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Owner: hdoman78
Created: Feb 28, 2013
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Zestimate vs Sale Price Tucson, AZ-H.Domanski

The housing market can be a volatile place; multiple variable impact the sale price and final sale price.  Zillow has come up with a way to account for the market variability in their "Zestimate" price.  A direct application of Zestimate vs. Actual Sale Price for the period from January 23 to February 23, 2013 in Tucson, Arizona is shown in the statistical data.  With 13 sales for the aforementioned period, a few factors indicating a positive linear relationship emerge:

1.- The critical value  is .576 for the sample size of 13.  The sample correlation co-efficient is .896, which is greater than the critical value.

2.-The scatter plot has no discernable pattern when Zestimate residuals are plotted.

3.-When viewing the scatter plot and least squares regression line, there is a discernable pattern of positive correlation between the Zestimate and the Actual Sales Price. That is to say, for every \$1 of Zestimate value, the Actual Sales Price goes up .963.

4.-The co-efficient of determination is .802 which is close enough to one to indicate that the line of regression does a good job of explaining the variation of the response variable.

There is no need to interpret the y-intercept since the value of x (price) will never be zero.  Would that it were true!  A free home!

Upon assembly of the box plot however, there are extreme variables that emerge that indicate the case for linear relationship may not be so air-tight. Upon investigation of these two outliers, the following was found:

1.-The Zestimate that overstated a possible sales price (selling for \$70,000 when the Zestimate was \$106,477) was on a home in danger of a "short sale" and was marketed to be a sold quickly.

2.-The Zestimate that overstated a possible sales price (selling for \$120,000 when the Zestimate was \$176,706) was on a home also in danger of a "short sale".

These outliers would seem to indicate that the Zestimate is not a viable tool, when perhaps the reason for the unexplained variability is related to lurking variables such as a short sale when the house is sold far below market value.  Instead, it would be fair to say that a Zestimate for a house when all of the available variables (such as area values, other sales of comperable properties, condition of home) are taken into account is an accurate tool; keeping in mind that when people are put into the mix anything can happen.

Overall, a linear model does work for this set of values (and probably for any market for Zestimate vs. Actual Sales price) when the prices are tempered with knowledge of the circumstances surrounding the sale of the house (a standard sale vs a short sale).

Result 1: Simple Linear Regression for Zestimate vs Actual Sales Price   [Info]
Simple linear regression results:
Dependent Variable: Selling Price
Independent Variable: Zestimate
Selling Price = -2746.139 + 0.96284103 Zestimate
Sample size: 13
R (correlation coefficient) = 0.896
R-sq = 0.8028648
Estimate of error standard deviation: 21291.787

Parameter estimates:
 Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept -2746.139 16398.111 ≠ 0 11 -0.16746677 0.87 Slope 0.96284103 0.14385307 ≠ 0 11 6.6932254 <0.0001

Analysis of variance table for regression model:
 Source DF SS MS F-stat P-value Model 1 2.03093094E10 2.03093094E10 44.799267 <0.0001 Error 11 4.9867423E9 4.53340224E8 Total 12 2.52960522E10

Result 2: Scatter Plot Zestimate vs Actual Sale price   [Info]

Result 3: Boxplot Residuals for Zestimate   [Info]

Result 4: Scatter Plot Zestimate vs Residuals   [Info]

Data set 1. Zestimate 2013   [Info]