Polynomial Regression Calculator
Fit data to a quadratic or linear polynomial, showing the equation and R² fit quality.
Category: Statistics
About this tool
What Is polynomial regression? Polynomial Regression Calculator. The polynomial regression calculator fits your points to y = a·x² + b·x + c when curvature is visible, or the straight line y = m·x + b when it is not, returning the equation plus the R² goodness of fit. Polynomial regression extends least squares from a line to a curve. The quadratic model solves a 3×3 system for a, b, c; the linear model solves the classic 2×2 system for slope and intercept. A positive a opens upward (fast rebound), negative opens downward (peaks and declines). The tool takes every point into account by minimising the sum of squared vertical distances. y = a·x² + b·x + c via normal equations (or y = m·x + b when trajectory is linear). How to Use Add rows with matching x, y values (three or more for a quadratic). Enter all your points, adding or removing rows as needed. Read the fitted polynomial, its R², and predicted values for new x you enter. Worked Example Points (0,3), (1,2), (2,3), (3,6) fit to y = x² − 2x + 3 with R² = 1 exactly, since the data lie precisely on that parabola. Predicting at x = 4 returns 11. Common Use Cases cost curves and diminishing returns projectile height over time temperature daily-swing modelling sensor curve calibration Important Notes Three points or more are required for the quadratic fit. R² near 1 indicates a strong fit; values far below suggest a different mo