A regression of sale price on gross living area for 60 recent sales of tract homes in one subdivision has a coefficient of determination (R-squared) of 0.78. What does this figure indicate?
Correct Answer
B) About 78% of the variation in sale prices is explained by GLA
The coefficient of determination measures how much of the variation in the dependent variable (sale price) is explained by the independent variable in the model (GLA); 0.78 means about 78% of the variation in these prices is associated with GLA and 22% with other factors. It is not an error band for individual predictions, not a price per square foot (that is the slope), and not a count of sales on the line.
Why This Is the Correct Answer
Option B is correct because R-squared is the share of the variation in the dependent variable explained by the model. An R-squared of 0.78 means GLA accounts for about 78% of the variation in sale prices among these 60 sales.
Why the Other Options Are Wrong
Option A: Predicted prices fall within 22% of the actual prices
Option A reads 0.78 as meaning predictions fall within 22% of actual prices. The unexplained 22% is a share of variation, not a percentage error band around each prediction.
Option C: Each added square foot of GLA adds $0.78 to the sale price
Option C reads 0.78 as $0.78 per added square foot. The amount added per square foot is the slope coefficient, a separate figure; R-squared has no dollar unit.
Option D: About 78% of the 60 sales lie exactly on the regression line
Option D says 78% of the sales lie exactly on the line. R-squared measures overall fit; a model with an R-squared of 0.78 may have no sales falling exactly on the line.
R-squared is the share explained
Read R-squared as a percentage of price variation explained by the model's variables. It is a share, not dollars and not an error margin.
How to use: Use this when an R-squared value appears and the options mix shares, dollars and error bands.
Exam Tip
If an option turns R-squared into dollars per square foot, it has confused R-squared with the slope.
Common Mistakes to Avoid
- -Treating R-squared as a dollar coefficient
- -Reading R-squared as a prediction error range
- -Assuming a high R-squared validates every coefficient
Concept Deep Dive
Analysis
This tests the meaning of R-squared, the most common measure of how well a regression fits. It is a share of variation explained, a number between 0 and 1, and it says nothing about the size of the adjustment.
Background Knowledge
In regression analysis, R-squared (the coefficient of determination) ranges from 0 to 1. Values closer to 1 mean the independent variables explain more of the variation in price, but a high R-squared alone does not prove the coefficients make economic sense.
Real-World Application
An appraiser's regression of price on GLA for a tract shows an R-squared of 0.78. She notes in the report that size explains most of the price differences and looks to location and condition for the rest.
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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In the usual sequence of adjustments, why is the market conditions adjustment applied after property rights, financing and non-realty adjustments?
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A single-family home with a permitted garage apartment is being appraised, and a comparable sale has no apartment. Leases in the neighborhood show homes with a garage apartment rent for $2,950 per month and similar homes without one for $2,350. Leased separately, a garage apartment rents for about $850 per month. The owner pays about $100 per month for the apartment's utilities. The apartment cost $84,000 to build six years ago. Rented single-family homes in the neighborhood sell for about 150 times their monthly rent. What adjustment amount is indicated for the garage apartment?