# 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:

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

### The Quadratic Regression Calculator uses the following formulas:

Quadratic regression: y = **a**x^{2} + **b**x + **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} (x_{1}, x_{2}, ... ,x_{n}) are the x values,*

*y _{i} (y_{1}, y_{2}, ... ,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 _{i}^{2} is the sum of squares of x values,*

*∑x _{i}^{3} is the sum of the cubes of x values,*

*∑x _{i}^{4} 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