A simple linear regression of 55 townhouse sales in one development, with living areas from 1,100 to 1,900 square feet, gives: sale price = $41,500 + $142 x gross living area. What does the $41,500 figure represent?
Correct Answer
D) The line's predicted price at zero square feet
In a simple regression, the constant is the intercept: the point where the fitted line meets zero on the gross living area axis. It anchors the line within the 1,100 to 1,900 square foot range of the data and has no separate meaning there; no townhouse has zero living area. The model did not measure land, other features or the lowest sale, so the intercept cannot be read as any of those.
Why This Is the Correct Answer
Option D is correct because the intercept, $41,500, is the price the line predicts when gross living area is zero. It positions the line so that predictions within the 1,100 to 1,900 square foot range fit the sales, but it does not measure any property component.
Why the Other Options Are Wrong
Option A: The value of the site under a typical townhouse
Option A reads the intercept as the site value of a typical townhouse. The model has no land variable and no sales near zero square feet, so it measures nothing about the site.
Option B: The value of the features other than living area
Option B reads the intercept as the value of all features other than living area. Other features were not measured as variables; their effects are mixed into the scatter around the line, not isolated in the intercept.
Option C: The lowest price paid for a townhouse in the data
Option C reads the intercept as the lowest price paid in the data. The lowest sale would be a home of about 1,100 square feet, which the line predicts at about $41,500 + $142 x 1,100 = $197,700, far above $41,500.
Slope measures, intercept anchors
The slope is what each added square foot adds; the intercept just pins the line where living area is zero.
How to use: Use this when asked what the constant in a price regression means.
Exam Tip
Do not give the intercept an economic meaning such as land value unless the model actually includes data near zero for that variable.
Common Mistakes to Avoid
- -Reading the intercept as land or site value
- -Treating the intercept as the value of all other features
- -Applying the line far outside the range of the data
Concept Deep Dive
Analysis
The question tests reading the parts of a regression equation. The slope measures the change in price for each added square foot; the intercept is where the line crosses zero living area. Because zero lies far outside the data, the intercept has no real-world meaning on its own.
Background Knowledge
Statistical techniques such as linear regression can measure adjustments for the elements of comparison included as variables. In a one-variable model of price on gross living area, the slope is the market's marginal price per square foot. The intercept anchors the line and is meaningful only if the data include values near zero, which home sales never do.
Real-World Application
An appraiser runs a price-on-size regression for a townhouse development and reports the slope as the size adjustment rate. When a reviewer asks whether the constant is the land value, she explains that it is only the line's starting point and lies far outside the range of the sales.
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?
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