MUTIPLE REGRESSION MODEL

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Title: MUTIPLE REGRESSION MODEL

Introduction

Just like in a normal market situation, housing market also experience the forces of demand and supply. Real housing price is generally the actual price that a home is sold for. Therefore, house price and selling price can be easily interchanged. The real house price is the price of the house adjusted for inflation; it is usually lower than the nominal house prices. Several factors are responsible for the decline or rising of the real housing prices. Among these factors are: population, GDP, unemployment and interest rates. Despite the fact that there are numerous factors affecting the housing market, this paper will focus mainly on these four factors since they are the greatest determinants of the housing market.

The comparison between real house prices and unemployment rates is rather an interesting one. The 1970s and 1980s national housing bubbles showed the true relationship between unemployment and house prices. The data from the housing bubbles indicated that real house prices declined until the rate of unemployment was at peak. Following the late 1980s housing bubbles, the Caser-Shiller index was of the suggestion that prices reduced for a few years after the unemployment rate peaked. Several studies also support this arguments hence the conclusion that house prices and unemployment rate exhibit a rather negative relationship.

There is a correlation between house prices and inflation. In fact several researchers show that the relationship these two variables are 0.18-which is not strong but positive. The fact is; the global inflation has been relatively low for quite a lot of time and the interest rates have fallen dramatically during this low inflation rate period. An increase in money supply in the economy causes inflation and house prices to increase. As mentioned earlier, there are a lot more factors that affect house prices and the relationship they exhibit is not as strong compared to the relationship that exist between inflation and house prices. One of the other factors is the rate of interest in the economy. Low interest rates means that home buyers can easily afford to buy a home. This will increase the demand hence eventually increasing the demand of the homes. In large cities like London-where availability to land is limited-you will realize a more distinct effect of inflation. Countries with high population are always characterized with high house prices. This is because high population will always increase the demand for the houses hence pushing up the housing prices. The bottom line is; if the construction industry is not able to satiate the demand for homes, the supply-demand imbalance will explain the unprecedented increase in real house prices. The economical state of the country is also important in determining prices of the houses. Countries with high GDP are experienced with high per capita income hence high demand for housing units which results to higher housing prices. This explains the reason as to why buying a house in a developed country is expensive as compared to underdeveloped or developing countries. This paper will try to analyze the relationship that exists between house prices; GDP, interest rates, population and unemployment rates. Through these variables, the paper will try to determine how house prices are affected by interest rates, GDP, population and unemployment rate in a country. A regression model will be developed: that will eventually be used to project the level of house prices in the future.

Objective of the study

The main goal of this study is to determine how house prices are affected by factors such as interest rates, GDP, population and unemployment rates.

Assumptions of the study

Assumptions are vital concept of empirical studies. Just like any other empirical study, this study applies some statistical assumptions in order to achieve the much needed results. These assumptions include:

The mean difference is zero

The data is normally distributed

The variance of the two variables are equal (homoscedasticity)

Methodologies

The data are derived from the U.K. Bureau of Statistics. The independent variable of the study is house prices while the dependent variables are interest rates, GDP, population and unemployment rates. The study will mainly duel on correlation and regression for data analysis. The analysis will involve getting the correlation and regression coefficients for both the variables. Correlation coefficient is important in showing whether and how strongly house prices and; interest rates, GDP, population and unemployment rates are related. The study is linear in nature hence Pearson product-moment correlation coefficient will be used to determine the strength and direction of the linear relationship between house prices and other dependent variables. The value of Pearson’s correlation coefficient is influenced by the distribution of the independent (house prices) variable in the sample. Regression analysis defines the relationship between house prices and; interest rates, GDP, population and unemployment rates. T-test will be used to determine the significance of the regression model before using it to predict the value of house prices. Apart from; regression, correlation coefficient and t-tests: the study will also utilize the E-views software to determine the relationship that exists between house prices and; interest rates, GDP, population and unemployment rates.

The model

The following regression model will be used during the study: Y=Bo + BX1 + BX2 + BX3 + BX4 + e (where; Y= house prices, X1= population, X2= GDP, X3= unemployment, X4= interest rates Bo=constant, e=error term).

