Week 5 Regression Team Paper (Real Estate)
Week 5 Regression Team Paper (Real Estate)
CSU - Dominguez hills
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Date Created: 11/16/15
Regression Analysis on Real Estate Data Set – Team B RES 342 Week 5 Page 1 Regression Analysis in Real Estate Data Set Learning Team B RES342 Research and Evaluation II Date Teacher Regression Analysis on Real Estate Data Set – Team B RES 342 Week 5 Page 2 Regression Analysis in real Estate Data set During a research all variables must be considered and closely examined by the researcher. From the introduction of the research to the closing decision the researcher must carefully review the details and make adjustments to the test accordingly. This research project will examine housing sales and the impact of certain independent variables on the dependent variable – price. Purchasing a home can be one of the most complicated processes an individual will encounter in life. Many factors must be considered to ensure the right purchase for the family making the decision. An individual should consider the size of the home, number of bedrooms, amenities, and the location of the home. As a part of Team B’s research the group will test to determine if the distance of the home from the town center is a variable that shows a significant effect on the prices of a house. In week three and four, Team B tested the impact of the number of bedrooms on pricing of houses. The research focused in on houses with four or more bedrooms versus houses with less than four bedrooms. Parametric hypothesis testing and nonparametric testing both did not provide data that would allow the rejection of the null hypothesis that houses with four bedrooms or more do not have a higher mean selling price per square foot that houses with less than four bedrooms. This week Team B will conduct regression analysis to determine if there is a correlation between the distance of the home from the town center and the price of the home. The regression analysis will indicate the Regression Analysis on Real Estate Data Set – Team B RES 342 Week 5 Page 3 impact on the price that the variable distance accounts for in the dependent variable, pricing. The testing will begin with a line test to determine if there is a linear relationship between the variables, test the variables for significance, perform a regression analysis and provide a business case analysis of the data. The Line Test Hypothesis Statement The null hypothesis is that there is no linear relationship between the variables. The Alternate hypothesis is that there is a linear relationship between the variables. This project examines the relationship between two variables distance and price; therefore the problem is appropriate for the use of regression analysis. The first step in examining the data is to create a visual display – a scatter plot to determine if there appears to be an initial relationship between the variables. (Doane & Seward, 2007). Regression Analysis on Real Estate Data Set – Team B RES 342 Week 5 Page 4 The scatter plot reveals that there may be some linearity to the data however the correlation does appear weak. The scatter plot will provide the initial indication that a weak negative correlation exists between price and distance from the town center, however; the scatter plot does not allow the researcher to definitively quantify the strength of the relationship between the variables. The test statistic on the linear relationship and a sample correlation coefficient needs to be calculated. Decision rule If the probability value calculated is less than, 0.05, reject the H0. Test Statistic The calculated test statistic is 0.003. Decision The calculated test statistic is less than 0.05. therefore the null hypothesis is rejected. Variables test A variables test is conducted to determine if the variable distance from the town center is statistically significant. Hypothesis statement Regression Analysis on Real Estate Data Set – Team B RES 342 Week 5 Page 5 The null hypothesis, H0, is the variable distance from the town center is not statistically significant. The alternate hypothesis is that the variable distance from the town center is statistically significant. Decision rule If the probability value calculated is less than, 0.05 reject the null hypothesis. Test Statistic The test is 0. Decision The calculated test statistic 0 is less than .05. so the null hypothesis is rejected. Regression analysis Regression Analysis r² 0.120 n 105 r 0.347 k 1 Price Std. Error 44.392 Dep. Var. ANOVA table Source SS df MS F pvalue Regression 27,791.4863 1 27,791.4863 14.10 .0003 202,976.102 Residual 9 103 1,970.6418 230,767.589 Total 1 104 Regression output confidence interval Regression Analysis on Real Estate Data Set – Team B RES 342 Week 5 Page 6 p 95% 95% variables coefficients std. error t (df=103) value lower upper 1.38E Intercept 270.1670 13.7646 19.628 36 242.8681 297.4658 Distance 3.3540 0.8931 3.755 .0003 5.1253 1.5827 The null hypothesis that there is no relationship between price and distance from the town center has been rejected. The correlation coefficient r= .0347 show that there is a negative correlative relationship between price and distance from the town center, in other words, homes with less distance from the town center have been shown to have higher prices than towns with greater distance from the town center. The critical value for a left handed test of significance is t.05 1.6596. The t statistic for significance of the correlation is 3.755, which is less than the critical value of t.05 1.6596, therefore we conclude that the true correlation is negative. Conclusion Team B concludes that a significant correlation exist between prices of a homes when compared to the distance from the center of the city in miles. Based on this linear regression analysis of a sample of 105 previously sold homes Team B rejects the null hypothesis that no significant correlation exist between the prices of a house compared to the distance from the center of the city in miles. Team B does submit a caution that whereas the correlation is statistically significant, the practical application of this 2 information to use in pricing homes has to be moderated by the fact that the r calculated in the regression analysis is low, only 0.120, which indicates that only 12% of the change in price is explained by distance from the town center. The 88% of unexplained variance Regression Analysis on Real Estate Data Set – Team B RES 342 Week 5 Page 7 reflects other factors (e.g. size of home, number of bedrooms, number of bathrooms, presence or absence of a swimming pool, presence or absence of an attached garage, condition of the home, quality of the local schools, and other variables.) References Doane, D. P. & Seward, L. E. (2007). Applied statistics in business and economics. Boston, MA: McGrawHill Irwin. Retrieved March 12, 2011 from University of Phoenix, Resource, RES342—Business Research Methods II:
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