Regression

Regression Paper

What impacts the value of a home's selling price compared to the way taxes are assessed? Are taxes based on the square footage, lot size, or average income in the area? There are countless possible impacts to the value of a home that could exist for determining a home's selling price and taxes that may be assessed. For the purpose of deeply analyzing this question even further, the authors decided to use not only their own analysis of home sales as compared to square footage, but also a peer reviewed supporting article that may provide a different perspective into the effects of home selling prices and how these homes are taxed. This paper will attempt to analyze the hypothesis that the slope of the regression line is equal to zero. In order to prove this hypothesis statement to be true, a regression test will be performed to further analyze this topic further along with a 5 step hypothesis test.

Testing Results

To analyze this hypothesis statement to be true, a 5 step hypothesis test was performed. (Test 1 - Appendix B). The null hypothesis identified for analysis, is that the slope of the regression line is equal to zero. Therefore, the alternative hypothesis is that the slope of the regression line is not equal to zero. In order to validate this research, data was used from the real estate data set for analysis. Since a 95% confidence is expected in our data, the significance level used was a value where α is equal to .05. The real estate data set was used to compare the independent variable of price to the dependent variable of size in square feet.

However, to reject the null hypothesis, one more step is critical. A regression test is performed to determine whether or not, the null hypothesis will be rejected. (Appendix B - Table 1) Since it is especially important in regression analysis to determine the direct relationship between the variables of the home selling price, and the square footage of a home, a scatter plot is used to show this relationship. As displayed in the scatter plot, the slope starts at $125,000 and for every increase of $1000 an additional 2 square feet is also added. (Figure 1 - Appendix A)

Figure 1: Home sale price by square footage

Source: Lind, Marchal, and Wathen. (2008). Real Estate Data Set, Statistical Techniques in Business & Economics, 13th edition. New York, NY: McGraw-Hill, Retrieved February 11, 2008, from rEsource.

In this particular analysis the intercept is not valid because the data suggests that at zero square foot home would cost $1790.70. It was also determined that the coefficient of determination is 0.1337, and because this number is close to zero, the fit is relatively good. The null hypothesis will be rejected if the calculated value of t-value is greater than the critical value. From a t-table the value for a right, one-tail test with an α of .05 is 1.645. (Figure 2) The actual calculated value of t for H0 1.671 is which is greater than the critical t-value of 1.645. (Figure 2) Therefore, we will reject the null hypothesis in favor of the alternate. This would indicate that the slope of our regression line is not equal to zero and it has a positive slope.

Although the regression test was performed and full analysis was completed this is not without some limitations to the data. The real estate data itself was limiting because there was no reference to the year the data was gathered or the market where the homes were located in. Because home location and the year the data was gathered have impacts to the data this analysis may or may not be reflective of the full real estate market as a whole.

Comparing Analyses

As stated directly above, the authors identified that finding further research in a similar topic might help strengthen the previous hypothesis. Using peer-reviewed articles can provide a great support if a similar topic has already been researched. Following the data collection and conclusions of this article allows the authors to better identify the situation of their 5 step process. The article that the team decided to use was written by John F. Mcdonald, Are Property Taxes Capitalized in the Selling Price of Industrial Real Estate?, where he presented an empirical study to analyze certain trends in the real estate market in Chicago. By the end, the authors will tie all of the information together.

Article Analysis

The study presented in the article contributes to the topic by looking at the industrial real estate market near O'Hare Airport in metropolitan Chicago for 2001-2004. The study found that comparable properties located in suburban Cook County--the central county in the metropolitan area--sold at a 16.2% discount compared to the adjacent county (DuPage County) because of