and services in the economy and have fluctuated in value over time in

order to determine the precise relationship between some of these economic variables and the

change in home prices.

Data and Variables under Consideration

The independent and dependent variables considered in this study are listed below.

Dependent Variables

Annual Home Prices: The independent variable used in this analysis is annual home

prices in Ottawa. While HPI (Home Price Index) provides a true measure of the variation

in home prices over time (CREA, n.d.), for the purpose of this project, annual home

prices was selected as the dependent variable since a dollar amount is more accessible

than an index. It was a judgement call.

Independent Variables

The independent variables considered include:

1. CPI- Consumer Price Index: This is the most relevant measure of inflation

according to the Bank of Canada (Inflation, n.d.). This is because it is a measure of

the change in cost of living for Canadians. An increase in the cost of living would

suggest a decrease in the purchasing power of Canadians and a decrease in demand

for goods and services. Hypothesis: We can thus hypothesize that as the demand for

homes decreases, home prices should fall provided all things remain equal since less

people would be able to afford to buy a home

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2. Over-Night Lending Rate: The Bank of Canada carries out monetary policy by

influencing short-term interest rates (Key Interest Rates, n.d.). This is accomplished

by either raising or lowering the overnight rate – the rate at which financial

institutions borrow from or lend to each other. The overnight rate has a direct impact

on the liquidity within the economy since it directly impacts the interest rate of

consumer loans which also impacts disposable income.

3. Mortgage Rate: This is the rate at which a home buyer can borrow funds for a home

purchase from a financial institution. The higher the mortgage the more funds are

needed for monthly payments.

Hypothesis: We can hypothesize that the higher mortgage rates and monthly rates

will dis-incentivize home buyer which will in turn lead to lower demand for homes

and lower house prices.

4. Hourly Rate:

Fig 4: Graph of Average wage vs Inflation rate -2010-2013

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This is the average hourly earnings as determined by Statistics Canada. Higher wages

increase disposable income which would tend to exert upward pressure on prices

which leads to cost-push inflation. When the rate of inflation outpaces the rise in

wages as has been the case in the Canadian economy according to the data from

Statistics Canada (Rozworski, M., 2014), demand falls including the demand for real-

estate.

A fall in demand, increases supply which in turn drives down prices of real-estate

Hypothesis: We will hypothesize that as hourly rate of income rises home prices fall.

Sources of Data

The primary sources of data used to conduct the statistical analysis in this project are

from the following sources::

a) Bank of Canada which also relied on (Summary of Key, n.d.)

b) Statistics Canada and

c) AgentInOttawa.com for housing prices in Ottawa (Ottawa home sales, n.d.)

d) Workingdays.ca – to determine working days in a yar (Working days, n.d.)

Statistical Analysis

Statistical Tools Used

The following statistical tools were employed in the analysis of the data used in this project:

Excel`s Descriptive Statistics

Hypothesis Testing

Chi-Test and

Regression Analysis.

Data Used

The data including all analysis is included in the excel file attached to this report.

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Period under Review

The statistics used for this study ranged from 2012 to 2015.

Results of analysis

All Analysis and results are contained in the attached spread sheet under their respective green

tabs. Screen captures of the different results have also been included in this report to

demonstrate the steps.

Descriptive Statistics

Results

Statistic

House Price

(Average) Mortgage rate Total CPI Overnight rate Hourly earnings

Mean 359619.75 5.015 1.372916667 0.906845833 2.422916667

Standard Error 847.3591038 0.039668395 0.079154418 0.025286373 0.089781037

Median 359527.5 5.14 1.2 0.9983 2.35

Mode 351792 5.24 1.2 0.9978 2.2

Standard Deviation 5870.67608 0.274830702 0.548397892 0.175189134 0.622021271

Sample Variance 34464837.64 0.075531915 0.300740248 0.030691233 0.386910461

Kurtosis 1.266854046 1.697698444 0.380575653 1.034901401 -0.146124222

Skewness 0.042254178 0.180481872 0.643252093 1.599233717 0.457399249

Range 15840 0.8 2.2 0.5147 2.7

Minimum 351792 4.64 0.4 0.4967 1.2

Maximum 367632 5.44 2.6 1.0114 3.9

Sum 17261748 240.72 65.9 43.5286 116.3

Count 48 48 48 48 48

Confidence Level (95.0%) 1704.666639 0.079802517 0.159238149 0.050869622 0.180616149

