Quadratic Regression Calculator

This Quadratic Regression Calculator quickly and simply calculates the equation of the quadratic regression function and the associated correlation coefficient. In addition, it generates a scatter plot that depicts the curve of best fit.

You can use the quadratic regression calculator in three simple steps:

1. Input all known X and Y variables in the respective fields.
2. Click on the "Calculate" button to compute the quadratic regression equation.
3. Click on the "Reset" button to clear all fields and input new values.

The Quadratic Regression Calculator uses the following formulas:

Quadratic regression: y = ax² + bx + c, where a ≠ 0

Coefficients (a, b, c):

Mean x: x̄ = ∑x_i / n

Mean y: ȳ = ∑y_i / n

Correlation coefficient r:

Where:

n  is the total number of samples,

x_i (x₁, x₂, ... ,x_n) are the x values,

y_i (y₁, y₂, ... ,y_n) are the y values,

∑x_i  is the sum of x values,

∑y_i  is the sum of y values,

∑x_i y_i  is the sum of products of x and y values,

∑x_i²  is the sum of squares of x values,

∑x_i³  is the sum of the cubes of x values,

∑x_i⁴  is the sum of the fourth powers of x values.

You may also be interested in our Linear Regression Calculator or Least-Squares Circle Calculator