Polynomial regression calculator
Fit a second- or third-degree curve to paired X and Y observations.
Fit and residuals
| Row | X | Y | Ŷ | Residual |
|---|---|---|---|---|
| Fill in the fields above — the result is computed on this page. | ||||
How to use this page
- Paste X and Y pairs in matching order.
- Choose degree 2 or 3.
- Review coefficients, R², RMSE and residuals.
What this page does not do: Extrapolation outside the X range can quickly become unrealistic. The calculator supports one predictor and degree 2 or 3; it does not establish causality.
Further reading
Polynomial regression extends a linear model with powers of X. A quadratic model is ŷ = b₀ + b₁x + b₂x², while a cubic model adds b₃x³. Coefficients are fitted by least squares.
R² is the share of Y variation reproduced in this sample. Adjusted R² accounts for the parameter count, and RMSE reports typical residual size in Y units.
Frequently asked questions
When should I choose degree 3?
When the relationship and validation evidence support it and a quadratic model leaves systematic residuals.
Does a high R² guarantee useful predictions?
No. A high in-sample R² can coexist with overfitting and poor predictions outside the observed range.
See also
Beta distribution calculator
Calculate beta density, CDF, upper tail and quantile together with its mean and variance.
Chi-square test calculator
Calculate chi-square goodness of fit, independence, or a chi-square critical value.
Continuous uniform distribution calculator
Calculate density, CDF, upper tail, quantile, mean and variance for U(a,b).