#### What is Regression Analysis?

Regression analysis is defined as a method that examines the relationship between one or more independent variables and a dependent variable by plotting points on a graph and through statistical analysis; used to identify and weight analytical factors and to make forecasts. (Dictionary of Real Estate Appraisal,4th Edition)

Regression analysis is used by many different professions to determine the impact different variables may or may not have on a dependent variable. For instance, some companies will use regression analysis to determine if the number of days it rains impact sales. Any business that has access to data and can study different variables to see of there is an impact. This analysis, if performed correctly, can be very useful for businesses.

#### Why Do Appraisers Use it?

Regression analysis is one tool or method that real estate appraisers use in or to determine value adjustments. When appraisers use regression analysis they will compare the sale price (dependent variable) to many independent variables. Appraisers can use statistical data and analyze it.

A part of the appraisal process is to determine value adjustments. Appraisers will find sales of properties that are similar to the property they are appraising. They will then make adjustments for differences in those properties to determine the value of the property. For example, an appraiser is appraising a single family residence that is 2,100 sq ft , 3 bedrooms, 2 bathrooms with a 2 car garage located in Smith Valley Subdivision. The appraiser finds three sales also located in Smith Valley Subdivision that sold within the past three months. This is a very simplified example but you can see there are differences between the size, bedroom counts, bathroom counts and garage size.

As a part of the appraisal process, the appraiser will use different methods to determine the amount to adjust for different features or variables. One of the most common ways to determine value adjustments is the use of paired sales, where the appraiser will pair a sale that is similar to another sale with only one difference or variable. The difference in sale price will determine the amount that was attributed to the feature. Example: Two matched sales are both 2,500 sq ft, have 3 bedrooms and 2 Car Garages but one has 3 bathrooms and the other has only 2 bathrooms. The sale with 3 bathrooms sold for $5,000 more thus the value attributed to bathrooms is $5,000 per bath. I will say that in the real world, rarely do you have two sales that match up in every aspect but one. Thus, regression analysis is another method that can be used by appraisers to help determine value adjustments. Since FNMA's implementation of Collateral Underwriter (CU), more appraisers have begun to use regression as more and more appraisers are having to show how they arrived at their value adjustments.

#### How Do Appraisers Use it?

If you have enough data, regression analysis can be used to see the relationship of several different variables in relationship to the sale price. When looking at a large number of sales within a neighborhood certain variables can be determined by using a regression analysis. Here is a look at a regression for a property in a subdivision.

In this regression, we looked at a large number of sales within the subdivision. There is a slope of $47 per square foot, meaning for every increase in the size of square feet the price increase $47.

Here is a look at the same data but comparing it to site area or lot size.

As you can see, there is a much less difference in site area, in this subdivision, most sites were less than one-half acre. There is not much evidence for any adjustments to be made for differences in lot size based on this data.

Both of the above examples came from using ACI Analytics which are a part of our ACI software, which we use. We mostly use Statwing, for regression because there are more variables that we can single out and run a regression analysis on. Here is a look at the same data in Statwing:

As you can see the GLA price is similar at $44 per square feet but you can also see the difference in lots that are adjacent to greenbelt and how the sale price responds to pools. When you are working with Statwing, you can hover your mouse over the adjustment and it will actually give you a range.

What I personally like about Statwing is that you can work with the data and add different features to determine if there is any market reaction to them. Please note that the amounts in regression will not necessarily be the amount we will use. With the data from the regression, we will look at it and analyze it. We will also look at paired sales. We use this information ,along with our knowledge of the local markets ,to determine the adjustments.

We also use Statwing to show sale price trends when comparing median sale price over time as in the graph below.

A couple of final thoughts about regression analysis for appraising. Regression analysis is not a magic tool where you plug in numbers and get adjustments. There is a learning curve and training needed to feel confident in regression analysis. Sometimes the numbers just don't make sense. As in any analysis, the better the data, the better the analysis. If a property is located in a rural area, there will not be as much data available thus the regression will have less reliable or credible results. The data really must be analyzed and outliers removed prior to running the regression. So far in our experience, we have found that regression analysis is really reliable for gla adjustments but less reliable for things such as fireplaces or bathroom count adjustments.

There are many different regression tools now available to appraisers.We use Statwing because of the greater ability to single out different variables such as views, location, amenities like pools, guest quarters, barns, etc. We also use ACI Analytics because it is integrated into our current software and we like the graphics that it provides. We have no vested interest in either Statwing or ACI Analytic but are just sharing our experiences.

I hope this was helpful in explaining what regression analysis is and how appraisers use it.

If you are interested in Statwing you can click this link:

We both can save 10%. They do have a free trial and I recommend going through the tutorial video first.

As always, let us know if you have any questions or comments about real estate appraisals or appraising.