To validate the functional form of a regression model used for adjustments, an appraiser plots residuals against predicted values and observes a clear inverted-U pattern. What does this pattern indicate, and what is the most defensible corrective action?
Correct Answer
B) The linear specification is misspecified; add a quadratic term for the relevant predictor (e.g., GLA²) to capture nonlinearity.
A systematic curved pattern (e.g., inverted-U) in a residual-vs-fitted plot signals nonlinearity — i.e., the true relationship is not adequately captured by a straight-line functional form. Adding a quadratic term (e.g., GLA²) is the standard remedy to model curvature. While heteroscedasticity (A) often manifests as a funnel shape, not an inverted-U; autocorrelation (C) is irrelevant in cross-sectional appraisal data (no time ordering); and automatic outlier removal (D) violates USPAP Standards Rule 2-2(c), which requires objective, documented justification for excluding data points — not mechanical truncation. AO-21 states that appraisers must assess model assumptions, including linearity, and modify specifications when diagnostic plots indicate misspecification.
Why This Is the Correct Answer
A systematic curved pattern (e.g., inverted-U) in a residual-vs-fitted plot signals nonlinearity — i.e., the true relationship is not adequately captured by a straight-line functional form. Adding a quadratic term (e.g., GLA²) is the standard remedy to model curvature. While heteroscedasticity (A) often manifests as a funnel shape, not an inverted-U; autocorrelation (C) is irrelevant in cross-sectional appraisal data (no time ordering); and automatic outlier removal (D) violates USPAP Standards Rule 2-2(c), which requires objective, documented justification for excluding data points — not mechanical truncation. AO-21 states that appraisers must assess model assumptions, including linearity, and modify specifications when diagnostic plots indicate misspecification.
More appraisal-statistical-methods Questions
A price index rises from 100 to 121 over two years. What compound annual rate does this represent?
A sample of four sales drawn from a market with 200 annual transactions is:
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?
An appraiser includes both 'total room count' and 'bedroom count' as independent variables in a regression model estimating single-family home sale prices. The variance inflation factor (VIF) for 'bedroom count' is calculated as 12.3. What is the most appropriate appraisal action based on this result?
An appraiser runs a regression of sale price on GLA, age, and a binary variable for 'renovated' (1 = yes, 0 = no). The estimated coefficient for 'renovated' is $18,400 with a standard error of $6,200 and a t-statistic of 2.97. Assuming a two-tailed test at α = 0.05 and 42 degrees of freedom, what conclusion is supported regarding the market's recognition of renovations?
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?
An appraiser includes months elapsed since each sale as a variable in a price model. What is this intended to capture?
Capitalization rates in one segment range from 7.8 to 8.2 percent, and in another from 6.0 to 10.5 percent. What does this suggest?
People Also Study
Valuation Principles & Procedures
25% of exam
Property Description & Analysis
20% of exam
Market Analysis & Highest/Best Use
15% of exam
Appraisal Math & Statistics
15% of exam
USPAP (Ethics & Standards)
15% of exam