A model built on condominium sales is applied to a detached house. What is wrong?
Correct Answer
A) The model was fitted to a different property type
Why this is correct: A regression model's coefficients are derived from and specific to the population of data used to create it. Applying a model built on condominium sales to a detached house constitutes applying it to a different property type (a different population), which is invalid because the market behaviors and value drivers are not the same. Why the other choices are wrong: While detached houses might require a different sample size, that is not the core issue here. R-squared can be computed, but it would be meaningless. The intercept is part of the model and is not recalculated for each subject. Exam tip: A regression model is only valid for the population from which the sample was drawn. Don't apply it to different property types or markets.
Why This Is the Correct Answer
The model was fitted to a different property type, so its coefficients describe a market the subject does not belong to. That is the fundamental validity problem, and it holds no matter how large the sample or how high the fit statistics. A model's inferences extend only to the population from which its sample was drawn. The correct remedy is to fit a model on detached house sales in the subject's market or to use a different technique entirely.
Why the Other Options Are Wrong
Option B: Detached houses require a larger sample size
Sample size affects the precision of coefficient estimates and the model's statistical power, but no sample size can cure the problem of estimating from the wrong population. A condominium model built on ten thousand sales would still be a condominium model. The option names a real modeling consideration that is simply not the defect at issue.
Option C: R-squared cannot be computed for detached homes
R-squared is computable for any regression on any dataset; it measures the proportion of variance in the dependent variable explained by the model. The problem is not that the statistic cannot be produced but that a high value computed on condominium data says nothing about performance on detached houses. Confusing a fit statistic's availability with its relevance is the error.
Option D: The intercept must be recalculated for each subject
The intercept is an estimated parameter of the fitted model, not a per-subject input that gets recalculated. Re-estimating it for each subject would be meaningless, since a single observation cannot support estimation. This option describes a procedure that does not exist in regression practice.
Coefficients Carry a Passport
Every coefficient is stamped with the population it came from. Condominiums, one market. Detached houses, another. Taking a coefficient across that border is extrapolation, and extrapolation outside the fitted range is where models fail hardest.
How to use: When a question describes applying a model somewhere, ask what population it was fitted to and whether the subject belongs to it. If the subject is a different property type, market area, or price tier, the population mismatch is the answer.
Exam Tip
Fit statistics describe performance on the training data only. A high R-squared is never evidence that a model transfers to a different population.
Common Mistakes to Avoid
- -Applying a model outside the property type or market it was calibrated on
- -Reading a high R-squared as evidence of transferability
- -Failing to disclose the model's specification and data source in the report
Concept Deep Dive
Analysis
A regression model estimates coefficients that describe how price responded to each variable within the specific sample it was fitted to. Those coefficients are statements about one population, not universal constants. Condominium prices are driven by unit size, floor level, view, parking, building amenities, association dues, reserve adequacy, and owner-occupancy ratios that affect financing eligibility. Detached house prices are driven by lot size, gross living area, bedroom and bath counts, garage capacity, school assignment, and site characteristics. Several variables that matter enormously to one type are absent or meaningless in the other, and even shared variables such as square footage carry different coefficients because the buyer pools differ. Applying a condominium model to a detached house is therefore extrapolation outside the fitted population, which produces an estimate with no statistical support regardless of how strong the model's fit statistics looked on its own data.
Background Knowledge
You need the basics of regression: dependent and independent variables, coefficients as marginal effects estimated from a sample, and the principle that inference extends only to the sampled population. You should also know the Competency Rule's requirement that the appraiser have the knowledge and experience to apply a technique, and that any model must be tested for appropriateness in each assignment.
Real-World Application
An appraiser with a well-performing condominium model is asked to value a detached house two blocks away. She declines to apply the model, explains that its coefficients reflect floor level, dues, and amenity variables that have no analogue in the subject, and builds a conventional grid supported by paired sales instead.
More Statistics Questions
A set of comparable sales has a mean of $250,000 and a standard deviation of $20,000. What is the coefficient of variation?
A property sold for $400,000 and resold three years later for $463,050 with no physical change. What compound annual rate does this indicate?
A histogram of neighborhood sale prices shows two distinct peaks. What does this most likely mean?
What does it mean to validate a regression model?
In a market study, what does a frequency distribution of sale prices show?
An appraiser includes months elapsed since each sale as a variable in a price model. What is this intended to capture?
An appraiser presents a statistical analysis in a report. What must accompany it for the reader to weigh it?
An R-squared of 0.86 in a sales model indicates that:
Which measure would best summarize the most common lot size in a subdivision?
Paired sales analysis and regression differ mainly in that regression:
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