Economic Indicator Monetary Policy Inflation Monetary Policy GDP

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Table 1: Descriptive Statistics

The table above is the modified output of the descriptive statistics function in excel. This table

gives the values of several key statistics about the values of the variables under consideration in

order to provide some idea as to their characteristic. Some of the descriptive statistics include:

Mean(average), Median (the data at the center if the entire data on a particular statistic

were placed in order) and Mode (the most occurring value ): These are all measures of

central tendency

The Variance and The Standard Deviation (the square root of the variance)provide a

measure of dispersion where one standard deviation represents 68% of the data if the

distribution can be described as normally distributed

The Maximum and the Minimums enable us to calculate the range which is the

difference.

The sum provides a total of all values of a particular variable while the count of 48 for

each variable demonstrates the data for each variable is monthly over a 4 year period.

Note: Monthly data was not available for house prices so annual data was used in this study.

This means that the monthly home prices are constant over yearly periods as shown in the data

in the excel sheet.

Graphical Representation and Analysis of Results

Skewness and Kurtosis

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Fig 5: Graphic Demonstration of Skewed Data

Skewness is a measure of the lack of symmetry in a distribution, or data set. A distribution like

the normal distribution is symmetric because the left and right side of the data look alike

(1.3.5.11. Measures of Skewness, n.d.). Data can be positively or negatively skewed as shown

in the figure above with a left or right tail.

Kurtosis measures the amount of data in the tail relative to a normal distribution. The descriptive

data highlighted the values for skewness and kurtosis for the different variables. The skewness

shall be demonstrated in the preceding histograms where the nature of the skew and the

direction of the tail are be observed

Pie-Chart of Hourly Wages

Fig 6: Graph of Percentage of Income Earners by hourly rate

The pie chart above shows the range of hourly salaries by percentage for four years between

2012 and 2015. The pie chart is based off reformatting the data in a pivot table as shown in the

excel sheet. The data and the Chart are both identified as Fig 5 in the excel sheet.

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Note: The dollar amounts for hourly rate are unusually low because the data does not back out

workers who do not work full hours ($7.5hrs) a day and those that do not work the full working

days in a year which is approximately 252 days per year.

Bar Char of Hourly Rate Data

Fig 7: Bar Chart of Frequency of Hourly Rate by Class Range

The bar chart above is a graphical representation of the frequency distribution of hourly wage

rate on Canada between 2012 and 2015. Similar to the pie chart above, it shows a different view

of the data with the Mode of $2.2/hour within the tallest bar above and shown in the descriptive

statistics.

Bar Chart – CPI Data

Fig 8: Bar Chart of Frequency of CPI by range classes

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Positive Skew Right Tail

Positive Skew Right Tail

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The histogram above shows the frequency of the different ranges of CPI values between 2012

and 2015. The CPI values range from 0.4 to 2.6 as shown by the graph and validated by the

descriptive data results. The graph further validated the CPI value of 1.2 as the value with the

most occurrence and highest bar – Mode in the descriptive statistics.

Graph of Overnight Rate

Fig9: Histogram of Overnight Rates showing Negative Skew

The Hisogram above is a plot of the overnight rates from the data sample used in this study. It

shows that the mode is in the range :0.9967 – 1.0167. This corresponds to a mode of 0.9978 as

shown in the table of descriptive statistics. The Histogram shows a negative skew and left tail

for the data.

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Hypothesis Testing

DescriptionHypothesis testing involves making a judgement call and then subjecting the available

data to analysis in order to determine if the call made is right or wrong. Usually there is a null

hypothesis (H0) which is a position or statistic we want to accept and then there is the alternative

hypothesis (Ha) which holds true if the null hypotheses can be not be proven to be false.. At the

end of the analysis there is usually enough evidence to either: fail to reject the null (Ho is true

and Ha is false) or to reject the null in favors of the alternative hypothesis (Ha is true and Ho is

false).

