Multiple Regression

Multiple Regression Analysis is a statistical technique used to analyze data in order to predict the value of one variable (i.e. market value) based on known values of other different variables (ie square footage). A mathematical equation (a model) is established that describes how variables are related. Essentially, the equation “models” the buyer decision making process.

Why Use Multiple Regression Analysis?

Colorado State Statutes require all county assessors to value residential real property solely by the market approach.

Colorado State Statute 39-1-103(5)(a)…The actual value of residential real property shall be determined solely by consideration of the market approach to appraisal… Colorado State Statute 39-1-108(8)(a) …Use of the market approach shall require a representative body of sales, including sales by a lender or government, sufficient to set a pattern, and appraisals shall reflect due consideration of the degree of comparability of sales; including the extent of similarities and dissimilarities among properties that are compared for assessment purposes.

As indicated by Statute, the only requirement for residential valuation is by the market approach. There are no specifics regarding the methodology. There are several market analysis methods used to estimate value contribution for characteristics: Paired Sales, Market-adjusted Cost Approach and Multiple Regression Analysis.

Paired Sales is the primary method of single-property appraisal. This methodology measures one property sale against a similar property sale to determine a specific adjustment for specific amenities. An example would be two ranch style home sales. Both have the same square footage and age, but one has a garage and the other does not. This method is generally impractical in mass appraisal because of the quantity of sales to individually analyze for each attribute adjustment.

Market-Adjusted Cost Approach relies on the premise that a certain quality of property has a base value of X dollars per square foot, with added factors for every additional amenity. A final market adjustment is applied to each neighborhood, positive or negative, to bring the neighborhood to “market value”. The fundamental weakness with this process is that the Cost Approach does not reflect the supply and demand relationship in the market place because the market adjustment factor is applied to every amenity, whether or not the market reflects it.

Multiple Regression explores and quantifies the relationship between two or more components of known and available data (sale prices and property characteristics) to predict a market value. In essence, this methodology uses aspects of the paired sales approach by determining which property characteristics are the primary contributors to value and the amount they contribute. Multiple Regression Analysis (MRA) is efficient because it starts with any number of sales prices and develops adjustments for characteristics found to be important in the market. Greater accuracy can be gained because it adjusts appropriately for market preferences and trends. Adjustments can then be applied with consistency and fairness. Because it is based on recent sales, MRA reflects the local real estate market.

For mass appraisal, the unknown data are market values. The known data are sales prices and property characteristics. Regression ESTIMATES the value contribution for each characteristic using a “goodness of fit” or error minimizing technique. The statistical confidence measures that are generated by MRA are not available with any other valuation technique.

Steps to develop a Multiple Regression Model

  • Define the sales sample
  • Select the appropriate property characteristics
  • Code the property characteristics
  • Create the model
  • Analyze and calibrate the regression model
  • Verify the regression model

In Douglas County’s valuation process, computerized statistical techniques are used to analyze single-family sales over eight economic areas. The economic areas are further divided into neighborhoods to account for location differences in the market. For each economic area, a Multiple Regression Analysis model is built that shows how sale prices are influenced by neighborhood (location), lot size, building square feet, construction quality, and other key features that affect property values. Sales used in the analysis have been screened to eliminate other than valid, open market transfers and adjusted to remove the value of any personal property included in the sale. Per Colorado Statute, all sales are adjusted for time to reflect the base assessment date.

The model developed for each economic area determines the contributory value of the residential characteristics that are found to be statistically significant. Residential values are then calculated based on the contribution associated with size, construction quality, age, garages, basements, and so forth.

The contributory values and adjustments are applied equally to all properties in a neighborhood. Thus, two homes of the same description and location will always have the same value. Values have been tested and analyzed to ensure that they are consistent and equitable among size groups, age groups, and so forth. The overriding objective of the Douglas County Assessor is to assign similar values to similar homes and properly reflect market differences among properties.

Using Time Trending and Multiple Regression Analysis

Residential properties, by law, must be valued solely by the market approach, using comparable verified sales from the 18 month study period ending the June 30th prior to January of the reappraisal year. Assessor’s may go back in time in six month increments for their study period data. In Douglas County, we use a 24 month study period to eliminate seasonal differences that may affect the market in an 18 month period.

These same statutes require the adjustment of sales prices within this study period to the end of the data period. Sales of residential homes taking place during the 24 month period are analyzed to establish the residential time trend adjustments. Since the law requires that sales prices be adjusted for time to the end of the study period on the June 30 appraisal date, it’s as if all homes that sold during the study period were sold on the June 30 end date and the time adjusted sales prices (TASP) reflect market conditions on that date.

Time Trend Adjustments are applied using this formula:

Number of Months from Date of Sale to end of study period x Appreciation Per Month x Original Sale Price = Amount of Adjustment + Original Sale Price = Time Adjusted Sale Price.

Example for Home Sold January 2012 for $400,000:

                5                         (Five months to June 2012)

x .01                      (calculated trend %)

                           = .05                    (Total appreciation since sale date)

 x 400,000           (Original sales price)

20,000                  (adjustment)

    + $400,000                    (Original sales price)

= $420,000            Sale Price as of June 30, 2012 (Time Adjusted Sale Price)