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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
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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
RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS
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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RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS
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;
Ha: β2 ≠ 0 Relationship is Linear
Overnight rate -4.08627 T-stat < t critical;
H0: β3 = 0 In rejection region; Reject H0;
Ha: β3 ≠ 0 Relationship is Linear
Hourly Rate -4.94699 T-stat < t critical;
H0: β4 = 0 In rejection region; Reject H0;
Ha: β4 ≠ 0 Relationship is Linear
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±2.009
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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
Construction. (n.d.). Retrieved April 09, 2016, from http://www.statcan.gc.ca/pub/11- 402-
x/2011000/chap/construction/construction-eng.htm
11-402-X
CREA. (n.d.). MLS® Home Price Index. Retrieved April 09, 2016, from
http://www.crea.ca/housing-market-stats/mls-home-price-index/ Canadian Real Estate
Association
Demographia. (n.d.). Rating Middle-Income Housing Affordability. Retrieved March 8, 2016,
from http://www.demographia.com/dhi.pdf
12th Annual Demographia International Housing Affordability Survey: 2016
First-Time Home Buyers - Be Prepared! (2015, May 28). Retrieved April 09, 2016, from https://www.realtyexecutives.com/Office/Realty-Choice/blog/First-Time-Home-Buyers-Be-Prepared- Realty Executives By Realty Choice; Springfield, MO Real Estate Company
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functions/monetary-policy/inflation/ Bank of Canada
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