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

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

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

1
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).

2
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.

3
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.

4
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.

5
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

6
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

7
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.

8
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
Table 1: Descriptive Statistics
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

9
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
Fig 5: Graphic Demonstration of Skewed Data

10
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.

11
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
Positive Skew
Right Tail
Positive Skew
Right Tail

12
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.

13
Hypothesis Testing
Description
Hypothesis 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.

14
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

15

16
This has consequently led to a lower inflation within a 90% confidence level

17
Hypothesis 2 – Testing Overnight Rate in 2015 and beween 2012 and 2015
As a result, overnight rate is less in 2015 when compared to 2012 to 215 within a 90%
confidence level

18
Hypothesis 3 – Testing HourlyRate in 2015 and beween 2012 and 2015

19
Hypothesis 4 – Testing Mortgage Rate in 2015 andbeween 2012 and 2015

20
Hypothesis 5 – Testing Two Sample Mean Mortgage Rate in 2015 and 2012

21
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)
Fig11- Screen capture of partial chi tablewith Chi critical marked

22
Calculations
OBSERVED
Mortgage Rate
House hold Price 4.64-5.14 5.14-5.64
Grand
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
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.

23
y(CPI) =-861.17x +360802
R² = 0.0065
y(Ngt) = -24961x +382256
R² = 0.5548
y(Mrtg) = -18760x +453702
R² = 0.7713
y(HrlyEarn) = -1545.4x+363364
R² = 0.0268
$350,000
$355,000
$360,000
$365,000
$370,000
$375,000
0 1 2 3 4 5 6
Scatter Plot of Average House Price against Multiple Independent Variables -
Mortgage Rate, CPI, Overnight Rate, Hourly Wage rate (values 2012-15)
CPI
OverNgtRate
MortgageRate
HourlyEarn
Linear (CPI)
Linear (OverNgtRate)
Linear (MortgageRate)
Linear (HourlyEarn)
Regression Analysis
Scatter Plot
The 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
Fig 13: Scatter plot of House Price (y) against CPI values (X) – 2012 - 2015
y(CPI) = -861.17x + 360802
R² = 0.0065
$348,000
$354,000
$360,000
$366,000
$372,000
0 0.5 1 1.5 2 2.5 3
Scatter Plot of Average House Price against CPI(values 2012-15)
CPI
Linear (CPI)

24
Fig 14: Scatter plot of House Price (y) against Overnight Rate (X) – 2012 - 2015
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.
y(Ngt) = -24961x + 382256
R² = 0.5548
$348,000
$354,000
$360,000
$366,000
$372,000
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
Scatter Plot of Average House Price against Overnight Rate(values2012-15)
OverNgtRate
Linear
(OverNgtRate)
y(Mrtg) = -18760x + 453702
R² = 0.7713
$348,000
$354,000
$360,000
$366,000
$372,000
4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5
Scatter Plot of Average House Price
vs Mortgage Rate, (values2012-15)
MortgageRate
Linear
(MortgageRat
e)

25
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 Results
Regression 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.
y(HrlyEarn) = -1545.4x + 363364
R² = 0.0268
$348,000
$354,000
$360,000
$366,000
$372,000
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Scatter Plot of Average House Price against Hourly Wage rate (values2012-15)
HourlyEarn
Linear
(HourlyEarn)

26
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.942672201
R Square 0.888630878
AdjustedRSquare 0.878270959
StandardError 2048.260633
Observations 48
ANOVA
df SS MS F Significance F
Regression 4 1439446389 359861597.3 85.77585723 6.43812E-20
Residual 43 180400979.8 4195371.622
Total 47 1619847369
Coefficients
Standard
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
Overnightrate -12744.76111 3118.925366
-
4.086266779 0.000187805 -19034.67357 -6454.85 -19034.7
-
6454.848655
Hourlyearnings -2846.452977 575.3909657
-
4.946989345 1.20396E-05 -4006.839449 -1686.07 -4006.84
-
1686.066505

25
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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Hourly Earnings (b4 = -2846):
This defines the relationship between Hourly Earnings and House price. Eliminating other
independent variables, the price of a house should decrease by 2846 for every additional increase
in Hourly Earnings. This shows an inverse relationship
Interpretation of other Regression Characteristics
Coefficient of Determination R2 = 0.888630878 = 88.86%
R2 = explains the contribution of the regression model to the dependent variable
This means that only 88.86% of the house price can be explained by the regression model.
The balance of 11.14 % is unexplained by the identified independent variables used in the model
Standard Error (Se) = 2048.260633
Se ranges from 0 for perfect fit to infinity. It measures the fitness of the data to the regression
line. The ratio of Se to average of House prices (Y) provides a comparison with the independent
variable as a measure of the error.
Average of the House price data (Ybar) = $359,620
Se/Ybar = 0.00569563 0.5696%
The ratio is very close to zero suggesting a very good fit of the data to the regression line
Testing the Validity of the Model
A regression model is valid if at least one of the coefficients of the independent variable has a
linear relationship with dependent variable
This is tested with the F statistic.
Hypothesis
H0: bi = 0 or Model is not valid (i.e. either b1 or b2 or b3 or b4 = 0)
Ha: at least one bi ≠ 0 or Model is valid (i.e. at least one b1, b2, b3 or b4 ≠ 0)

27
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 Variables
While 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:
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.

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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;
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.
±2.009

29
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.
- For β0
- For β1
- For β2
- For β3
- For β4

30
Conclusion from Regression Analysis
While 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.
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

31
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.

32
REFERENES
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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
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Enter Specific Date Range for Results
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x/2011000/chap/construction/construction-eng.htm
11-402-X
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Association
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12th Annual Demographia International Housing Affordability Survey: 2016
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Buyers-Be-Prepared- Realty Executives By Realty Choice; Springfield, MO Real Estate
Company
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functions/monetary-policy/key-interest-rate/ Bank of Canada

33
Parkinson, D. (2014, September 15). Canadians' household debt burden edges higher in second
quarter. Retrieved April 09, 2016, from http://www.theglobeandmail.com/report-on-
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Sturgeon, J. (2015, March 13). Home prices are cooling everywhere but red-hot Vancouver,
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