Factors Affecting Residential Housing - Statistics Project Example

Factors Affecting Residential Housing The main objective of this study was based on data obtained from 37 residential housing. There are factors that were presumed to affect the price of housing. The factors include the cost of construction, inflation rates, interest rates and real property gains tax and population. Therefore, the main aim of the study was to analyze the collected data and determine the level of influence of these variables on the price of housing using different model of regression. These five variables were taken to be independent variables but the price of housing was taken to be dependent. The main procedure utilized in this study was regression analysis. It was utilized to explain the total variation of the dependent variable, the price of housing. The dependent variable was accompanied by 5 variables, which were tested against the dependent variable to determine how much of the total variation is explained. The analyses also discussed the comparison of the different regression models, and determine which model is the most effective. In regards to the regression analysis results, it is clearly evident that model 4 and 5 are the strongest model and model 1 being the weakest. Model 2 and 3 does not apply because of the reasons given. Regression Analysis The first regression analysis step was to input all the collected data from the surveys into a spreadsheet. This process allows efficient running of regression models. After all the data was entered, there was formulation of the initial regression model. The analysis was done as in the next section. SUMMARY OUTPUT Regression Statistics Multiple R 0.664436 R Square 0.441475 Adjusted R Square 0.348387 Standard Error 18.20258 Observations 36 ANOVA   df SS MS F Significance F Regression 5 7856.883 1571.377 4.742576 0.002605 Residual 30 9940.019 331.334 Total 35 17796.9         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 156.4318 27.7526 5.636653 3.86E-06 99.75339 213.1101 99.75339 213.1101 X Variable 1 -0.5373 0.340822 -1.57649 0.1254 -1.23335 0.158747 -1.23335 0.158747 X Variable 2 3.660519 2.871782 1.27465 0.212218 -2.20444 9.525481 -2.20444 9.525481 X Variable 3 -2.21714 2.767943 -0.80101 0.429426 -7.87004 3.43575 -7.87004 3.43575 X Variable 4 -6.45855 3.056208 -2.11326 0.043006 -12.7002 -0.21694 -12.7002 -0.21694 X Variable 5 -2.21357 1.609478 -1.37534 0.179211 -5.50056 1.073419 -5.50056 1.073419 Y = housing price X1 = ln(cost of construction) X2 = ln(population) X3= inflation rate X4 = interest rate X5= RPGT The estimated regression equation can be written in the format as: Y= -156.43 -0.5373X1 +3.66X2 -2.217X3 -6.458X4 -2.21X5 R squared=0.44 The above multiple regression analysis can be written in the real format as Housing price = -156.43 -0.5373(cost of construction) +3.66(population) -2.217(inflation rate) -6.458 (interest rate) -2.21 (RPGT) In summary, basing on the multiple regression above it is observed that the cost of construction, inflation rates, interest rates and real property gains tax influence negatively the price of housing. On the other hand population influences positively the price of housing. The analysis of this model can be further analyzed to ascertain the strength of the influence as seen in the next section. Model 1 The general regression equation: Y= a+b1x1 Specific regression equation: Housing price = a + b1 (cost of construction) SUMMARY OUTPUT Regression Statistics Multiple R 0.204902 R Square 0.041985 Adjusted R Square 0.013808 Standard Error 22.39334 Observations 36 ANOVA   df SS MS F Significance F Regression 1 747.1991 747.1991 1.490042 0.230608 Residual 34 17049.7 501.4619 Total 35 17796.9         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 137.0933 11.93214 11.48941 2.97E-13 112.8443 161.3423 112.8443 161.3423 X Variable 1 -0.46633 0.382026 -1.22067 0.230608 -1.2427 0.310041 -1.2427 0.310041 This first regression analysis shows a relatively weak model. The coefficient of Determination(R squared) shows that only 4% of the total variation is explained by the cost of construction factor. The standard error is 22.39, determined by the low R squared. In regards to the hypothesis testing, by considering an alpha of 0.05, the results indicate that this age variable is to be rejected. The independent variable of cost of construction demonstrates that the higher the cost of construction is, the less the price of housing and this is in line with several studies done. Thus the performance is less by -0.46633. Despite this is a low number, the results clearly ascertains what the research indicate about the cost of construction and price of housing. The final regression equation for model 1: Price of housing=137 -0.46633 (cost of construction) Model 2 The general regression equation:Y= a+b2x2 Specific regression equation: Price of housing = a + b2 (Population) SUMMARY OUTPUT Regression Statistics Multiple R 0.312687 R Square 0.097773 Adjusted R Square 0.071237 Standard Error 21.73155 Observations 36 ANOVA   df SS MS F Significance F Regression 1 1740.06 1740.06 3.684537 0.063343 Residual 34 16056.84 472.2601 Total 35 17796.9         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 82.75834 21.40798 3.86577 0.000475 39.25209 126.2646 39.25209 126.2646 X Variable 1 5.855501 3.050511 1.919515 0.063343 -0.34388 12.05489 -0.34388 12.05489 This second regression analysis shows a relatively weak model similar to the first one. The R squared shows that 9.7% of the total variation is explained by the number of population factor. The standard error is 21.73, determined by the low R squared. In regards to the hypothesis testing, by considering an alpha of 0.05, the results indicate that this population variable can’t be rejected. The independent variable of population demonstrates