📈 Cubic Regression Calculator
Fit a best-fit cubic curve (y = ax³ + bx² + cx + d) to your data. Enter six x,y data points to get the least-squares cubic coefficients.
What This Calculator Does
Cubic regression fits a third-degree polynomial curve, y = ax³ + bx² + cx + d, through a set of data points, capturing more curvature than a straight line or a quadratic can.
How the Math Works
The calculator uses the least-squares method: it finds the coefficients a, b, c, and d that minimize the sum of squared differences between the actual y values and the curve’s predicted values. This is done by solving a system of four normal equations built from power sums of your x and y values (Σx, Σx², up to Σx⁶, and Σxy through Σx³y), solved here with Gaussian elimination.
- Enter six (x, y) data points.
- The calculator returns the best-fit coefficients a, b, c, and d for y = ax³ + bx² + cx + d.
With exactly four well-spread points a cubic can fit perfectly; with six points, small deviations show that the curve is the closest overall fit rather than passing through every point exactly. This tool is for general educational and analytical use.