Polynomial Regression Calculator
Fit polynomial curves to your data using least squares method with R² analysis
Polynomial Regression Settings
Higher degrees may overfit with small datasets
Number of decimal places in results
Data Points
Need at least 3 points for degree 2 polynomial. Current: 5 points.
Regression Results
Polynomial Equation
Coefficient of Determination
Polynomial Coefficients
Example: Quadratic Growth
Sample Data
Points: (1,2), (2,5), (3,10), (4,17), (5,26)
Pattern: Quadratic relationship y ≈ x² + 1
Degree: 2 (quadratic polynomial)
Expected Results
Equation: y = 1.000000x² + 0.000000x + 1.000000
R² = 1.000000 (perfect fit)
Coefficients: a₀ = 1, a₁ = 0, a₂ = 1
Polynomial Degrees
R² Interpretation
Quick Tips
Higher degrees may overfit small datasets
Need at least n+1 points for degree n
R² measures goodness of fit (0 to 1)
Use cross-validation for model selection
Understanding Polynomial Regression
What is Polynomial Regression?
Polynomial regression is a form of regression analysis where the relationship between the independent variable x and dependent variable y is modeled as an nth degree polynomial. It's particularly useful when the relationship between variables is non-linear.
When to Use It?
- •Data shows curved relationships
- •Linear regression doesn't fit well
- •Growth/decay processes
- •Physical phenomena with polynomial behavior
Mathematical Foundation
The general form of a polynomial regression equation is:
Coefficients are found using the least squares method by minimizing the sum of squared residuals.
Matrix Formula
Where X is the design matrix and y is the response vector