Given the above we can perform several hypothesis tests such as the following:

1. Until recently, oil prices have been on the rise(higher inflation). We hypothesize that CPI

which is a measure of inflation is higher in 2015 than all four years combined.

2. Rising all prices also slowed growth of the economy. We can hypothesize that Bank of

Canada used monetary policy to try to stimulate the economy. We can hypothesize that

Overnight rates are lower in 2015 than all 4 years

3. We can hypothesize that hourly rates were higher in 2015 than in all four years

4. We can furhter hypothesize that Mortgage rates in 2015 are not the same as the last four

years

5. We can hypothesize that Mortgage Rates in 2015 are not equal to 2012 using the 2 sample

test.

To test each of these hypothesis, we set up a null hypothesis (H0) and an alternate hypothesis

(Ha) and analyze the findings.

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Hypothesis testing –

Analysis @ 90% confidence level = 10% significance level

Hypothesis 1 – Testing CPI in 2015 and beween 2012 and 2015

Until recently, oil prices have been on the rise(higher inflation). We hypothesize that CPI which

is a measure of inflation is lower in 2015 than all four years combined

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This has consequently led to a lower inflation within a 90% confidence level

Hypothesis 2 – Testing Overnight Rate in 2015 and beween 2012 and 2015

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As a result, overnight rate is less in 2015 when compared to 2012 to 215 within a 90%

confidence level

Hypothesis 3 – Testing Hourly Rate in 2015 and beween 2012 and 2015

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Hypothesis 4 – Testing Mortgage Rate in 2015 and beween 2012 and 2015

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Hypothesis 5 – Testing Two Sample Mean Mortgage Rate in 2015 and 2012

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Chi Test of Independence

The table above represents a count of average house prices and the corresponding count within

each mortgage range.

A Chi-test s conducted to determine if the house prices was independent of mortgage rates.

With a 90% confidence, can we conclude from the available data that

Mortgage rate is independent of house prices?

Null Hypothesis- Ho = Average home prices is independent of mortgage rates

Alternate Hypothesis - Ha = House prices is dependent on Mortgage rates

Degree of Freedom (DF)

No of rows= 2

No of Col = 4

DF = (4-1)*(2-1) =3

Alpha = 0.1

Chi Critical X(0.1, 3) = 6.25

Reading the Chi Distribution table (Note the Red dot)

Fig 11- Screen capture of partial chi table with Chi critical marked

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Calculations

OBSERVED

Mortgage Rate

House hold Price 4.64-5.14 5.14-5.64Grand Total

$351,792.00 0 12 12 $357,348.00 0 12 12 $361,707.00 10 2 12 $367,632.00 12 0 12 Grand Total 22 26 48

EXPECTED

Price 4.64-5.14 5.14-5.64 $351,792.00 5.5 6.5 $357,348.00 5.5 6.5 $361,707.00 5.5 6.5 $367,632.00 5.5 6.5

Chi Statistic

Price 4.64-5.14 5.14-5.64 $351,792.00 5.500 4.654 $357,348.00 5.500 4.654 $361,707.00 3.682 3.115 $ 367,632.00 7.682 6.500 Chi Stat = 41.29

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Interpretation of Results

Chi stat is greater than Chi critical and is in the rejection region

There is enough evidence to reject to reject the Null hypothesis (Ho)

We can conclude that:

House prices are not independent but are dependent on Mortgage rates.

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Regression Analysis

Scatter PlotThe data used in this analysis can be presented in a scatter diagram as shown below.

