Mass Appraisal Techniques

Multiple Linear Regression(MRA) is used in Yakima County to value most Residential Properties.

The best way to describe MRA is that we are determining the linear relationship between a variable (for example: main floor size, age of structures, condition of structure, etc.) and sales price.  Some relationships are positive (more sqft = higher price), while others are negative (older home = lower price). The linear relationship determined with statistical software will give us a coefficient for each variable.  The multiplication of a coefficient and a variable is called a model term. Once we have determined the mathematically significant variables and coefficients we can add all the Model Terms for a given property together plus an intercept to get a final value for each property.

A simple version of a valuation model may be: Assessed Value = Intercept + Age*YearBuiltCoefficient + LivingArea*LivingAreaCoefficient + GarageArea*GarageAreaCoefficient + Many other Model Terms

Linear relationship of Main Floor Area, Upper Floor Area, Finished Basement, and Unfinished Basement vs Assessed Value
Sometimes, the relationship is not linear, and we perform a transformation.  A good example of this is parcel size. The closest relationship to the effect on values from the size of a property can be found when we take the Natural Log of the Parcel Size to see the coefficient.

Logarithmic Relationship of Land Size vs Assessed Value
Not all relationships are positive. A lower quality home for example would be assessed lower than a high quality home.  That is to say, an average buyer will pay more for a home of better quality.  It should be noted that this model term would be added to all the other residential ones, including the intercept to achieve a final value.  It should not be taken to state that a lower-quality home is worth nothing.

Linear relationships of Quality Ratings with Total Sqft and the effect on Assessed Value.  Because the base value per square foot is positive, some qualities take away from that value, while others are additive.  In other words, a Very Good Quality Home adds more per square foot than a Fair Quality home adds per square foot.

As stated, not all impacts on Assessed Value are positive.  Here is an example of Effective Age pulled straight from our statistical software. There appears to be no impact from Effective Ages 0 - 20 years and then the impact increases until the rate of change levels off after around 50 years.

This is a quick overview and I hope itis helpful. If you have any questions, I am happy to speak with others about our modeling.

Thank you!

Jacob Tate, Yakima County Assessor