An appraiser develops a multiple regression model to estimate residential sale price using GLA, age, number of bathrooms, and distance to nearest highway. The model yields an adjusted R² of 0.72 and a standard error of the estimate of $24,500. Which statement best reflects the appropriate interpretation of the standard error of the estimate in this context?
Correct Answer
B) Approximately 68% of the predicted sale prices fall within ±$24,500 of the actual sale prices, assuming residuals are normally distributed.
The standard error of the estimate (SEE) is the standard deviation of the residuals — i.e., the typical magnitude of prediction error. Under normality and homoscedasticity assumptions, approximately 68% of residuals lie within ±1 SEE of the regression line (by the empirical rule). Option A misstates it as an average absolute difference (it’s a standard deviation, not mean absolute error). Option C incorrectly conflates adjusted R² with residual variance; while SEE is the square root of the mean squared error, adjusted R² does not directly quantify residual standard deviation. Option D confuses SEE with the standard errors of individual coefficients. USPAP Advisory Opinion 21 (AO-21) emphasizes that appraisers must understand and correctly interpret statistical output used in valuation support.
Why This Is the Correct Answer
The standard error of the estimate (SEE) is the standard deviation of the residuals — i.e., the typical magnitude of prediction error. Under normality and homoscedasticity assumptions, approximately 68% of residuals lie within ±1 SEE of the regression line (by the empirical rule). Option A misstates it as an average absolute difference (it’s a standard deviation, not mean absolute error). Option C incorrectly conflates adjusted R² with residual variance; while SEE is the square root of the mean squared error, adjusted R² does not directly quantify residual standard deviation. Option D confuses SEE with the standard errors of individual coefficients. USPAP Advisory Opinion 21 (AO-21) emphasizes that appraisers must understand and correctly interpret statistical output used in valuation support.
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