English

A quadratic regression is a method of determining the equation of the parabola that best fits a set of data. The good method to find this equation manually is by the use of the least squares method. This page shows you the Quadratic regression formula that helps you to calculate the best fit second-degree quadratic regression which will be in the form of y = ax2 + bx + c on your own. Based on that achieved equation you can plot the simple graph.

#### Formula:

Quadratic Regression Equation(y) = a + b x + c x^2
c = { [ Σ x2 y * Σ xx ] - [Σ xy * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }
b = { [ Σ xy * Σ x2x2 ] - [Σ x2y * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }
a = [ Σ y / n ] - { b * [ Σ x / n ] } - { a * [ Σ x 2 / n ] }

###### Where ,

Σ x x = [ Σ x 2 ] - [ ( Σ x )2 / n ]
Σ x y = [ Σ x y ] - [ ( Σ x * Σ y ) / n ]
Σ x x2 = [ Σ x 3 ] - [ ( Σ x 2 * Σ x ) / n ]
Σ x2 y = [ Σ x 2 y] - [ ( Σ x 2 * Σ y ) / n ]
Σ x2 x2 = [ Σ x 4 ] - [ ( Σ x 2 )2 / n ]
x and y are the Variables.
a, b, and c are the Coefficients of the Quadratic Equation
n = Number of Values or Elements
Σ x= Sum of First Scores
Σ y = Sum of Second Scores
Σ x2 = Sum of square of First Scores
Σ x 3 = Sum of Cube of First Scores
Σ x 4 = Sum of Power Four of First Scores
Σ xy= Sum of the Product of First and Second Scores
Σ x2y = Sum of Square of First Scores and Second Scores

#### Related Calculator:

You can make use of the related calculator designed based on the Quadratic regression formula to verify the graph which has plotted on your own.