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

(0, 1)
(1, 2.5)
(2, 8)
(3, 18)
(4, 35)

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

1

Linear

y = ax + b (straight line)

2

Quadratic

y = ax² + bx + c (parabola)

3

Cubic

y = ax³ + bx² + cx + d

4

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:

  1. Create design matrix with powers of x
  2. Set up normal equations
  3. Solve linear system using Gaussian elimination
  4. 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