Fig12. Scatter plot of all the data with a line of best fit through each independent variable

0 0.5 1 1.5 2 2.5 3$342,000

$348,000

$354,000

$360,000

$366,000

$372,000

f(x) = − 861.167627161112 x + 360802.061388123R² = 0.00647128769947891

Scatter Plot of Average House Price against CPI(values 2012-15)

CPI

Linear (CPI)

Fig 13: Scatter plot of House Price (y) against CPI values (X) – 2012 - 2015

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0 1 2 3 4 5 6$340,000

$345,000

$350,000

$355,000

$360,000

$365,000

$370,000

f(x) = − 1545.44663008237 x + 363364.23839747R² = 0.0268128055646142

f(x) = − 18760.2253521127 x + 453702.280140845R² = 0.771312482948067

f(x) = − 24961.3306096695 x + 382255.828657835R² = 0.55484740704877

f(x) = − 861.167627161112 x + 360802.061388123R² = 0.00647128769947891

Scatter Plot of Average House Price against Multiple Independent Variables - Mortgage Rate, CPI, Overnight Rate, Hourly Wage rate (values 2012-15)

CPI

Linear (CPI)

OverNgtRate

Linear (OverNgtRate)

MortgageRate

Linear (MortgageRate)

HourlyEarn

Linear (HourlyEarn)

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0.4 0.5 0.6 0.7 0.8 0.9 1 1.1$342,000

$348,000

$354,000

$360,000

$366,000

$372,000

f(x) = − 24961.3306096695 x + 382255.828657835R² = 0.55484740704877

Scatter Plot of Average House Price against Overnight Rate(values 2012-15)

OverNgtRate

Linear (OverNg-tRate)

Fig 14: Scatter plot of House Price (y) against Overnight Rate (X) – 2012 - 2015

4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5$342,000

$348,000

$354,000

$360,000

$366,000

$372,000

f(x) = − 18760.2253521127 x + 453702.280140845R² = 0.771312482948067

Scatter Plot of Average House Price vs Mortgage Rate, (values 2012-15)

MortgageRate

Linear (MortgageR-ate)

Fig 15: Scatter plot of House Price (y) against Mortgage Rate (X) – 2012 - 2015

Note that each scatter has a line of best fit in the form Y= mX +C. This shows that the plot is

for only one independent variable and all and the Slope m represents the rate of change of the

dependent variable with each additional unit increase in the independent variable – house prices

while the intercept on the y axis – is the House price when the independent variable is zero.

The coefficient of determination R2 is the percentage of housing prices explained or contributed

by the independent variable under consideration.

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1 1.5 2 2.5 3 3.5 4 4.5$342,000

$348,000

$354,000

$360,000

$366,000

$372,000

f(x) = − 1545.44663008237 x + 363364.23839747R² = 0.0268128055646142

Scatter Plot of Average House Price against Hourly Wage rate (values 2012-15)

HourlyEarn

Linear (HourlyEarn)

Fig 16: Scatter plot of House Price (y) against Hourly Wage Rate(X) – 2012 - 2015

The scatter was plotted first together and then separately. A line of best fit was also plotted ( y =

mx + C) . This line represents an expression of the relationship between the respective

independent variables and Average home price when taken separately. The slope of the various

lines of fit represent an increment in price resulting from a unit change of the independent

variable whereas the constant term in the line of best fit represents the intercept on the y-

Average home price axis.

Regression ResultsRegression Analysis is a statistical tool that develops a model that expresses a relationship

between two or more independent variables and a dependent variable. Such a model can then be

characterized by coefficients and the resulting regression line amongst other things tested for

fitness to the data, standard error etc.

The following table provides the results of applying the Excel Regression tool to build a

statistical model of the data of dependent variable (House Prices) and a set of related

Independent Variables:

1. CPI (Total Consumer Price Index)

2. Mortgage Rate

3. Overnight Rate and

4. Hourly Wages.

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SUMMARY OUTPUT

Regression StatisticsMultiple R 0.942672201R Square 0.888630878Adjusted R Square 0.878270959Standard Error 2048.260633Observations 48

ANOVAdf SS MS F Significance F

Regression 4 1439446389 359861597.3 85.77585723 6.43812E-20Residual 43 180400979.8 4195371.622Total 47 1619847369

CoefficientsStandard

Error t Stat P-value Lower 95%Upper 95%

Lower 95.0% Upper 95.0%

House Price Intercept 446700.7369 7268.362081 61.45823941 1.54866E-43 432042.6878 461358.8 432042.7 461358.786

