An ordinary least squares regression of sale price, including an intercept, reports in-sample R-squared = 0.82. What does this mean?
Correct Answer
D) The model explains 82 percent of price variation
In ordinary least squares with an intercept, R-squared is the fraction of in-sample response variation accounted for by the fitted model. Here it is 82% of sale-price variation about the sample mean. It is not an accuracy probability, each predictor’s value contribution or a statement that 82% of observations fall within an unspecified interval. Out-of-sample prediction requires separate validation.
Why This Is the Correct Answer
Option D is correct because, in ordinary least squares with an intercept, R-squared is the fraction of in-sample response variation accounted for by the fitted model. An R-squared of 0.82 means the model explains 82 percent of the variation in sale prices about their sample mean. How well it predicts new sales requires separate validation.
Why the Other Options Are Wrong
Option A: Eighty-two percent of sales fall within the range
Option A says eighty-two percent of sales fall within the range. R-squared does not count how many observations fall inside any interval; it measures the share of price variation explained.
Option B: Each variable contributes 82 percent of the value
Option B says each variable contributes 82 percent of the value. R-squared describes the model as a whole and does not assign a percentage of value to each predictor.
Option C: The model will be accurate 82 percent of the time
Option C says the model will be accurate 82 percent of the time. R-squared is not a probability of accuracy and does not by itself describe out-of-sample predictive performance.
R-squared explains spread
R-squared tells how much of the spread in prices the model explains, not how often it is right.
How to use: Use this to reject answers that turn R-squared into an accuracy rate or a per-variable share.
Exam Tip
Choose the answer about the share of variation explained. Answers that convert R-squared into a probability or a count of sales are distractors.
Common Mistakes to Avoid
- -Reading R-squared as the percentage of time the model is correct
- -Assigning the R-squared percentage to each variable
- -Assuming a high R-squared guarantees good predictions on new data
Concept Deep Dive
Analysis
This question tests interpretation of R-squared in an ordinary least squares regression with an intercept. R-squared is the share of the in-sample variation in the response that the fitted model accounts for. It is not a probability of accuracy, a per-variable contribution or a count of observations within an interval.
Background Knowledge
R-squared compares the variation explained by the regression with the total variation of the response around its mean. Values range from 0 to 1 in ordinary least squares with an intercept. A high R-squared does not by itself show the model is correctly specified or will predict new sales well.
Real-World Application
An appraiser's regression on 150 sales reports an R-squared of 0.82. She explains to a reviewer that the model accounts for 82 percent of price variation in those sales, then tests it on a holdout set before relying on its predictions.
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