that it has no influence on the dependent variable or on the performance. Despite the coefficient being too low, it is clearly evident that the population has no influence on the Price of housing. The final regression equation for model 2 can’t be created basing on the results outcome. Model 3 The general regression equation:Y= a+b3x3 Specific regression equation: The price of housing = a + b3 (Inflation rate) SUMMARY OUTPUT Regression Statistics Multiple R 0.301633 R Square 0.090982 Adjusted R Square 0.064247 Standard Error 21.81317 Observations 36 ANOVA   df SS MS F Significance F Regression 1 1619.206 1619.206 3.403019 0.073804 Residual 34 16177.7 475.8146 Total 35 17796.9         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 130.8634 5.496403 23.80892 8.73E-23 119.6934 142.0334 119.6934 142.0334 X Variable 1 -5.06968 2.748202 -1.84473 0.073804 -10.6547 0.515335 -10.6547 0.515335 This third regression analysis also shows relatively weak model similar to the first 2. The R squared shows that 9 % of the total variation is explained by the inflation rate factor. The standard error is 21.81, determined by the low R squared. In regards to the hypothesis testing, with an alpha of 0.05, the results indicate that this inflation rate variable can’t be rejected. The independent variable of inflation rate demonstrates that it has no influence on the dependent variable or price of housing. The final regression equation for model 3 can’t also be created basing on the results outcome. Model 4 The general regression equation:Y= a+b4x4 Specific regression equation: Price of housing = a + b4 (Interest rate) SUMMARY OUTPUT Regression Statistics Multiple R 0.551202 R Square 0.303823 Adjusted R Square 0.283347 Standard Error 19.08941 Observations 36 ANOVA   df SS MS F Significance F Regression 1 5407.111 5407.111 14.83817 0.000494 Residual 34 12389.79 364.4056 Total 35 17796.9         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 176.7946 14.25756 12.40006 3.61E-14 147.8198 205.7695 147.8198 205.7695 X Variable 1 -10.5316 2.734042 -3.85203 0.000494 -16.0879 -4.97538 -16.0879 -4.97538 The fourth regression analysis shows a moderate strong model. The coefficient of Determination(R squared) shows that approximately 30% of the total variation is explained by the interest rate factor. The R 2 is so high when compared with R2 of the model 1, 2 and 3.The standard error is 19.09, determined by the low R squared. In regards to the hypothesis testing, by considering an alpha of 0.05, the results indicate that this interest rate variable is to be rejected, the p value being less than 0.05(0.0004). The independent variable of interest rate demonstrates that the higher the interest rate, the lower the price of housing and this is in line with several studies done. Thus the interest rate is less by -10.5316. The final regression equation for model 4: The price of housing=176.8 -10.53 (interest rate) Model 5 The general regression equation:Y= a+b5x5 Specific regression equation: Price of housing = a + b5 (real property gains tax) SUMMARY OUTPUT Regression Statistics Multiple R 0.458605 R Square 0.210318 Adjusted R Square 0.187092 Standard Error 20.331 Observations 36 ANOVA   df SS MS F Significance F Regression 1 3743.013 3743.013 9.055318 0.004907 Residual 34 14053.89 413.3497 Total 35 17796.9         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 135.9628 5.413376 25.11609 1.56E-23 124.9615 146.9641 124.9615 146.9641 X Variable 1 -4.39752 1.461356 -3.00921 0.004907 -7.36735 -1.42769 -7.36735 -1.42769 The fifth regression analysis shows a moderate strong model. The R squared shows that approximately 21% of the total variation is explained by the real property gains tax. The R 2 is relatively high when compared with R2 of the model 1, 2 and 3,but almost the same as that of model 4.The standard error is 20.33, determined by the R squared. In regards to the hypothesis testing, by considering an alpha of 0.05, the results indicate that this real property gains tax variable is to be rejected at p value of less than 0.05(0.0004). The independent variable of the price of housing run demonstrates that the more the real property gains tax , the lower the price of housing becomes. This is indicated by a negative value and it is in line with several studies done. Thus the price of housing is less by -4.39752. The final regression equation for model 5: The price of housing=135.96 -10.53 (real property gains tax) In regards to the above regression analysis, it is clearly evident that model 4 and 5 are the strongest model and model 1 being the weakest. Model 2 and 3 does not apply because of the reasons above. Therefore, the cost of construction, inflation rates, interest rates and real property gains tax influence negatively the price of housing. On the other hand population influences positively the price of housing.. The interest rates and real property gains tax have a negative moderate influence on the Price of housing, while the population has a weak positive influence on the price of housing. Improvements Exploring the influence of several factors to price of housing is the matter of future research. More factors that affect the price of housing should be explored. There were some high p values in the analysis indicating that some of the data was not good enough to infer and majorly it could be due to small sample size, confounding factors and outliers. This work is led to another level despite the availability of data is expected to be a major challenge. Small sample size may result to higher P values than 0.05 and also it can result to wrong estimates which can give wrong interpretation. Works Cited Megbolugbe, I.F. and Cho, M. (1993) An empirical analysis of metropolitan housing and mortgage markets. Journal of Housing Research, Vol 4, no2, pp 191-210. Read More