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Multiple regression works very well under some conditions.  We ask:  Are these conditions true in most real property valuations?

This is actually a vast topic, so we can only reflect on some of the conditions or assumptions which are required for a multiple regression to be valid.

Much (if not all) “advanced” appraiser education makes some sweeping or hidden assumptions about the underlying data.  We start with the most common “statistical errors and mistakes.”

Regression math is a completely separate model from the inferential probability model.  Yet current “advanced” appraiser education assumes somehow that the regression model always magically rests on a random sampling model.  (Gotta show off those clever statistical tests!)

There is a major problem here.

First, the population to be studied is not the census tract, or the zip code, or the neighborhood, or the whole town.  It is certainly not all the houses, or properties in an area.  It is just the sales.  Sales of similar properties.  (Some have argued that we can pretend that all the houses in the neighborhood sold, and that ‘picking comps’ is somehow a random experiment.) Right!

Second, seldom do we have the dozens of similar/competitive/recent sales required for a statistically significant sample in order to approximate multiple regression coefficients.  Sold transactions are our ‘population’, not all the houses.  My house is not for sale.  Neither is the apple in my refrigerator.  Neither is part of the supply.  I’m gonna eat the apple, and live in my house.

Thirdly, and laughingly simple.  Given today’s instant, complete (or substantially complete) data and computer power . . .  there is absolutely no reason to not analyze the whole data set.  No reason.  Using full set of similar competitive sales provides better accuracy, reduced variation, and clearer communication of the market situation.

Multiple regression coefficients provide a marginal result.  This means that at a given number (let’s say the subject square feet), all other predictors are not at their fixed point, but also vary in their own different ways.  Unfortunately, this does not coincide with appraiser thinking and “appraiser adjustment tables” shown as “reasonable” adjustment amounts.  In marginal models, some coefficients, at their margin, may be even negative, and different from ‘rule of thumb’ appraiser adjustments.  (This difference is due to correlation “multicollinearity” as between predictor variables, like living area, bedrooms, site size, baths, . . .)

Appraiser adjustments tend to be conditional.  This means you pretend you hold all other variables constant.  This is a fiction.  In reality, appraiser mental analysis is somewhere like a combination of both conditional and marginal thinking.  To my knowledge, ‘conditional’ versus ‘marginal’ has never been clearly defined in the appraisal literature.  (It’s a clumsy topic to address.)

Worse yet, there are a pile of other assumptions under the math of regression.  One of these is that you did not leave out any functional variables.  Another is that categorical or ordinal variables have been properly transformed to a numerical (interval or ratio) variable prior to input.  But wait, there are other assumptions:  homoscedasticity, normality, no serial correlation, and linearity.  Seldom or never are these assumptions true for real estate market segments.  Real estate market data is heteroskedastic, skewed, autocorrelated, and nonlinear.  Darn.

Ban Multiple Regression!