F-statistic
An F-statistic is a ratio of variance estimates used to compare explained or between-group variation with unexplained or within-group variation.
Effective Data Analysis
An F-statistic is a test statistic that compares explained variation with unexplained variation in an analysis of variance or regression model.
- How it is used
- Tests whether a regression model’s predictors collectively influence its outcome.
- How deep it goes
- Explains the collective test and accompanying p-value, then interprets model output without deriving the statistic.
- Examples
- Uses housing-price and daily rat-sighting regressions to interpret F-statistics alongside model summaries and residual plots.
- What you can do after
- Evaluate/understand it in a regression summary to assess collective predictor significance while checking residuals before trusting the model.
Statistics Every Programmer Needs
An F-statistic measures the overall significance of a regression by comparing explained variance with unexplained variance relative to a model containing only an intercept.
- How it is used
- Evaluates whether a regression explains significant response variance beyond an intercept-only model.
- How deep it goes
- Explains calculation inputs, F-table comparison, and p-value interpretation, while deferring formal decisions to the model p-value.
- Examples
- Uses a stage1-to-stage2 regression with F = 24.35, a 5% critical value of 4.38, one predictor, and 19 observations.
- What you can do after
- Evaluate overall regression significance using an F-table or model p-value alongside fit measures and assumption checks.
Read how Statistics Every Programmer Needs explains f-statistic →
Related concepts
- linear regressionmeasures · Linear regression is a statistical modeling method that estimates a continuous response as a linear combination of predictor variables and fitted coefficients.
- p-valueproduces · A p-value is the probability, assuming a specified null hypothesis, of obtaining a test statistic or result at least as extreme as the observed one.
- inputmeasures · An input is a value, information, or signal supplied to a system, computation, or interface for processing or to influence its behavior.
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