A regression coefficient for a fireplace comes out negative in a market where fireplaces are valued. What is the most likely explanation?
Correct Answer
B) The sample or model specification is inadequate
Why this is correct: A negative coefficient for a feature known to add value indicates a problem with the regression model, such as omitted variables, multicollinearity, or an unrepresentative sample. Why the other choices are wrong: 'Fireplaces genuinely reduce value in that market' contradicts the given fact that fireplaces are valued. 'The dependent variable was entered incorrectly' is possible but less likely than model specification issues. 'Negative coefficients are normal in this analysis' is false; they should align with market behavior. Exam tip: When regression contradicts market evidence, check the model first—sample size, variable selection, and data quality.
Why This Is the Correct Answer
Option B is correct because a sign that contradicts established market behavior points to inadequacy in the sample or the model specification. Omitted variables, multicollinearity, small or unrepresentative samples, and limited variation in the fireplace variable are the usual suspects, and each is a property of the analysis rather than of the market. The remedy is diagnostic: examine correlations among the independent variables, check the sample's size and homogeneity, add the omitted characteristic, or fall back on paired sales for that element. Reporting the negative coefficient as a market finding would produce a misleading conclusion.
Why the Other Options Are Wrong
Option A: Fireplaces genuinely reduce value in that market
This contradicts the premise the stem supplies, which states that fireplaces are valued in this market. A model result cannot overturn a stated market fact; where they conflict, the model is the thing to examine. It is also worth noting that a genuinely negative contribution would need independent market support, such as paired sales, before an appraiser could report it.
Option C: The dependent variable was entered incorrectly
Entering the dependent variable incorrectly, meaning the sale price, would corrupt the entire model rather than flip the sign on one coefficient. Every coefficient would be nonsensical, and basic diagnostics would reveal the problem immediately. A single implausible coefficient in an otherwise reasonable model points to specification issues around that variable, not to a mangled dependent variable.
Option D: Negative coefficients are normal in this analysis
Negative coefficients are perfectly normal for characteristics that genuinely detract, such as age, distance from an amenity, or backing to a busy road, but they are not normal for features the market pays for. Treating any sign as unremarkable abandons the appraiser's judgment in favor of whatever the software returns. Reasonableness testing of both sign and magnitude is a required part of using statistical output.
Wrong sign, check the model
When a coefficient's sign fights the market, the market wins the argument. A negative fireplace is a symptom; the disease is in the data or the specification.
How to use: Read the sign of any coefficient in a stem before the number. If the direction is implausible, choose the answer that questions the analysis rather than the one that rewrites market behavior.
Exam Tip
Distinguish a problem with the whole model from a problem with one variable. Errors in the dependent variable break everything; specification problems typically distort particular coefficients.
Common Mistakes to Avoid
- -Accepting counterintuitive output because the software produced it
- -Dropping a variable to fix a sign without diagnosing the cause
- -Ignoring multicollinearity among correlated property characteristics
- -Reporting coefficients without testing them for reasonableness against market knowledge
Concept Deep Dive
Analysis
This tests the interpretation of a regression result that contradicts known market behavior, and the discipline of trusting well-established market knowledge over a single model output. A coefficient carries a sign and a magnitude, and when the sign runs opposite to what the market plainly does, the model rather than the market is usually at fault. The common causes are omitted variable bias, where fireplaces correlate with some unmeasured characteristic such as older housing stock or smaller floor plans and the coefficient absorbs that effect; multicollinearity, where fireplaces travel with other variables in the model so the coefficients become unstable and can flip sign; a sample too small or too heterogeneous to isolate a modest contributor; and insufficient variation, where nearly every sale has a fireplace so there is little contrast to measure. The professional response is to diagnose and respecify the model, not to publish a counterintuitive result or to quietly discard the variable.
Background Knowledge
You need a working understanding of multiple regression in valuation: coefficients as estimated contributions holding other variables constant, and the common threats of omitted variable bias, multicollinearity, small samples, and limited variation. You also need to know that statistical output must be tested for reasonableness against market knowledge, and that the appraiser remains responsible for the credibility of results produced by any model.
Real-World Application
A regression on 300 sales returns a negative fireplace coefficient. Checking the data, you find fireplaces cluster in older homes and the model has no age or condition variable, so the fireplace term was absorbing an age penalty. Adding effective age flips the coefficient positive and brings it in line with your paired sales evidence.
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?
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In a market study, what does a frequency distribution of sale prices show?
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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:
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Paired sales analysis and regression differ mainly in that regression:
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