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Polynomial Regression Calculator — result sheet
Fit an ordinary least-squares polynomial of degree 1 to 5 to paired observations and report the equation, R², and RMSE.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Choose coefficients β that minimize Σ(yᵢ − f(xᵢ))² for f(x)=β₀+β₁x+…+βₖxᵏ; solve the normal equations (XᵀX)β=Xᵀy.
This calculator fits a one-variable polynomial by ordinary least squares, then reports the fitted equation, coefficient of determination, root mean square error, and observation count.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- X values — Enter 2–30 finite numbers separated by commas or spaces.
- Y values — Enter paired Y values in the same order as X.
- Polynomial degree — degree; minimum 1; maximum 5
Worked example
| Input | Value |
|---|---|
| X values | 0, 1, 2, 3, 4 |
| Y values | 1, 3, 7, 13, 21 |
| Polynomial degree | 2 |
The exact quadratic fit is y = 1 + 1x + 1x² with R² = 1 and RMSE = 0.
Assumptions and limits
- X and Y contain the same number of finite numeric observations.
- There are at least degree plus one paired observations.
- The entered design has enough independent information for the chosen degree.
- The fit uses ordinary unweighted least squares and gives each observation equal weight.
- R² summarizes fit to these observations and is not a causal measure.
- High-degree fits can be sensitive to outliers, scaling, and extrapolation.
- The calculator does not provide confidence intervals, prediction intervals, diagnostics, or a model-selection test.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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