The two-story home being appraised has 1,750 square feet of above-grade gross living area and a 400-square-foot finished basement. A simple linear regression of 41 recent sales of competing two-story homes, ranging from 1,300 to 2,300 square feet of above-grade GLA, gives: sale price = $48,500 + $132 × above-grade GLA. None of the 41 sales has a finished basement. The sales averaged $165 per square foot of above-grade GLA. What sale price does the model predict for the subject before any adjustment for the basement?
Correct Answer
A) $279,500
The model's variable is above-grade GLA, and the subject's 1,750 square feet lies inside the 1,300 to 2,300 square foot range of the sales, so the line can be read directly: $48,500 + $132 × 1,750 = $279,500. Adding the basement area to GLA gives $332,300, and also dropping the intercept gives $283,800; the basement is outside what the model measured and needs its own analysis. Multiplying the $165 average price per square foot by 1,750 gives $288,750, which is not what the fitted line predicts.
Why This Is the Correct Answer
Option A is correct because the subject's above-grade GLA of 1,750 square feet falls within the range of the sales, so the line gives $48,500 + $132 × 1,750 = $48,500 + $231,000 = $279,500. The basement is handled separately because none of the sales had one.
Why the Other Options Are Wrong
Option B: $283,800
Option B, $283,800, comes from dropping the $48,500 intercept and multiplying $132 by 2,150 square feet that include the basement. Both steps are wrong: the prediction needs the intercept, and the model measured above-grade GLA only.
Option C: $288,750
Option C, $288,750, multiplies the $165 average price per square foot by 1,750. The average price per square foot is not the fitted line; the line predicts $48,500 + $132 × 1,750 = $279,500.
Option D: $332,300
Option D, $332,300, adds the 400-square-foot basement to GLA: $48,500 + $132 × 2,150. Basement area was not in the model and none of the sales had a finished basement, so the line cannot price it.
Plug in what the model measured
Put into the equation only the quantity the model measured, here above-grade GLA, and check it sits inside the data range.
How to use: Use this when a question gives an equation plus extra areas or averages that tempt you to add them.
Exam Tip
Check two things before predicting: the variable definition (above-grade or total area) and whether the subject sits within the range of the sales.
Common Mistakes to Avoid
- -Adding below-grade area to above-grade GLA
- -Leaving out the intercept when predicting a price
- -Substituting the average price per square foot for the fitted line
Concept Deep Dive
Analysis
This tests reading a prediction off a fitted line for a subject inside the data range, while keeping the model's variable definition. The basement is not above-grade GLA, so it stays out of the prediction, and the average price per square foot is a different statistic from the line.
Background Knowledge
A fitted regression line predicts the dependent variable for values of the independent variable within the range of the data used to build it. The prediction is only as good as the match between the subject's characteristics and the variables, and their definitions, in the model.
Real-World Application
An appraiser's regression of two-story sales uses above-grade area from public records. The subject has a finished basement, so she predicts from above-grade GLA and then looks for separate market evidence on basement finish.
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?
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