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- 1. 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
- 2. 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
- 3. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 4. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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).
- 5. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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.
- 6. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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.
- 7. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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.
- 8. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 9. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 10. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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.
- 11. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 12. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 13. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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.
- 14. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 15. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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.
- 16. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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.
- 17. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 18. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 15
- 19. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 16 This has consequently led to a lower inflation within a 90% confidence level
- 20. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 21. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 18 Hypothesis 3 – Testing HourlyRate in 2015 and beween 2012 and 2015
- 22. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 19 Hypothesis 4 – Testing Mortgage Rate in 2015 andbeween 2012 and 2015
- 23. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 20 Hypothesis 5 – Testing Two Sample Mean Mortgage Rate in 2015 and 2012
- 24. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 25. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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.
- 26. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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)
- 27. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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)
- 28. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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)
- 29. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 30. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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.
- 31. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 26 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)
- 32. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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.
- 33. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 28 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 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
- 34. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 35. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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
- 36. RELATIONSHIP BETWEEN HOME PRICES AND ECONOMIC FACTORS 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.
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