Mortgage rate -13196.38401 1868.438541-

7.062787304 1.04388E-08 -16964.44944 -9428.32 -16964.4-

9428.318576

Total CPI -1782.241643 612.0432175-

2.911953914 0.005673586 -3016.544425 -547.939 -3016.54-

547.9388606

Overnight rate -12744.76111 3118.925366-

4.086266779 0.000187805 -19034.67357 -6454.85 -19034.7-

6454.848655

Hourly earnings -2846.452977 575.3909657-

4.946989345 1.20396E-05 -4006.839449 -1686.07 -4006.84-

1686.066505

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Interpretation of the Regression Summary Output

Based on the Regression output, the Model is of the form

Y = b0 + b1 X1 + b2 X2 + b3 X3 + b4 X4

Where coefficient are: 446701, -13196, -1782, -12745, -2846

In an equation it is of the form

Y = 446701 - 13196X1 - 1782X2 - 12745X3 - 2846X4

Interpretation of Regression Model Coefficients

Intercept (b0 = 446701):

Eliminating all other independent variables (mortgage rate, cpi, overnight rate and hourly

earnings are zero), the model suggests that the Price of a House (y) is 446701. This is also the

intercept of the regression line on the Y axis.

Mortgage Rate (b1 = -13196):

This defines the relationship between Mortgage rate and House price. Eliminating other

independent variables, the price of a house decreases by 13196 for every additional increase in

mortgage rate. This shows an inverse relationship

Total CPI (b2 = -1782):

This defines the relationship between Total CPI and House price. Eliminating other independent

variables, the price of a house decreases by 1782 for every additional increase in CPI rate. This

shows an inverse relationship

Overnight Rate (b3 = -12745):

This defines the relationship between Overnight Rate and House price. Eliminating other

independent variables, the price of a house decreases by 12745 for every additional increase in

Overnight rate. This shows an inverse relationship.

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F critical = F (k, n-k-1, α) n=48; k=4; α = 0.05

= F (4, 43, 0.05) = 2.58

Fstat. (Regression table output) = 85.78

Interpretation

Fstatistic is greater than Fcritical and is in the rejection region

There is therefore enough evidence to reject the null hypothesis

We can infer that the Model is valid within a 95% confidence level

This means that within a 95% confidence interval, at least one of the independent variables

(CPI, Mortgage rate, Overnight rate or Hourly wages ) has a linear relationship with average

house prices the dependent variable.

Testing the Linear Relationships of the Independent VariablesWhile an F-test tells enables us to determine the validity of the regression model, the individual

independent variables may still not have a linear relationship with the dependent variable when

examined individually. Examining the t-statistic of each independent variable and determine its

linearity by comparing it to the t-critical for the model will allow for the testing of each

independent variable for linearity – i.e. if it has a linear relationship with the dependent variable

house prices. The test and results are as shown in the table below:

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Note: Null Hypothesis (H0), implies a non-linear relation; Ha - the Alternate Hypothesis implies

a linear relation; If t-stat is in the rejection region, we have enough evidence to reject the null

hypothesis or else we do not.

Independent Variable

T Critical T-Stat (from

regression table)Is there a linear Relationship?

Hypothesis Note: n-k-1 = 48-4-1= 43

Mortgage Rate

tcritical (df , α/2) =

tcritical (n-k-1 , 0.05/2) =

tcritical (43 , 0.025) = 2.009

-7.06279 T-stat < t critical;

H0:β1 = 0 In rejection region; Reject H0;

Ha: β1 ≠ 0 Relationship is Linear

Total CPI -2.91195 T-stat < t critical;

H0: β2 = 0 In rejection region; Reject H0;


Overnight rate -4.08627 T-stat < t critical;



Hourly Rate -4.94699 T-stat < t critical;



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Conclusion: We can conclude within a 90% confidence level that there is a linear relationship

between Housing prices and CPI, Mortgage Rate, Overnight Rate and Hourly Rate.

