In an intercept regression used to estimate a garage-capacity coefficient, which is a necessary data condition, though not sufficient by itself for reliable adjustment support?
Correct Answer
A) Enough sales that vary in garage capacity
A predictor that is constant across all observations cannot have its separate effect estimated in a regression with an intercept. Variation in garage capacity is necessary. Reliable adjustment support also requires suitable data, control of other relevant differences, adequate sample information and model validation. Merely supplying the subject’s characteristics does not fix an unidentifiable coefficient, and separate models for each sale are not required.
Why This Is the Correct Answer
Option A is correct because a predictor that has the same value in every sale cannot have its separate effect estimated in a regression with an intercept; its influence is absorbed into the intercept. Sales must vary in garage capacity for a garage coefficient to be estimated. Reliable support still requires suitable data, control of other differences, adequate sample information and model validation.
Why the Other Options Are Wrong
Option B: Sales that all share an identical garage size
Option B, sales that all share an identical garage size, is the opposite of what is needed. If garage capacity never changes, the regression has no variation from which to estimate a garage coefficient.
Option C: A separate model built for each comparable
Option C, a separate model built for each comparable, is not required. A single regression uses the variation across many sales to estimate the coefficient.
Option D: That the subject property be excluded from the sample
Option D, excluding the subject property from the sample, does not create the variation needed to estimate the coefficient. Whether the subject is in or out does not fix a predictor that is constant across the sales.
No change, no coefficient
If a feature never changes in the data, the model cannot learn what changing it does.
How to use: Use this phrase to check whether a regression can estimate a given adjustment.
Exam Tip
Watch the wording necessary but not sufficient. Choose the answer that names a required data condition without claiming it guarantees a reliable adjustment.
Common Mistakes to Avoid
- -Using data in which the feature of interest never varies
- -Assuming variation alone makes the coefficient reliable
- -Believing separate models for each comparable are required
Concept Deep Dive
Analysis
This question tests a basic identification condition for regression coefficients. A regression can only estimate the separate effect of a variable if that variable actually changes across the sales. The question also stresses that this condition is necessary but not enough by itself to make the adjustment reliable.
Background Knowledge
Regression estimates how the response changes when a predictor changes, so each predictor must vary in the data. A constant predictor is perfectly collinear with the intercept and cannot be separately identified. Adequate market and property characteristic data are needed for reliable, defensible estimates.
Real-World Application
An appraiser tries to estimate a garage adjustment from sales in a tract where every house has a two-car garage. The regression cannot estimate the garage effect, so she expands the market area to include sales with one-car and three-car garages and then validates the result.
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