Portland Area Real Estate Appraisal Discussion

Many in the profession know that I am a fan of statistics.  As a matter of routine, I have been using linear regression analysis in every appraisal for many years, either as primary or secondary support for at least one adjustment.  Lately, there has been plenty of talk in Portland, Oregon and elsewhere about using linear regression analysis in real estate appraisal to support adjustments.  In the process, it seems that a lot of misinformation about statistics and regression is also being circulated.  Consequently, I will attempt to set the record straight by discussing the proper use of R squared in real estate appraisal linear regression.

R squared, also known as the coefficient of determination, is a measure (between zero and one) of how well a regression line fits the data points.  An R squared of numerical one means that the model has perfect correlation and predicts every outcome.  Here is a table of data and a very simple regression example with perfect correlation.

In the above regression chart, it is easy to see that prices are increasing at $75 per square foot as indicated by the slope (75x in the regression formula).  The R squared value of one says that these sales fit the line perfectly.  An appraiser can also pair any of the sales in the above table and the result will also be exactly $75 per square foot.  The next chart and regression graph does not have perfect correlation due to large and small site sizes mixed in the data.  Remember that the large and small site sizes are just an example.  In reality, site size differences could represent any type of variation commonly found in sales of homes (e.g. condition, features, etc.).

In the above regression chart, I have introduced three new sales with large site sizes.  If an appraiser pairs the large site sales with the small site sales, the adjustment is $25,000.  If an appraiser pairs any of the sales for GLA, the answer will also be exactly $75 per square foot.  R squared is less than the numeral one, but the slope and the adjustment are still $75 per square foot.  This is because the data are no longer a perfect fit along the line, but the sales all still increase at $75 per square foot.  The next chart has a lower R squared value because the adjustment for site size is $45,000, rather than $25,000 and the adjustment per square foot remains the same.

 

In the above chart, the larger variation for sales price results in a smaller R squared value but the adjustment for square footage remains the same.  R squared is only a measure of how well the data points fit the line.  In real estate appraisal, the fit of R squared will usually be much less than ideal.  An R squared that is low does not mean that the adjustment provided by regression is less accurate or less valid.  An R squared that is low does not change the adjustment that the appraiser should apply for that factor being measured.  In the above examples, we are only solving for GLA and it does not matter that there are other factors of variation (in this case site size), as the other variables are evenly dispersed along the trend line.

The appraiser should not rely on R squared as an indicator of reliability in the regression adjustment.  The appraiser should examine the raw data or the scatter chart and look for factors that might be skewing the data or pushing the line in one direction or another.  Common factors that can skew a GLA regression line is sometimes larger homes also have larger sites or higher quality.  It is essential for the appraiser to carefully control the search parameters of sales data in ways that avoid skewing and collect large enough samples that normal variation of other factors can balance out and not skew the results.  Appraisers should ask themselves, “If I remove just one data point from this scatter chart, will the trend change dramatically?”  If the answer is yes, then maybe the regression model is too small.  In that case, a larger sample or a more controlled sample might be necessary.  I recommend leaving the R squared off the trend line chart and out of the appraisal report.  R squared values will only confuse the reader of the appraisal report and will not strengthen the appraiser’s argument for or against the regression results.  

The following is my most popular video on YouTube that gives an example of how to support a GLA adjustment using simple linear regression. 

Did I leave anything out or do you want to join in the conversation?  Let me know by commenting below.

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Thanks for reading,

Gary F. Kristensen

Many of my blog readers are looking for ways to easily include simple regression to their appraisal reports. Dynamo Appraiser contacted me today and let me know that they now have simple regression outputs included in their software that look very similar to the charts above. This could be a great tool for appraisers. Here is a link: http://www.dynamoappraiser.com/dynamo-mc-now-includes-gla-charts-and-reports/

Nice tutorial Gary. What would you recommend if the MLS does not have GLA or what they do have is not very reliable?

Thank you Tom for the comment and that is a great question for appraisers to hear. If your MLS does not have GLA or that figure is not reliable, then you would need to use another source for the GLA used in your regression analysis or use another approach to estimate the adjustment for GLA. If the GLA numbers are not reliable, simple linear regression might be useful for other factors like using vacant land sales to estimate the contributory value of site size or extracting a market change adjustment (in that case the slope would be in dollars per day).

Very good! Thanks.

Thank you for your support John. I appreciate it.

What tyoe of info & regression graphs are you using for the following, Total Bsmt Sq Ft adjustments vs subject, Total finished basement Sq FT adjustment, Also what regression charts & inof do yuo need to find out what full bath & half baths are and how much of an adjustment for the Q & C rating differences. I think I have the GLA regression chart learned but these other have me stumped as Im using Excel 2013

Thank you Jon for your comment. That is a great question that many people have been asking me. Regression analysis is just one tool that appraisers have to help support adjustments. It does not always work and it does not work for all factors. Only those factors that can be controlled and are linear. However, when the search parameters are carefully controlled, regression works well in my market for using vacant land sales to estimate a site size adjustment, GLA adjustments, and time adjustments (if the trend is linear and not up and down). Linear regression can be troublesome for basement adjustments because properties with larger basements tend to have larger GLA and the results will get skewed. I have come up with a few advanced tricks to help control for basements. That might be a good topic for a future blog, but there is so much to say I might need to write a book.

Great info Gary! I am still learning regression and have read a couple of your posts on this topic that have been extremely helpful. You are clearly one of the most knowledgeable Portland appraisers and are at the cutting edge of appraisal techniques.

Thank you for your kind comments Paul. I appreciate that. Linear regression is a great tool and I'm afraid that too many real estate appraisers write off.

Great information Gary. Gathering a large enough sample size that is the result of well thought out search parameters is important for a more accurate regression.

Thank you Lucas for your comment. You're absolutely correct. A key to regression analysis is proper controlling and filtering of data.

Indeed when one data point exerts a significant power over the trendline results one possible interrogation is that the sample is too small. Another equally valid interpretation is that the data point itself represents an atypical property and therefore it should be removed. Culling data, even after a carefully crafted pull, is often a legitimate and responsible necessity.

Michael, thank you for the comment on my appraiser blog. I agree, that one option is to remove the outlier. Often, outliers can teach us a lot about the sample. Sometimes it is the outlier itself that is the only property that is actually like the subject and the outlier is telling us the model is not representative of the subject. The best way to remove outliers is to research them first, determine why they are an outlier, and remove if necessary and when there is a logical reason to do so.

Hi Gary, I am trying to figure out how to apply the final formula. In your case of regression with a large data set and a scattered chart. The final formula... how to apply that to the report as an adjustment for all comps. Thanks, Aletha

Aletha, thank you for the question. The adjustment from regression can be found in the formula after the "Y=" and before the "x". In the three yellow shaded graphs above, the adjustment is always $75 per square foot. I hope that helps.

please send any other information that you might have to help me explain to someone how regression works in comp selection and how significant it is thank you tom

Hi Tom, It sounds like you must be getting pushback from a client regarding use of regression in an appraisal report. My answer would depend on the audience. However, I would first point out that regression is not a method for selecting comparable sales. Regression is a tool to analyze trends or patterns in data. It is up to the appraiser to select and filter the sales data. The level of significance of regression is related to the quantity and quality of the data. If your client is skeptical of use of regression in appraisal process in general, then point them to any of the many peer reviewed studies that use regression analysis or one of the many books on regression analysis like the Appraisal Institute’s, A Guide to Appraisal Valuation Modeling by Linne, Kane, and Dell. I hope that helps, Gary