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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