One observation in a regression has a very large residual. What should the appraiser do?
Correct Answer
D) Investigate that sale before deciding anything
A large residual flags an observation poorly fitted by the model. Investigate the sale facts, relevant characteristics, model specification and influence or leverage before deciding treatment. An observation may be genuine and important rather than erroneous. Automatic deletion, unexamined acceptance or adding predictors solely to fit it is not justified. A large raw price and a large conditional residual are different concepts.
Why This Is the Correct Answer
Option D is correct because a large residual only shows that the model fits that observation poorly. Investigating the sale facts, property characteristics, model specification and the observation's influence reveals whether the sale contains an error, was a non-market transaction, or is a genuine and informative data point. Treatment should follow from those findings.
Why the Other Options Are Wrong
Option A: Delete it so the model fits the remaining data
Option A says to delete the observation so the model fits the remaining data. Deleting a sale only to improve fit can discard genuine market evidence and bias the model; the observation should be examined first.
Option B: Accept it, since each model has some error
Option B says to accept it because each model has some error. A very large residual is a reason for scrutiny, and accepting it without review could leave a data error or non-market sale distorting the results.
Option C: Refit the model with more variables included
Option C says to refit the model with more variables included. Adding predictors just to fit one observation, before understanding why it differs, risks an overfitted model and does not address whether the sale data are correct.
Investigate before you eliminate
When a point sits far from the line, ask why before you act: check the facts, the property and the model.
How to use: Use this when a question asks what to do with an outlier or a large residual.
Exam Tip
For outlier questions, the best answer usually involves investigating the sale before choosing a treatment. Be cautious of choices that delete or accept the data without review.
Common Mistakes to Avoid
- -Deleting an outlier purely to improve model fit
- -Ignoring a large residual as ordinary error
- -Confusing a high sale price with a large residual
Concept Deep Dive
Analysis
This question tests how to treat an observation that a regression model fits poorly. A large residual is a signal for scrutiny, not a verdict. The appraiser should find out why the sale differs before deciding whether to correct, keep or exclude it.
Background Knowledge
A residual is the difference between an observed value and the value the model predicts. The preferred handling of an outlier is additional scrutiny to determine whether the sale is a non-market transaction or contains an error in fact. A large raw sale price and a large residual are different things: the residual is measured relative to the model's prediction.
Real-World Application
In a regression of neighborhood sales, one home sold far below its predicted price. The appraiser calls the listing agent and learns the house needed a new foundation, a condition the model did not capture, which guides how that sale is treated.
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Previous Question
Assessment-to-sale ratios are 0.85, 0.92, 1, 1.08, 1.15; corresponding sale prices are $500,000, $400,000, $300,000, $200,000, $100,000 in the same order. Compute PRD as the arithmetic mean ratio divided by the sale-price-weighted mean ratio. Round to two decimals.
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