Quartic Regression Calculator
Fit a fourth-degree polynomial to your data using the least squares method. Enter summary statistics and get the quartic equation, R-squared value, and predicted values.
Quartic regression fits a fourth-degree polynomial to your data, capturing complex curves with up to three turning points.
The Model: y = ax⁴ + bx³ + cx² + dx + e
The five coefficients are found by solving a 5x5 system of normal equations derived from minimizing the sum of squared residuals.
When to Use Quartic Regression:
- Your data shows a complex curve with multiple bends
- Lower-degree polynomials (linear, quadratic, cubic) give poor fits
- The relationship has up to three turning points
Cautions:
- Higher-degree polynomials can overfit, especially with few data points
- Quartic models can behave unpredictably outside the range of your data (extrapolation risk)
- Always check if a simpler model (quadratic or cubic) fits nearly as well
- You need at least 6 data points, but more is better for a reliable fit
Required Summary Statistics: You need n, Σx through Σx⁸, Σy, Σxy through Σx⁴y, and Σy². Compute these from raw data in a spreadsheet.