Polynomial Regression Calculator (Quadratic)
Fit a quadratic (degree-2 polynomial) curve y = ax² + bx + c to a set of x and y data points using least-squares regression.
About the Polynomial Regression Calculator (Quadratic)
Polynomial regression extends simple linear regression to fit a curved, U-shaped or arc-shaped trend instead of a straight line. This calculator fits the most common case — a quadratic (degree-2) curve — by solving the least-squares normal equations that minimize the total squared error between the curve and your data.
Formula: Fits y = ax² + bx + c by solving the 3×3 system of normal equations derived from ∑xⁱ, ∑xⁱ², ∑xⁱ³, ∑xⁱ⁴, ∑yⁱ, ∑xⁱyⁱ and ∑xⁱ²yⁱ for least-squares fit
R² again measures fit quality from 0 to 1, just as in linear regression. Quadratic curves are useful whenever a relationship rises then falls (or vice versa) rather than moving steadily in one direction — modeling projectile trajectories, diminishing-returns effects, or U-shaped cost curves. With exactly three data points the curve will always pass through them perfectly (R² = 1); more points let the fit average out noise. If your data instead trends steadily in one direction without curving, the linear regression calculator will usually fit it just as well with a simpler, easier-to-interpret result.