Two correctly computed OLS models use the same sale observations and area units but different predictor specifications. They yield area coefficients of $62 and $91 per square foot. What does this illustrate?
Correct Answer
A) The estimated conditional area association can be sensitive to specification
With identical data, encoded units, deterministic fitting method and correct implementation, differing conditional area coefficients from differently specified models illustrate sensitivity to specification. Inspect controls, functional form, diagnostics and applicability. The discrepancy alone does not prove an arithmetic error, justify an unweighted average or rule out regression as a tool.
Why This Is the Correct Answer
Option A is correct because, with identical data, units and correct implementation, different conditional area coefficients from differently specified models illustrate sensitivity to specification. Each coefficient estimates the area association holding that model's other predictors constant, so changing the predictors can change the estimate. The appropriate response is to inspect controls, functional form, diagnostics and applicability.
Why the Other Options Are Wrong
Option B: At least one of the two regression calculations must contain an error
Option B claims at least one calculation must contain an error, but the stem says both models were correctly computed. Different predictor sets can legitimately produce different area coefficients of $62 and $91 per square foot.
Option C: Their unweighted average of $76.50 must be the correct adjustment for living area
Option C asserts the unweighted average of $76.50 must be the correct adjustment, but averaging two specification results has no inherent support. The appraiser should evaluate which specification is better supported rather than split the difference.
Option D: Regression cannot be used to support adjustments in appraisal
Option D says regression cannot support adjustments, which overreaches. Specification sensitivity calls for careful model evaluation, not abandoning regression as a tool.
Coefficients depend on company
A coefficient's value depends on which other variables share the model with it, so changing the company changes the estimate.
How to use: Use this when a question shows the same variable getting different coefficients in different models.
Exam Tip
When the stem says calculations are correct, reject answers that blame arithmetic errors and look for the one about model specification.
Common Mistakes to Avoid
- -Assuming different coefficients prove a calculation error
- -Averaging coefficients from different models as the adjustment
- -Rejecting regression entirely because results vary by specification
Concept Deep Dive
Analysis
This question tests understanding that regression coefficients depend on which other predictors are included. With the same data and correct computation, different specifications can produce different conditional estimates for area. The reasoning is to recognize specification sensitivity rather than assume an error or a simple averaging fix.
Background Knowledge
In multiple regression, each coefficient reflects the relationship between that variable and price while holding the other included variables constant. Omitting or adding correlated variables can shift a coefficient substantially. Sound modeling relies on market reasoning, diagnostics and testing alternative specifications.
Real-World Application
An appraiser runs one regression with only living area and age, and another that adds lot size and garage count, and sees the area coefficient change notably. The appraiser examines which variables are correlated with area and which model better fits market behavior before choosing a supported adjustment.
More Statistics Questions
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