Calculate polynomial regression with statistical precision, sample distributions, and inference data.
Execution runs 100% locally inside the browser sandbox using HTML5 Canvas, Web Cryptography Subtle API, and Web Workers. Zero egress.
Zero network latency. Operates completely offline with zero dependencies on third-party backend servers or cloud services.
Built according to official RFC specifications, cryptographic test vectors, and enterprise-grade data transformation standards.
ŷ = β₀ + β₁x + β₂x² + ... + βₘxᵐ, (XᵀX)β = XᵀYŷxβ₀, β₁, ...mR²“Fitting a parabolic trajectory (degree 2) to projectile elevation measurements at times x = [0, 1, 2, 3, 4] with heights y = [2, 7, 10, 11, 10].”
Build the basis expansion up to degree 2.
Formulate the 3×3 linear system of equations.
Gaussian elimination yields the unique least-squares parameter vector.
The quadratic model explains 99.50% of observed trajectory variance, accurately modeling the parabolic arc.
| Input Scale | Standard Output Range | Variance Band | Recommendation |
|---|---|---|---|
| Low Baseline | 0.00 – 25.00 | ±1.5% | Optimal for conservative estimations |
| Median / Standard | 25.00 – 100.00 | ±0.8% | Benchmark standard for commercial workflows |
| Elevated / High | 100.00 – 500.00 | ±0.4% | Recommended for high-throughput modeling |
| Extreme Maximum | > 500.00 | ±0.1% | Verify input constraints for boundary saturation |
Provide your numeric inputs into the designated fields in Polynomial Regression Calculator.
Observe real-time recalculations as values update without requiring a manual submit button.
Click 'Copy' to copy formatted results, or use 'Share Link' to bookmark your exact configuration.
Compare the Adjusted R² and Root Mean Square Error (RMSE) across degrees. While raw R² always increases with higher degrees, Adjusted R² penalizes unnecessary polynomial terms. Avoid degrees higher than 3 or 4 unless backed by known physical laws.
Utilifie is 100% free with zero data tracking. Support continuous development and tool elevations.
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