A regression of sale price on living area returns a coefficient of 85 for square footage. How should this be read?
Correct Answer
C) Each additional square foot adds about $85
Why this is correct: The original explanation defines the slope coefficient as the estimated change in the dependent variable (price) for a one-unit change in the independent variable (square footage). Therefore, a coefficient of 85 means each additional square foot adds about $85 to the sale price, all else equal. Why the other choices are wrong: The model explains 85 percent of price variation confuses the coefficient with R-squared. Eighty-five sales were used to fit the model confuses the coefficient with sample size. The typical home in the sample has 85 rooms confuses square footage with room count. Exam tip: In a regression output, the coefficient for a size variable is your adjustment factor per unit.
Why This Is the Correct Answer
A regression coefficient is the estimated change in the dependent variable for a one-unit change in the predictor, so 85 indicates about $85 of price per additional square foot.
Why the Other Options Are Wrong
Option A: The model explains 85 percent of price variation
The proportion of price variation explained by the model is R-squared, a separate statistic.
Option B: Eighty-five sales were used to fit the model
Sample size is reported separately and is unrelated to the coefficient's magnitude.
Option D: The typical home in the sample has 85 rooms
The coefficient describes the price effect of square footage and says nothing about room counts.
Dollars Per Unit
Dollars Per Unit of whatever the variable measures. Eighty-five dollars for one more square foot.
How to use: Name the units on both sides before interpreting. That prevents confusing a coefficient with a fit statistic.
Exam Tip
The coefficient depends on which other variables are in the model. Omitting a correlated variable such as quality inflates the size coefficient.
Common Mistakes to Avoid
- -Reading a coefficient as a percentage or a fit measure
- -Extrapolating beyond the sample's range of values
- -Ignoring omitted variable effects on the coefficient
Concept Deep Dive
Analysis
In a regression of sale price on living area, the coefficient on square footage is the estimated change in price associated with a one-unit change in that variable, holding the model's other variables constant. A coefficient of 85 therefore reads as roughly $85 of price per additional square foot, which is precisely the kind of figure an appraiser might use to support a size adjustment. The distractors each name a different regression output: R-squared is the proportion of variation explained, the sample size is a separate figure entirely, and the coefficient has nothing to do with room counts. Two cautions belong with the interpretation. The relationship is associational rather than causal, and the coefficient reflects the sample and the model specification β omit a correlated variable such as quality and the size coefficient absorbs part of its effect. And extrapolating beyond the range of sizes in the sample is unreliable, since the price-per-foot relationship is rarely linear across a wide range.
Background Knowledge
In regression analysis a coefficient estimates the change in the dependent variable associated with a one-unit change in a predictor, holding other variables constant. Interpretation is limited by model specification and by the sample's range.
Real-World Application
An appraiser supports an $85 per square foot size adjustment with a regression coefficient, noting the sample's size range and the variables controlled for.
More appraisal-statistical-methods Questions
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An appraiser includes both 'total room count' and 'bedroom count' as independent variables in a regression model estimating single-family home sale prices. The variance inflation factor (VIF) for 'bedroom count' is calculated as 12.3. What is the most appropriate appraisal action based on this result?
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