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Fitted values

As explained in Statistics Slam Dunk

A fitted value is the response value predicted by a fitted statistical model for an observation or predictor setting.

A fitted value is the response predicted by a fitted statistical model for an observation or predictor setting. In a regression model, it is the model’s estimated win count for a team-season, alongside the observed win count. section 5.7.3

Use fitted values to:

  • Compare predictions with actual responses by calculating residuals or absolute prediction errors. section 5.7.3
  • Measure typical prediction error; the NBA regression’s average absolute difference was 8.27 wins. section 5.7.3
  • Inspect model assumptions through Residuals vs. Fitted plots, which place residuals against fitted values. section 5.7.5

NBA win prediction

For Miami’s 2017 team-season, the regression equation predicts 39 wins after combining the intercept with hustle-statistic values. Increasing loose balls from 7.2 to 8.2 changes the rounded prediction to 44 wins. Using broom, augment(fit1) adds observed wins and fitted values in the .fitted column; the first predictions are 37.84, 41.64, and 40.53.

How Statistics Slam Dunk covers it

How deep it goes
Explains extraction, error calculation, and diagnostic plotting, but stops short of deriving fitted values mathematically.
Examples
Uses NBA hustle statistics, Miami’s 2017 prediction, absolute win errors, and ANOVA group means.
What it assumes
Assumes a fitted regression or ANOVA model and basic R functions, while demonstrating extraction with broom.
What you can do after
Evaluate model predictions, calculate average absolute error, and inspect assumptions with fitted-value diagnostic plots.
How it connects
Connects fitted values with regression models, residuals, prediction error, model diagnostics, and ANOVA.
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This explainer was generated by Manning's knowledge graph from the text of Statistics Slam Dunk. The section links point to the parts of the book it draws on.