I apologize to my loyal subscribers who have recently tried (unsuccessfully) to comment on my blog postings through the AQA website. The website software company, A La Mode Software, has been working (unsuccessfully) on a fix for over a month now. Needless to say, I am getting impatient.
Last week’s blog, Statistics Work for Real Estate Appraisers, Even with Few Sales, did generate quite a bit of interest; consequently, I received many appraiser questions about it thru our email and social media links. Here are some great comments that I received along with my responses to them.
Question: Several people asked about how to make a simple regression chart using Excel and what the formula on the graph indicates.
Response: To make a simple regression chart, all you need to do is make a scatter chart of the data with the Y-axis being Reported Sales Price and X-axis being the variable that you want to solve for. In this example, we want to solve for a living area adjustment, but we could also solve for sales date, site size, or any variable that we think might have some linear relationship to sales price. Here is a video showing how a simple regression analysis can be added to an appraisal report in about one minute (the video takes longer because I’m talking).
Question: Edd asked, “I also use simple regression for many of the same reasons and in similar circumstances as you do. The problem I am concerned about is that statisticians (not appraisers) say small samples are not statistically significant. What if a sophisticated attorney were to ask on cross about the reliability of small sample or populations?”
Response: I would simply tell that attorney that we have to use what we have. Statisticians analyze data in crash testing of automobiles, but they do not use large samples for good reason. I don’t hear anyone saying that the small samples in crash testing are statistically insignificant. With that said, I do not solely rely on statistics and I always make sure that my sample sizes are large enough for a reasonable conclusion (little variation requires fewer sales than large variation). After I have developed an adjustment using statistics, I test the reasonableness using the cost approach (an adjustment of $20 per sf might not be reasonable for a like-new building that costs $150 per sf to build) and a test of paired sales when it is applied to the adjustment grid. If the adjustment is moving the adjusted indicators closer together than a higher or lower adjustment would (after other market derived adjustments have been applied), then the paired sales are validating the statistically derived adjustment. If not, then maybe we need to look at factors that might be skewing our sample.
Question: David asks, “What was your R-Square on this graph? Doesn’t look like it would be much more than 50-60% from the scatter graph. This could suggest that there are more variables at play in your data set than just size of the sales.”
Response: I do not know what the R-Squared is for the above data. It is not ideal. However, we have to work with what we have. R-Squared for regression are typically high when used in real estate, because as you point out, there are many variables. The thing to understand about the use of a simple regression in an appraisal is that we are not trying to solve for all of the variables in one simple regression analysis. A high R-Squared is not necessarily a bad thing in that context unless the outliers are clustered toward one end of the scatter chart, then they will be much more likely to change the slope of the trend, thereby skewing the adjustment.
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Thanks for reading,
If you are personally acquainted with me or merely follow my blog, you probably know that I am an appraiser who is a fan of using statistical regression to support adjustments and to analyze trends in the appraisal process. In fact, I recently made a video on the topic.
One comment often heard from other appraisers is that one needs large samples of data for statistical regression to work. This statement is only partially true. Large samples are required when there is great variation among the comparable sales or many outliers, as appraisers are familiar with when filling the 1004MC Market Conditions Addendum. However, if the sales are similar in most ways, the sample size may not need to be large. For example, I performed a regression analysis of land sales within a single development to determine the contributory value of each additional square foot of site size. Since all of the sales were very similar in terms of most factors (except for the size), only six sales were necessary to produce a strong estimate with near perfect linear correlation.
When working in rural areas or areas that have less comparable sales data, I actually use regression analysis more often than in urban areas. This is because when comparable sales are less than ideal, one needs to spend more time carefully supporting the adjustments to come to a credible opinion of value. On the other hand, if comparable sales are almost exactly like the subject, ranging little in sales price before adjustments, it is easy for appraisers to come to the most reasonable value opinion thru proper weighting in reconciliation, regardless of how large or small the individual adjustments are for each factor on each comparable sale. When comparable properties differ a great deal in terms of location, date of sale, site size, living space, or other factors, statistics can be used to better support these important quantifiable adjustments and to yield a more credible final opinion of value.
I recently appraised a rural manufactured home on 40 acres. There are few sales of similar properties, but I was able to take a sample of similar size and quality manufactured homes between one and two acres (there are lots of sales of these in the competitive market area) to support adjustments for the living area. In the absence of other data, I made a strong case that each additional square foot of living space on similar manufactured improvements with smaller sites is consistent with the adjustment for a property with 40 acres. Even if one could argue that the buyers of the 40-acre property would be willing to pay more or less per square foot of living space than the buyers of one and two-acre manufactured homes, analysis of the statistical data helps me have a starting point to make a more reasoned adjustment estimate.
For this same rural property, I also used statistical regression to support time adjustments (using market data from the entire competitive market area trended over time), site size adjustments (controlling my data by looking only at vacant land), and location adjustments (comparing samples of similar properties from different areas). The moral to the story is that appraisers should embrace statistics for help when little data exists, not pull away.
When I talk to my fellow real estate appraisers in Portland, OR, I’m surprised at just how few use statistical calculations in the appraisal process. With all of the online data and spreadsheet tools available today, refusal to use statistics in appraisals is like gauging public perception by polling three to six voters and ignoring hundreds or thousands of others. You may be able to get the right answer but, how sure can you be of it?
This week’s appraisal blog is a video that may help my Portland colleagues begin to use statistical tools. The video shows an example of how simple linear regression may be applied in calculating a living area adjustment. Once appraisers see how powerful statistical analysis is, I’m confident that they will want to learn more. Ultimately, the use of statistical analysis makes appraisals more precise and more easily defendable.
Working with statistics is just one way that A Quality Appraisal, LLC stays ahead of our Portland competition by producing more accurate appraisals.
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