The traditional approach to valuing property can be more qualitative and rely on intuition rather than sound reasoning. However, linear regression analysis can provide a robust model that uses past transactions to better guide property valuations.

## What is the value of the property?

The comparative sales approach, which is the most common in residential property, uses recent sales to determine a property’s value. The “comps'” sales prices are adjusted to reflect the differences between the comparable property and the subject. If a similar property is equipped with an extra bathroom, the estimated value of that bathroom will be subtracted from the observed sale price.

The comparable sales method is less common in commercial real estate because it is more heterogeneous. The Income Approach is based on the concept that an asset’s intrinsic value is equal to its discounted cash flow.

The direct cap rate is similar to a present-value annuity. It uses the net operating income of a property divided by the caprate to determine a value. The cap rate includes an implied discount rate as well as a future growth rate for net operating income.

The discounted cash flow method estimates the terminal value by using a cap rate.

The final method is the Cost Approach. This technique estimates value by comparing the cost to build a replica and acquire an identical plot of land. The cost of the project will be depreciated according to the current obsolescence state of the property. The goal of the cost approach is to match the subject property as closely as possible. The cost approach is used less often than the other approaches.

Due to the choice of inputs, all traditional real estate appraisal methods are subjective. The choice of cap rates can have a major impact on the valuation of a property. For example, a cap rate increase of 4% (from 6% up to 10%) would decrease the value by 40%.

## Regression models in real estate valuation: Benefits

Regression models are a powerful tool for valuing real estate. Retail has adopted its use of site choice, but the real estate industry has, for the majority, overlooked its benefits. The regression analysis is especially useful for large data sets. Regression modeling is a great way to narrow down the search.

## Flexibility

Regression modeling has the greatest flexibility. It can be used independently or with other models.

As an output, the most direct way to do this is to use the existing sales data. Many local, state, and federal agencies provide free data that can be complemented with data provided by private providers.

Regression models can be used to predict inputs more accurately for traditional valuation methods. When analyzing a commercial mixed-use project, for example, a developer can build a model that predicts the rental rates of the residential component and another to predict sales per square feet for the retail space. These two models could be inputs into an income-based approach to valuation.

## Objective Approach

It is possible to value a business objectively by using sound statistical principles. This is one of the most effective ways to avoid Confirmation Bias. This occurs when people look for information that confirms or denies new knowledge. Many retailers were surprised when I built models to predict the sales of new stores. My models often included colocation with Walmart – their biggest competitor. Using existing biases to make decisions can result in missed opportunities or, worse, hidden disasters.

Here are some of the advantages of statistical evaluation:

You can use statistical analysis to evaluate the reliability of the model by analyzing the factors.

While scenario and sensitivity analyses can give you an idea about input changes in more traditional methods, it is more like making multiple predictions than giving you a greater idea of the accuracy of the initial forecast. When building a regression, you’ll know the range of possible outcomes based on levels of confidence.

Regression models have an inherent accuracy check. You can test the model against data that is not part of the sample to see if there are any biases.

## Staying Focused on Your Core Competencies

All traditional valuation methods carry a high risk of bias. It’s easy to get caught up in the selection bias when choosing comparable properties. In the income approach, there is a strong emphasis on predicting certain variables, such as the return rate. Many real estate investors may find it attractive to eliminate the need for such a prediction, which is why regression-based valuation can be a useful method.

## Regression Analysis: Potential Problems

It is a joke in itself how many marks are made that quote different percentages. Media headlines are almost daily announcing the results of new research studies, some of which contradict those published last year. In the world of soundbites, there isn’t time to talk about the rigor of the research methods.

The most common type of regression is linear regression. To consider a linear regression valid, certain assumptions must be adhered to. Violation of these assumptions can distort statistical tests that calculate the predictive power and overall model.

## Linear Regression Assumptions

The inputs (independent variable) should have a linear relationship with the output (dependent parameter). We could, for example, assume that the heated square footage of a house is linearly related to its value. Due to diminishing returns, we may discover that the relationship between heated square feet and the overall value of a home is not linear.

The independent variables shouldn’t be random. The observations of each independent variable are assumed to be fixed, and their measurement is not subject to error. If we use the number of apartments to model the value of an apartment building, we will find that all the buildings in the sample data have the same number of apartments.

The residuals of the model (i.e., The difference between the predicted and actual results of the model will equal zero, or to put it simply, the model that we use will be the best-fit line.

Models should be accurate in all observations of each independent variable. We wouldn’t use a model that was very accurate for homes under 1,500 sq. ft. but had a lot of errors for those over 3,000 sq. ft. This is called heteroscedasticity.