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Testing the Slope (Confidence of the Estimators)We can also determine the confidence interval for each estimator of coefficient from the

Regression table as follows

From the table, we can determine the following Confidence intervals

β0 = b0 ± tα/2 sb0 = 432042.69 to 461358.8 (Lower to Upper Limit) House price - intercept

β1 = b1 ± tα/2 sb1 = -16964.45 to -9428.32 (Lower to Upper Limit) – Slope of Mortgage line

β2 = b2 ± tα/2 sb2 = -3016.54 to -547.94 (Lower to Upper Limit) - Slope of CPI line

β3 = b3 ± tα/2 sb3 = -19034.67 to -6454.85 (Lower to Upper Limit) – slope of Overnight rate line

β4 = b4 ± tα/2 sb4 = -4006.84 to -1686.07 (Lower to Upper Limit) – Slope of Hourly Earnings Line

Analysis of Regression Model Results

The regression model used key economic factors of CPI, Mortgage Rate, Overnight Rate and

Hourly Income within a 4 year span to create a regression equation. The Equation was also

evaluated.

The results show that while the while 88.66% of the price of a house is explained by the model,

the ratio of Standard error to the average home price which is a measure of fitness of data to

the regression model (0 being a best fit) was ).56%. This suggests a very good fit. All the

coefficients also showed a negative relationship with the independent variable even though

these relationships were all linear.

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- For β0

- For β1

- For β2

- For β3

- For β4

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Conclusion from Regression AnalysisWhile the regression line appears to be a good fit for the data with a standard error of 0.56% and

the Coefficient of Determination is 88.66%, the negative coefficient suggests that there are

indeed other variables that contribute significantly to the Average price of a home.

Conclusion

Summary

We proposed to study the effect of independent variables – CPI, Over-Night Rate, Mortgage

Rate and Hourly Earnings on House prices with a view of determining the relationship and

impact of these variables on the price of a home. We also explained the theories and market

forces in play with respect to home prices. Within the scope of our research, we succeeded. The

model developed suggests that these variables under investigation have a negative relationship

with home prices. In order words as they contribute to the decrease, home prices. Further study is

required on variables that increase average home prices.

Limitations of the Study

All the data used for this study was from a secondary source. Where the data collected did not

suit our analysis, the data was adapted to fit. For instance, while average annual home prices

were available, this data was extrapolated for the entire year – in order words the home price

was kept constant for the year. Further, while House Price Index which measures the variability

in home prices showed more variability, it was not used in this study because a base price was

not found in order to convert these price changes to dollar amounts.

Further, it was observed that the hourly wages were very low. Data for average hourly earnings

of permanent workers was provided by Statistics Canada - Statistics Canada's Labour Force

Information (Catalogue 71-001). However, the figures are unusually low due to the fact that

Statistics Canada does no separate part-time from full time workers who work on average 252

days per year and 7.5 hours per day with all other workers who work less hours and or less days.

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While are study was on the city of Ottawa, national economic indicators were applied in our

study. The economic indicators used may therefore not be a true reflection of the Ottawa

Economy. However, since the data was representative of economic indicators in Canada they

were used since they will provide a good estimate of the city’s values.

Areas for Future Study

A very high positive intercept and large negative coefficients points to the fact that there are

other variables that contribute to the Average price of homes. We can also infer that all the

independent variables considered in this study provide a negative contribution to the average

price of a home and have an inverse relationship. As such there is opportunity for further study

to determine other variables that have a direct relationship with home prices in order to fully

understand home price behavior.

The perspective of this analysis has been simplistic and significant assumptions have been made

especially with regards to hypothesis testing. More work needs to be done in terms of the scope

of variables studied and the time line of study as employing data for more years will provide

better results.

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REFERENES

1.3.5.11. Measures of Skewness and Kurtosis. (n.d.). Retrieved April 10, 2016, from http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm

Canadian Interest Rates and Monetary Policy Variables: 10-Year Lookup. (n.d.). Retrieved April

10, 2016, from

http://www.bankofcanada.ca/rates/interest-rates/canadian-interest-rates/

Enter Specific Date Range for Results

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x/2011000/chap/construction/construction-eng.htm

11-402-X

CREA. (n.d.). MLS® Home Price Index. Retrieved April 09, 2016, from

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12th Annual Demographia International Housing Affordability Survey: 2016

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