Adjusted r-squared
Adjusted R-squared is a regression goodness-of-fit statistic that modifies R-squared to account for the number of predictors and the sample size.
Effective Data Analysis
Adjusted R-squared is a version of R-squared that penalizes the score for additional variables included in a model.
- How it is used
- Uses adjusted R-squared to weigh regression fit against the complexity introduced by additional predictors.
- How deep it goes
- Defines the adjustment and interprets reported scores, without deriving its formula.
- Examples
- Uses housing-price and daily rat-sighting regressions to compare adjusted R-squared with R-squared in model summaries.
- What you can do after
- Evaluate/understand whether added regression predictors improve fit enough to offset their complexity, while checking other diagnostics.
Read how Effective Data Analysis explains adjusted r-squared →
Statistics Every Programmer Needs
Adjusted R-squared is a version of R-squared that penalizes a regression model for including additional predictors.
- How it is used
- Balances explanatory power and model complexity when evaluating regression fit or comparing models with different predictor sets.
- How deep it goes
- Explains the predictor penalty and model-reduction rationale but does not provide the adjusted R-squared formula.
- Examples
- Uses marathon Stage 1 and Stage 2 running times, fitted values, sums of squares, and a regression with R-squared near 0.575.
- What you can do after
- Evaluate regression models and diagnose unnecessary predictors by comparing R-squared with adjusted R-squared.
Read how Statistics Every Programmer Needs explains adjusted r-squared →
Statistics Slam Dunk
Adjusted R-squared is a regression-fit statistic that estimates explained response variance while accounting for the number of predictors.
- How it is used
- Evaluates regression fit while discouraging unnecessary predictors in NBA win models.
- How deep it goes
- Defines the complexity adjustment and interprets outputs, but stops short of deriving the formula.
- Examples
- Interprets adjusted R-squared values of 0.14 for fit1 and 0.16 for the reduced fit2 NBA wins regression.
- What you can do after
- Evaluate competing regression models by balancing explained variance against predictor count.
Related concepts
- coefficient of determinationkind of · The coefficient of determination, or R-squared, is a regression metric measuring the proportion of target variation explained by a fitted model relative to a mean-value baseline.
- linear regressionused by · Linear regression is a statistical modeling method that estimates a continuous response as a linear combination of predictor variables and fitted coefficients.
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