Cubic Regression Calculator
Find the cubic polynomial (degree 3) that best fits your data using least squares method
Data Input (Enter x,y coordinates)
Number of decimal places for coefficients (1-10)
At least 4 data points are required for cubic regression
At least 4 data points are required for cubic regression
Currently you have 0 valid data points.
Example Calculation
Sample Data
Points: (0,1), (2,0), (3,3), (4,5), (5,4)
Equation: y = a + bx + cx² + dx³
Result
y = 0.997 - 5.076x + 3.069x² - 0.387x³
R² ≈ 0.99 (excellent fit)
Interpretation
The cubic model explains 99% of the variance in the data, indicating an excellent fit.
Model Fit Guide (R²)
Coefficient Meanings
Understanding Cubic Regression
What is Cubic Regression?
Cubic regression is a type of polynomial regression that fits a cubic polynomial (degree 3) to your data points. The resulting equation has the form y = a + bx + cx² + dx³, where a, b, c, and d are coefficients determined using the least squares method.
When to Use Cubic Regression
- •Data shows S-shaped or complex curved patterns
- •Linear or quadratic models don't fit well
- •Data has multiple inflection points
- •You need to model complex relationships
Mathematical Method
Least Squares Method
β = (X^T X)^(-1) X^T y
Uses matrix operations to minimize squared residuals
Design Matrix X
[1, x, x², x³] for each data point
Contains powers of x values
Minimum Requirements
At least 4 data points needed for cubic fitting
Advantages
- ✓Models complex curved relationships
- ✓Can capture multiple turning points
- ✓More flexible than linear/quadratic
- ✓Good for S-shaped data patterns
Limitations
- •Can overfit with small datasets
- •Extrapolation can be unreliable
- •More complex than simpler models
- •Sensitive to outliers
Applications
- •Growth curve modeling
- •Economic trend analysis
- •Engineering curve fitting
- •Scientific data modeling