Least squares: minimize Σ(yᵢ−p(xᵢ))². For linear: y=mx+b, m=(nΣxᵢyᵢ−ΣxᵢΣyᵢ)/(nΣxᵢ²−(Σxᵢ)²). For polynomial: solve the normal equations AᵀAc=Aᵀy. R² = 1−SS_res/SS_tot measures goodness of fit.
How to Use
Enter data and fit:
- Points: (x,y) pairs
- Degree: 1 (linear) to 4
- Output: Coefficients + R²
R² Explained
R² = 1 − SS_res/SS_tot. R²=1: perfect fit. R²=0: predicts mean only. Higher degree always increases R² but risks overfitting. Adjusted R² penalizes extra parameters.
Overfitting
More parameters = better training fit but worse prediction. n points can be fit exactly with degree n−1, but the polynomial may oscillate wildly. Use cross-validation or information criteria.
Step-by-Step Instructions
- 1Enter data points.
- 2Select polynomial degree.
- 3View coefficients.
- 4Check R².
- 5Analyze residuals.