In an additive linear regression with an intercept and no transformations, what does the intercept represent?
Correct Answer
A) The predicted value when all independent variables are zero
In an additive regression with intercept, the constant is the fitted response when all encoded predictors equal zero. That predictor combination may be outside the data and lack practical property meaning. The intercept is not a correlation, a ranking of predictor importance or mean prediction error. The residual standard error is based on squared residuals and degrees of freedom, not their signed arithmetic mean.
Why This Is the Correct Answer
Option A is correct because in an additive regression with an intercept, the constant is the fitted response when all encoded predictors equal zero. That predictor combination may be outside the observed data, such as a home with zero square feet, so the intercept may lack practical property meaning even though its definition is clear.
Why the Other Options Are Wrong
Option B: The strongest predictor in the model
Option B calls the intercept the strongest predictor in the model, but the intercept is a constant, not a predictor, and it does not rank predictor importance.
Option C: The average prediction error across all of the observations
Option C describes the intercept as the average prediction error across the observations, which confuses it with a residual measure. In least squares with an intercept, signed residuals average to zero, and error size is summarized by measures based on squared residuals.
Option D: The correlation between price and size
Option D calls the intercept the correlation between price and size, but correlation is a separate unitless measure of linear association. The intercept is expressed in the units of the response variable.
Intercept Is Where X Is Zero
Picture the regression line crossing the vertical axis: that crossing point, where every predictor is zero, is the intercept.
How to use: Use this graph image when asked what the regression constant represents.
Exam Tip
Know the definition even when the zero point is unrealistic; the intercept still means the fitted value with all predictors at zero.
Common Mistakes to Avoid
- -Interpreting the intercept as a land or site value without support
- -Confusing the intercept with a correlation coefficient
- -Treating the intercept as a measure of prediction error
Concept Deep Dive
Analysis
This question tests interpretation of the intercept in an additive linear regression. The intercept is the fitted response when every predictor equals zero. That combination may lie outside the data and have no practical meaning, but that is what the constant represents mathematically.
Background Knowledge
A linear regression equation takes the form response = intercept + coefficient x predictor + ... . The intercept anchors the line where all predictors are zero, while each coefficient gives the change in the fitted response for a one-unit change in its predictor, holding the others fixed.
Real-World Application
An appraiser's regression of price on living area reports an intercept of $45,000. The appraiser recognizes this is the fitted value for a zero-square-foot home, outside the data, and does not treat it as a land value or any other meaningful figure.
More Statistics Questions
Sale prices are $270,000, $290,000, $300,000, $310,000, $330,000. Treat the listed observations as the complete population and divide by n when computing the standard deviation. Report to the nearest dollar.
A sales sampling frame systematically excludes a relevant part of the target market. What is the principal risk?
An appraiser estimates a market-wide price trend using only sales data from one brokerage that specializes in luxury homes, without checking how other segments are represented. What is the principal concern?
Compared with analyzing one matched sale pair for one feature, what can a suitably specified multiple regression do?
The base-period median sale price is $400,000 and the current-period median is $460,000. Compute the price relative defined as current ÷ base, as a decimal to three places.
The assessment-to-sale ratios are 0.8, 0.85, 0.9, 0.92, 0.95, 0.98, 1.02, 1.05, 1.08, 1.1, 1.15, 1.2. Calculate COD as [average absolute deviation from the median ÷ median]×100. For even n, average the two middle ratios. Report the COD as a percentage to two decimals.
Assessment-to-sale ratios are 0.94, 0.96, 0.98, 1, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
Market data show a first quartile sale price of $405,000 and a third quartile sale price of $495,000. What is the interquartile range, to the nearest dollar?
Assessment-to-sale ratios are 0.96, 0.98, 0.99, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
Given first quartile $400,000, median $440,000 and third quartile $500,000, compute the trimean (Q1+2×median+Q3)/4. Report to the nearest dollar.
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Previous Question
A set of adjusted sale prices has a mean of $250,000 and a standard deviation of $20,000. What is the coefficient of variation, and why might it be preferred to the standard deviation?
Next Question
In an approximately normal distribution, roughly what share of observations falls within one standard deviation of the mean?