An appraiser wants to support a garage adjustment using regression. What does the analysis require?
Correct Answer
A) Enough sales that vary in garage capacity
Why this is correct: Regression analysis estimates the marginal contribution of a property characteristic (like a garage) by analyzing how sale prices vary with changes in that characteristic across a dataset. To estimate a reliable coefficient, there must be sufficient sales where the characteristic varies (e.g., some homes have no garage, one-car, two-car garages). If all sales are identical for that feature, its effect cannot be measured. Why the other choices are wrong: "Sales that all share an identical garage size" would prevent regression from isolating the garage's value, as there is no variation to analyze. "A separate model built for each comparable" is not how regression works; a single model is built from all data. "That the subject property be excluded entirely" is incorrect; the subject's characteristics are input into the model to predict its value. Exam tip: For any statistical analysis, variation in the data is key. No variation in a feature means you cannot measure its impact on price.
Why This Is the Correct Answer
Option A states the necessary condition: the sample must include sales that differ in garage capacity, ideally with meaningful counts at each level such as none, one car, two cars, and three cars. Variation in the independent variable is what lets the model attribute a price difference to that feature rather than to something else. The appraiser then checks that the resulting coefficient is plausible, statistically meaningful, and consistent with other evidence such as paired sales before using it in the grid.
Why the Other Options Are Wrong
Option B: Sales that all share an identical garage size
Identical garage sizes would make the variable a constant, and a constant explains nothing about price differences. This is the exact condition that defeats the analysis, so the option describes the opposite of what is needed. Candidates fall for it by confusing the control requirement in paired sales, where everything else is held alike, with the variation requirement for the feature being measured.
Option C: A separate model built for each comparable
Regression builds one model from the whole data set and then applies it; it does not produce a separate equation for each comparable. Fitting a model per comparable would leave one observation per model and no ability to estimate anything. The option confuses a grid, which handles comparables one at a time, with a statistical model.
Option D: That the subject property be excluded entirely
The subject is not part of the sample of sales, since it has not sold, but its characteristics are the inputs used to predict its value or to select the applicable coefficients. Excluding the subject entirely would leave the analysis with no application. The distractor plays on a half-remembered rule that the subject is not a comparable.
No Variation, No Information
A model can only learn from differences. If every house in the sample has the same feature, the data are silent about what that feature is worth, no matter how many sales you gather.
How to use: For any statistics item asking what an analysis requires, check first whether the variable of interest actually varies in the data described. That single test answers most of these questions.
Exam Tip
Do not confuse paired sales with regression. Paired sales hold everything else constant and let one thing differ; regression needs many observations in which the thing of interest differs.
Common Mistakes to Avoid
- -Running a model on a sample with almost no variation in the feature of interest
- -Accepting a coefficient without checking sample size or plausibility
- -Ignoring correlation between garage capacity and house size when interpreting results
Concept Deep Dive
Analysis
Regression measures how price responds as a characteristic changes, so the analysis is only possible where that characteristic actually changes across the data set. A coefficient is an estimate of marginal contribution: hold everything else steady, add one more unit of the feature, and see what the price does. If every sale in the sample has the same garage capacity, the variable is constant, there is nothing for the model to observe, and no coefficient can be estimated. Beyond mere variation, reliable results need enough observations spread across the range of interest, along with attention to correlation among variables, since garage capacity often travels with house size and age.
Background Knowledge
You need the basic mechanics of regression: dependent and independent variables, coefficients as marginal contributions, and the need for adequate sample size and variation. You also need to know how a regression-derived adjustment is tested against other evidence before it is used.
Real-World Application
An appraiser wanting a garage adjustment pulls two years of neighborhood sales, finds only three homes without a two-car garage, concludes the sample cannot support a reliable coefficient, and derives the adjustment from matched pairs in a similar competing subdivision 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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