An appraiser is valuing a 3,300-square-foot custom home in a subdivision of one-story tract homes. A regression of 52 subdivision sales, which range from 1,150 to 2,050 square feet, gives sale price = $71,000 + $104 × GLA with an R-squared of 0.84. The appraiser applies the line to the subject and reports $414,200 as the indicated value. What is the main weakness in this analysis?
Correct Answer
C) The subject's size lies far outside the range of the sales
A regression line describes how buyers priced homes within the range of the data. The largest sale had 2,050 square feet, and the subject has 3,300, so applying the line ($71,000 + $104 × 3,300 = $414,200) extrapolates well beyond the evidence; buyers may pay a very different rate per square foot for a much larger custom home. An R-squared of 0.84 and 52 sales are reasonable for a one-variable model, and the intercept belongs in a predicted price.
Why This Is the Correct Answer
Option C is correct because the subject is 1,250 square feet larger than the largest sale in the model. A regression line measures the market's reaction only within the range of the data; projecting it far beyond that range assumes the same price per added square foot holds, which the sales do not show.
Why the Other Options Are Wrong
Option A: The R-squared of 0.84 is too low to rely on the model
Option A says an R-squared of 0.84 is too low. An R-squared of 0.84 means GLA explains about 84% of the price variation in these sales, which is a strong fit for a one-variable model; the problem is where the model is applied, not how well it fits.
Option B: The intercept should have been left out of the prediction
Option B says the intercept should have been left out. A predicted price needs the whole equation, $71,000 + $104 × 3,300; dropping the intercept would understate the prediction and would not cure the extrapolation.
Option D: Fifty-two sales are too few for a one-variable regression
Option D says 52 sales are too few for a one-variable regression. Fifty-two sales give a reasonable sample for a single variable; the data are adequate in number but do not include homes of the subject's size.
Stay inside the data fence
A regression line is fenced in by the smallest and largest sales used to build it. Inside the fence it speaks for the market; outside it is guessing.
How to use: Use this whenever a subject's size, age or other variable is compared with the range of the sales in a model.
Exam Tip
When a regression question gives the range of the data, compare it with the subject first; a subject outside the range points to extrapolation as the flaw.
Common Mistakes to Avoid
- -Treating a good R-squared as proof the model fits any subject
- -Ignoring the range of the data when applying a regression
- -Assuming the price per added square foot is the same at every size
Concept Deep Dive
Analysis
The question asks the candidate to spot extrapolation. The arithmetic is right, but the line was fitted to 1,150 to 2,050 square foot homes, and nothing in the data shows how buyers price a 3,300 square foot custom home.
Background Knowledge
A regression model is reliable for interpolation, meaning predictions within the range of the observed independent variable. Outside that range, the relationship between price and GLA may change, for example as buyers pay less for each added square foot in very large homes, so extrapolated results lack market support.
Real-World Application
An appraiser is asked to value the largest home ever built in a tract. Instead of stretching the tract regression, she searches nearby areas for sales of similar large custom homes and uses them to support the GLA adjustment.
More Sales Comparison Questions
Supported adjustments are: non-market financing $10,000, GLA $36/sf, garage $3,500 per car, pool/spa $12,500. A comparable identical to the 2,800 sf subject sold for $267,000 with non-market financing. What is its adjusted price?
Using GLA $36/sf and non-market financing $10,000: a 3,100 sf comparable sold for $277,000 with non-market financing; the subject has 2,800 sf. Bath count differences are not adjusted. What is the adjusted price?
Using garage $3,500 per car and pool/spa $12,500: a comparable with a 2-car garage and a pool/spa sold for $268,000. The subject has a 3-car garage and no pool. What is the adjusted price?
Using GLA $36/sf, garage $3,500 per car and pool/spa $12,500: a 2,600 sf comparable with a 2-car garage and a pool/spa sold for $264,000. The subject is 2,800 sf with a 3-car garage and no pool. What is the adjusted price?
In a neighborhood with declining values and marketing times over six months, what must Fannie Mae lenders confirm about the sales comparison analysis?
A house is a 4,000 square foot home in an area of 2,000 square foot homes. How must the appraiser treat this over-improvement in the sales comparison grid?
According to the Interagency Appraisal and Evaluation Guidelines, which items should an appraisal’s market conditions discussion include?
A comparable listed at $420,000 and sold for $399,000. What sale-to-list price ratio (sale price ÷ list price) does this indicate?
An appraiser wants to describe the neighborhood boundaries in a Fannie Mae report. Which approach is acceptable?
Which of these is listed by Fannie Mae as a sales or financing concession?
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An appraiser is ranking four sales against a subject in average condition on an interior street. All four homes are similar to the subject in size and sold within the last three months. Sale 1 was renovated and is on a similar interior street. Sale 2 was renovated and backs onto a highway. Sale 3 needs repairs and backs onto a golf course. Sale 4 needs repairs and is on a similar interior street. Market data do not measure the effect of either condition or location. Which sale can be ranked superior to the subject overall?