RESULTS

Correlation between house prices and population

  House price population

House price 1 population 0.883531 1

Correlation between house prices and GDP

  house prices GDP

house prices 1 GDP 0.790410293 1

Correlation between house prices and unemployment +16%

  house prices unemployment +16%

house prices 1 unemployment +16% -0.261299388 1

Correlation between house prices and interest rates

  house prices interest rates

house price 1 interest rates -0.411084402 1

SUMMARY OUTPUT 788035-6350

Regression Statistics Multiple R 0.90789 R Square 0.824264 Adjusted R Square 0.803589 Standard Error 19808.81 Observations 39 ANOVA   df SS MS F Significance F Regression 4 6.26E+10 1.56E+10 39.86792 2.18E-12 Residual 34 1.33E+10 3.92E+08 Total 38 7.59E+10         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -990612 261023.7 -3.7951 0.00058 -1521076 -460148 -1521076 -460147.975 56096677 0.018959 0.004554 4.162809 0.000203 0.009703 0.028214 0.009703 0.028214324 0 0.073902 0.064824 1.140048 0.262234 -0.05784 0.20564 -0.05784 0.205639921 4.3 -3821.77 1559.646 -2.45041 0.01957 -6991.35 -652.188 -6991.35 -652.187603 0 2074.545 1168.102 1.775996 0.084685 -299.324 4448.414 -299.324 4448.413918 INTERPREATATION OF RSULTS

Hypothesis

The following hypothesis was tested during the analysis and interpretation of the results.

Hypothesis one

Null hypothesis Ha: house prices are not positively affected by the population of the country

Alternative hypothesis Ho: house prices are positively affected by the population of the country

The p-value is 0.000203 which is less than significant value 0.05 hence we reject the null hypothesis and accept the alternative hypothesis. Therefore, house prices are positively affected by the country’s population.

Hypothesis two

Null hypothesis Ha: house prices are positively affected by the GDP of the country

Alternative hypothesis Ho: house prices are not positively affected by the GDP of the country

The p-value (0.262234)> 0.05 hence we accept the null hypothesis. Hence house prices are positively affected by the GDP.

Hypothesis three

Null hypothesis Ha: house prices are not positively affected by the unemployment rate

Alternative hypothesis Ho: house prices are positively affected by the unemployment rate

The p-value (0.01957) < 0.05 hence we reject the null hypothesis.

Hypothesis four

Null hypothesis Ha: house prices are negatively affected by the interest rate

Alternative hypothesis Ho: house prices are not negatively affected by the interest rate

The p-value (0.084685) > 0.05 hence we accept the null hypothesis. Therefore, house prices are negatively affected by the interest rates.

The correlation results indicate that population and unemployment both have a strong positive relationship house prices. On the other hand; inflation and unemployment rates exhibit a negative relationship with the house prices. The regression results, we can derive a more practical model using the coefficients as shown below:

Y=Bo + BX1 + BX2 + BX3 + BX4 + e

Y= -990612 + 0.018959X1 + 0.073902X2 -3821.77X3 + 2074.545X4 + e

From the regression model, we can be able to deduce some interesting facts. Holding other factors constant;

An increase in population by one unit will raise the house prices by 0.018959.

An increase in GDP by one unit will increase the house prices by 0.073902

An increase in unemployment rate by one unit will reduce the house prices by 3821.77

An increase in interest rates by one unit will increase the house prices by 2074.545

There is however, a very interesting relationship between house prices and interest rates. The correlation coefficient depicts a negative correlation between house prices and interest rates while regression results show that an increase in interest rates causes an increase in house price. This interesting fact can be explained by other lying factors which are not involved in the model. But the general argument is that house prices are affected by these four variables either negatively or positively. Hence the model: Y= -990612 + 0.018959X1 + 0.073902X2 -3821.77X3 + 2074.545X4 + e

References

Kleinbaum, David G, and David G. Kleinbaum. Applied Regression Analysis and Other Multivariable Methods. Australia: Brooks/Cole, 2008. Print.