One observation in a regression has a very large residual. What should the appraiser do?
Correct Answer
D) Investigate that sale before deciding anything
Why this is correct: A large residual (the difference between the actual sale price and the model's predicted price) is a red flag that warrants investigation. The cause could be a data error, a non-arm's length transaction, or an omitted property characteristic. The appropriate action depends on the finding. Why the other choices are wrong: Deleting it without investigation could improperly bias the model. Simply accepting it without inquiry ignores a potential problem with the data or model specification. Refitting with more variables might help, but should be done after understanding the cause of the outlier. Exam tip: Investigate outliers first. Don't delete data simply to improve model fit statistics.
Why This Is the Correct Answer
A large residual may indicate a non-representative sale, a data error, or a characteristic the model omits, and only investigation distinguishes among them.
Why the Other Options Are Wrong
Option A: Delete it so the model fits the remaining data
Deleting an observation to improve fit discards the evidence that would explain the discrepancy and biases the model.
Option B: Accept it, since every model has some error
Accepting it without inquiry misses a likely data error or an omitted variable the residual is pointing to.
Option C: Refit the model with more variables included
Adding variables before understanding the cause is guessing, and may fit noise rather than a real relationship.
A Big Residual Is a Question
A Big Residual Is a Question, not a nuisance. The model is telling you it does not understand that sale.
How to use: Verify the sale's terms and data first, then ask whether a missing variable explains it.
Exam Tip
Where exclusion is justified, document the reason. An undocumented deletion looks like fitting the data to a conclusion.
Common Mistakes to Avoid
- -Deleting outliers to improve model fit
- -Excluding without documenting the reason
- -Adding variables before diagnosing the cause
Concept Deep Dive
Analysis
A large residual means the model predicted a price far from what the property actually sold for, and that gap is information rather than noise to be tidied away. There are several possible explanations and they lead to different actions. The sale may be non-arm's-length, distressed or otherwise unrepresentative, in which case exclusion is proper once the reason is documented. The data may be wrong — square footage misrecorded, a feature omitted, a price including personal property. Or the property may have a genuine characteristic the model does not capture, such as a view, an easement or an unusual condition, which points at a specification improvement rather than a deletion. Investigation distinguishes these. Deleting the observation to improve fit is the one clearly wrong response: it makes the model look better while discarding the evidence that would have explained why it was wrong. Accepting it without inquiry misses a likely data error, and adding variables before understanding the problem is guessing.
Background Knowledge
Large regression residuals may indicate non-representative transactions, data errors or omitted variables. Investigation determines whether exclusion, correction or respecification is appropriate, and exclusions must be documented.
Real-World Application
An appraiser investigating an outlier residual finds the sale included a $40,000 boat dock omitted from the data, adds the variable, and the residual resolves.
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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