Quadratic Regression

The equation used in quadratic regression is as follows: 

y = ax2 + bx + c

The following formulas can be used to calculate the values of a, b, and c: 

a = { [ 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 }

c = [ Σ y / n ] – { b * [ Σ x / n ] } – { a * [ Σ x 2 / n ] }

Where, 

• x and y: The Variables
• a, b, and c: The Coefficients of the Quadratic Equation 
• n = Number of Values/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
• 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 ]