Term Paper on "Statistics Regression"

Term Paper 7 pages (2045 words) Sources: 1 Style: APA

[EXCERPT] . . . .

Statistical Analysis and Forecasting of Housing Prices

The property chosen for predicting its selling price using statistical analysis techniques including multiple regression, correlation analysis, and factor analysis is shown to the right. The property is located at 2834 N. Danbury Street in Orange, California.

The home has 4 bedrooms and 3 baths, and is located on a cul-de-sec street, which is ideal for children. The home is 2,240 square feet on a lot of 7,000 square feet, and was built in 1995. The most recent owners completely re-vamped the kitchen and downstairs floors, investing well over $40,000 in both projects. The downstairs bedroom has been converted to a home office and the upstairs master bedroom, custom children's bedroom and third bedroom are ideal for a young family. Appendix A provides several pictures of the living room, family room, kitchen, downstairs office, and upstairs bedrooms. This home is located in one of the best school districts in Orange County, and is accessible from major freeways that provide fast access to many Southern California cities including Los Angeles. Property taxes in the area average less than 7% of total assessed value of the home and property, and the homeowner's association dues are $55 per month - very reasonable for a community that has a homeowner's association and common landscaped areas.

Statistical Analysis and Modeling of Real Estate Pricing

Taking thirty homes recently sold (as of January 2007) from Zillow.com's database for the zip code 92867 yielded a pricing distribution shown to the left. Microsoft Excel was used for data analysis and SPSS Version 13 for Windows was used for graphing and further analysis of all data presented in this report. According to the analysis completed with SPSS Version 13, the mean price for a home in the 92867 zip code of Orange County, California is $871,716. The standard deviation is quite large at $297,550. Pricing behavior in this specific zip code of Orange County, California is erratic and widely distributed, and makes for a useful series of data for analysis due to its wide dispersion of values in a relatively small geographic area. Appendix 2 shows the sample data taken from Zillow.com.

As a first step in constructing a statistical model the correlation of each variable needs to be tested for statistical significance at both the 95% and 99% level of confidence, so that insights into their interrelationships can be used in constructing a prediction model. Table 1, Correlation Analysis of Factors in the 92867 Zip Code shows the statistical significance of each variable in a test of nonparametric correlations, testing for significance at the 95% and 99% levels of confidence.

Table 1: Correlation Analysis of Factors in the 92867 Zip Code

Price

Bedrooms

Size (sq ft)

Per Sq. Foot

Baths

Kendall's tau_b Price Correlation Coefficient 1.000.257(*).747(**) -.364(**).533(**) Sig. (1-tailed)..040.000.002.000 N. 30-30 30-30-30 Bedrooms Correlation Coefficient.257(*) 1.000.402(**) -.463(**).689(**) Sig. (1-tailed).040..003.001.000 N. 30-30 30-30-30 Size (sq ft) Correlation Coefficient.747(**).402(**) 1.000 -.618(**).602(**) Sig. (1-tailed).000.003..000.000 N. 30-30 30-30-30 Per Sq. Foot Correlation Coefficient -.364(**) -.463(**) -.618(**) 1.000 -.424(**) Sig. (1-tailed).002.001.000..001 N. 30-30 30-30-30 Baths Correlation Coefficient.533(**).689(**).602(**) -.424(**) 1.000 Sig. (1-tailed).000.000.000.001. N 30-30 30-30-30 Spearman's rho Price Correlation Coefficient 1.000.310(*).890(**) -.465(**).614(**) Sig. (1-tailed)..048.000.005.000 N. 30-30 30-30-30 Bedrooms Correlation Coefficient.310(*) 1.000.488(**) -.575(**).742(**) Sig. (1-tailed).048..003.000.000 N. 30-30 30-30-30 Size (sq ft) Correlation Coefficient.890(**).488(**) 1.000 -.782(**).705(**) Sig. (1-tailed).000.003..000.000 N. 30-30 30-30-30 Per Sq. Foot Correlation Coefficient -.465(**) -.575(**) -.782(**) 1.000 -.537(**) Sig. (1-tailed).005.000.000..001 N. 30-30 30-30-30 Baths Correlation Coefficient.614(**).742(**).705(**) -.537(**) 1.000 Sig. (1-tailed).000.000.000.001. N 30-30 30-30-30 * Correlation is significant at the 0.05 level (1-tailed).

Correlation is significant at the 0.01 level (1-tailed).

Descriptive Statistics

Mean

Std. Deviation

Price

Bedrooms

Baths

Size (sq ft)

Per Sq. Foot

What immediately becomes apparent from the initial analysis of all variables is that selling price is negatively correlated to selling price, a sure sign that the market is over-valued and there is a significant statistical difference between the price per square foot for the lower-priced vs. higher-end, more expensive homes in the same zip code.

