Goodness-of-fit measure
A goodness-of-fit measure quantifies how closely a statistical model or representation agrees with observed data or specified relationships.
Statistics Every Programmer Needs
Goodness of fit is the degree to which a statistical model's predictions agree with observed data.
- How it is used
- Assesses how well fitted regression or time-series models account for observed data and supports comparisons between competing fits.
- How deep it goes
- Derives linear-regression R² from sums of squares and interprets model outputs, while emphasizing diagnostics beyond a single statistic.
- Examples
- Uses marathon stage split times, a sum-of-squares table, a fitted-line plot, and time-series residual plots.
- What you can do after
- Apply it via NumPy and statsmodels to interpret fitted-model output and check whether a fit statistic warrants confidence.
Read how Statistics Every Programmer Needs explains goodness-of-fit measure →
Causal AI
A goodness-of-fit statistic quantifies how well a model fits or accounts for observed data.
- How it is used
- Evaluates how well a trained model fits its data and, in score-based discovery, ranks candidate causal DAGs.
- How deep it goes
- Defines fit against training data and contrasts it with held-out prediction, but stops short of identifying the true data-generating process.
- Examples
- Uses training-data fit statistics, held-out prediction statistics, and high-scoring causal DAGs as examples.
- What you can do after
- Evaluate model fit, distinguish it from predictive validation, and interpret goodness-of-fit scores during causal discovery.
Related concepts
- coefficient of determinationmeasured by · 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 regressionmeasured by · Linear regression is a statistical modeling method that estimates a continuous response as a linear combination of predictor variables and fitted coefficients.
- McFadden's pseudo R-squaredmeasured by · McFadden's pseudo R-squared is a likelihood-based goodness-of-fit measure comparing a fitted discrete-choice model with an intercept-only null model.
- cross-validationcontrasts with · Cross-validation is a resampling technique that evaluates a model by repeatedly fitting it on some portions of available data and assessing it on held-out portions.
- chi-square testmeasured by · A chi-square test is a statistical hypothesis test that uses a chi-square-distributed statistic to evaluate hypotheses about categorical data, goodness of fit, or variance.
- AICmeasured by · The Akaike information criterion is a model-selection score that balances goodness of fit against model complexity, with lower values generally preferred among comparable models.
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