Polynomial Fitting & Curve Fitting

Polynomial Fitting with polyfit

Fit a polynomial of degree n to data points:

# Fit a quadratic (degree 2) to noisy data
coeffs = np.polyfit(x, y, deg=2)
# Returns [a, b, c] for y = ax² + bx + c

# Evaluate the polynomial
y_fit = np.polyval(coeffs, x)

Polynomial Degrees

Caution: Overfitting

Higher degrees fit noise, not signal. Watch your validation error!

# Compare different degrees
for deg in [1, 2, 3, 5]:
    coeffs = np.polyfit(x, y, deg)
    y_fit = np.polyval(coeffs, x)
    rmse = np.sqrt(np.mean((y - y_fit)**2))
    print(f"Degree {deg}: RMSE = {rmse:.4f}")

Multi-dimensional Fitting

For more complex models, use least squares:

# y = a*x1 + b*x2 + c*x3 + noise
# Stack features as columns, solve: X @ w = y
X = np.column_stack([x1, x2, x3, np.ones_like(x1)])
w = np.linalg.lstsq(X, y, rcond=None)[0]

Best practice: Use train/validation split to choose polynomial degree.