Nowhere else in the definition of this model is the dispersion of values more pronounced that in the price per square foot differences by price point, which is shown in the graphic to the left. Notice the same price per square foot for $1M+ homes and those homes selling for less than $650K. This wide variation in price per square foot signals the market is ripe for a market correction, driven primarily by more discerning buyers forcing a tighter band of per square foot pricing relative to total home price.

Comparing Price vs. price per-square-foot

In the 92867 Zip Code

In constructing the forecast two models for completing stepwise regression the following table is first defined in SPSS:

Variables Entered/Removed (a)

Model

Variables Entered

Variables Removed

Method

Size (sq ft)

Stepwise (Criteria: Probability-of-F-to-enter <=.050, Probability-of-F-to-remove >=.100).

Per Sq. Foot

Stepwise (Criteria: Probability-of-F-to-enter <=.050, Probability-of-F-to-remove >=.100).

Dependent Variable: Price

Next, the model is constructed using stepwise regression with the inclusion of price per square foot in the second model. The result is a significant jump in R2 to.971 from.808, showing a significant increase in the variability in prices being defined, and further illustrated through ANOVA analysis.

Model

Square

Adjusted R. Square

Std. Error of the Estimate

Change Statistics

Square Change F. Change df1 df2 Sig. F Change 1.899(a).808.801 $132,648.33129.808-117.921 1-28.000 2.985(b).971.969 $52,666.85147.163-150.618 1-27.000 a Predictors: (Constant), Size (sq ft)

Predictors: (Constant), Size (sq ft), Per Sq. Foot

Dependent Variable: Price

ANOVA

Model Sum of Squares df Mean Square F. Sig. 1 Regression 2074882037756.179 1 2074882037756.179-117.921.000(a) Residual 492676234213.189 28 17595579793.329 Total 2567558271969.367 29 2 Regression 2492665746378.783 2 1246332873189.392-449.324.000(b) Residual 74892525590.585 27 2773797244.096 Total 2567558271969.367 29 a Predictors: (Constant), Size (sq ft)

Predictors: (Constant), Size (sq ft), Per Sq. Foot

Dependent Variable: Price

Presentation to Seller

Using the model as defined (Model 2) from the above set, the selling price for 2834 N. Danbury Street at its size of 2,240 square feet yields a variation in forecasted price depending on the forecasting methodology used. The highest price is delivered though simple exponential smoothing using the variables price per square foot and total square footage to yield selling price of $855,680. The most stringent of forecasting approaches yields a significantly lower price per square foot of $304, resulting in a price of $680,960. The wide variation in sales price of $174,720 is explained by the smoothing completed. SPSS Version 13 is useful for also defining and comparing variations in forecasts based on a comparison of forecasting methods. The table below comparing forecasting methods by price and size of home by square foot is shown below.

Given the statistical significance of both $304 and $382 price per square foot, there is considerable risk in pricing the home at the higher end of the market, as the higher the price of the home, the greater the tendency to have a lower per square footage price.

For the seller of the home then there are several key points to keep in mind:

Pricing at the median of the two prices per square foot of this analysis ($304 and $382 per square foot) is the best would be in the $340 to $350 range to fall more in line with where pricing is headed in the market. To exceed $382 is to send a message in the market that the home has exceptional value, and in the buyers' preferences in Orange County, this would signal either a view lot or one with a large, private backyard. As the home has neither of these features, the pricing per square foot needs to stay in the median levels.

There is also uncertainty about just how far the correction in price-per-square foot will occur and how quickly in the early months of 2007. While the broader economic climate of Sothern California is quite strong, the comps in the area and the focus on stabilizing prices per square feet. The fact that the cul-de-sac the property is located on is ideal for young families with children still does not make a higher price validated in the minds of potential purchasers.

Upgrades and enhancements aren't nearly as important as the ability of the new purchasers to quickly customize the home and also get an allowance for carpeting if they choose. The fact that the home today has hardwood floors is potentially a drawback for families with young children whose toys, bicycles and bouncers will be amplified on this type of floor.

Zillow Pricing Analysis

Looking at the services that Zillow.com offers in terms of a pricing service, their price point of $849,716 assumes a $379 price per square foot, which is well within the range of the analysis, completed showing $304 to $382 being the optimum price per square foot given statistical analysis of 30 different properties in the area.

Zillow.com clearly has an inherent interest In making sure every home referenced on their site sells at the higher end of the pricing spectrum so that potential homeowners will use it as a point of reference in deciding whether to… READ MORE

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