Quadratic regression calculator: definition, formula and calculation

Step 3: Substitute the values in the formula

Σ x x = [ Σ x 2 ] – [ ( Σ x )2 / n ]

∑xx = [77] – [(15)2 / 3]

∑xx = 77 – [225/3]

∑xx = 77 – 75

∑xx = 2

Σ x y = [ Σ x y ] – [ ( Σ x * Σ y ) / n ]

∑xy = [43] – [(15 x 9) /3]

∑xy = 43 – [135/3]

∑xy = 43 – 45

∑xy = -2

Σ x x2 = [ Σ x 3 ] – [ ( Σ x 2 * Σ x ) / n ]

∑xx2 = [405] – [(77 x 15) / 3]

∑xx2 = 405 – [1155 / 3]

∑xx2 = 405 – 385 

∑xx2 = 20

Σ x2 y = [ Σ x 2 y] – [ ( Σ x 2 * Σ y ) / n ]

∑x2y = [211] – [(77 x 9) / 3]

∑x2y = 211 – [693 / 3]

∑x2y = 211 – 231

∑x2y = -20

Σ x2 x2 = [ Σ x 4 ] – [ ( Σ x 2 )2 / n ] 

∑x2x2 = [2177] – [(77)2 / 3]

∑x2x2 = 2177 – [5929 / 3]

∑x2x2 = 2177 – 1976

∑x2x2 = 201

Step 4: Calculate a

a = { [ Σ x2 y * Σ xx ] – [Σ xy * Σ xx2 ] } / { [ Σ xx * Σ x2 x2] – [Σ xx2 ]2 }

a = {[-20 * 2] – [-2 * 20]} / {[2 * 201] – [20]2}

a = {(-40) – (40)} / {(402) – (400)}

a = -80 / 2

a = -40

Step 5: Calculate b

b = { [ Σ xy * Σ x2 x2 ] – [Σ x2y * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] – [Σ xx2 ]2 }

b = {[-2 * 201] – [-20 * 20]} / {[2 * 201] – [20]2}

b = {[-402] – [-400]} / {(402) – (400)}

b = -2 / 2

b = -1

Step 6: Calculate c

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

c = [9 / 3] – {-1 * (15 / 3)} – {-40 * (77 / 3)}

c = 3 – [-1 * 5] – [-40 * 25.66]

c = 3 – (-5) – (-1026.4)

c = 1034.4