Quartic Regression Calculator
Enter x-y pairs to estimate a quartic (degree-4) polynomial model, evaluate goodness-of-fit, and generate predictions.
Quartic model
y = 0.9365 + -0.3505·x + 3.8472·x² + -1.3241·x³ + 0.2083·x⁴
R² = 0.9996
| x | Observed y | Predicted y | Residual |
|---|---|---|---|
| 0 | 1.0000 | 0.9365 | 0.0635 |
| 1 | 3.0000 | 3.3175 | -0.3175 |
| 2 | 9.0000 | 8.3651 | 0.6349 |
| 3 | 15.0000 | 15.6349 | -0.6349 |
| 4 | 30.0000 | 29.6825 | 0.3175 |
| 5 | 60.0000 | 60.0635 | -0.0635 |
How to Use This Calculator
- Enter at least five paired observations (x, y).
- Review the fitted quartic equation and R² value.
- Use the prediction field to estimate y for new x values.
- Inspect residuals to assess model adequacy.
Formula
Quartic model: y = a₀ + a₁x + a₂x² + a₃x³ + a₄x⁴
Coefficients solve normal equations (XᵀX)a = Xᵀy
R² = 1 − SSres / SStot
Full Description
Quartic regression captures complex curvature with up to four turning points. It can model non-linear trends but risks overfitting if data is scarce or noisy. Always evaluate residual behavior and consider simpler models when appropriate.
Frequently Asked Questions
Why need at least five points?
A quartic polynomial has five coefficients. Fewer points yield an underdetermined system or perfect fit with no degrees of freedom.
Is the fit guaranteed to be stable?
High-degree polynomials can be numerically unstable. Ensure data scaling and distribution support quartic modeling.
Does R² capture model quality?
R² indicates variance explained, but inspect residuals and consider cross-validation to avoid overfitting.
Can I extend to higher degrees?
This tool focuses on quartic regression. For higher degrees, consider specialized software or polynomial fitting libraries.