Quartic Regression Calculator
Fit a 4th-order polynomial regression model to your data points
Enter Your Data Points
Data Points (5/30) - Minimum 5 required
Point 1
Point 2
Point 3
Point 4
Point 5
Example: Quartic Growth Pattern
Sample Dataset
Scenario: Complex biological growth with multiple inflection points
Expected Results
Pattern: Quartic equation with positive leading coefficient
R² value: Should be very high (close to 1.0) for polynomial data
Use case: Complex growth patterns, engineering curves, advanced modeling
Quartic Regression Formula
General Form
y = a₄x⁴ + a₃x³ + a₂x² + a₁x + a₀
Fourth-degree polynomial with five coefficients to determine.
R-squared (R²)
R² = 1 - (SS_res / SS_tot)
Coefficient of determination measuring goodness of fit (0 to 1).
Polynomial Regression Types
Linear
y = ax + b (straight line)
Quadratic
y = ax² + bx + c (parabola)
Cubic
y = ax³ + bx² + cx + d
Quartic
Complex curves with multiple turning points
Quick Tips
Need minimum 5 points for quartic regression
Higher R² values indicate better fit
Use for complex data with multiple curves
Avoid overfitting with too many parameters
Understanding Quartic Regression
What is Quartic Regression?
Quartic regression fits a fourth-degree polynomial to your data, allowing for more complex relationships than linear, quadratic, or cubic models. It can capture up to three turning points in the data pattern.
When to Use Quartic Regression
- •Data shows complex, non-linear patterns
- •Multiple peaks and valleys in the data
- •Lower-order polynomials don't fit well
- •Scientific or engineering applications
Mathematical Method
Least Squares Method
Uses matrix operations to find coefficients that minimize the sum of squared residuals:
- Create design matrix with powers of x
- Set up normal equations
- Solve linear system using Gaussian elimination
- Calculate R² for goodness of fit
Interpreting Results
R² ≥ 0.9: Excellent fit - model explains 90%+ of variance
R² 0.7-0.9: Good fit - reasonable predictive power
R² < 0.7: Consider simpler models or different approach