Good model
- Input
- R² = 0.92
- Expected output
- 92% da variância explicada
But checking residuals is still mandatory.
r-squared and regression model quality
R² — Coefficient of Determination in Regression
R² = 1 − (SSR / SST). An R² of 0.80 means 80% of Y's variance is explained by X in the linear model.
Limits of R² as a metric
- High R² does not guarantee causation, nor that the model is correct. An R² of 0.95 can appear with randomly ordered data that create an accidental linear pattern.
- R² alone does not detect homoscedasticity, residual normality, outliers, or curvilinear relationships. Always inspect the residual plot.
Examples
Anscombe's Quartet
- Input
- 4 datasets distintos
- Expected output
- todos R² ≈ 0.67
Identical R² for completely different patterns — always visualize your data.
Full tool FAQ
Simple linear regression is a statistical model that describes the linear relationship between an independent variable (X) and a dependent variable (Y) as a line: Ŷ = β₀ + β₁X.
Frequently asked questions
What R² is considered good?
It depends on the field. In physics: R² > 0.99 is expected. In social sciences: R² of 0.30 may be considered strong. There is no universal threshold.
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.