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How to Use the quadratic regression calculator?

Follow the below steps to use this calculator:
  • Enter the data set X
  • Enter the data set Y
  • Hit the “Calculate” button to get the answer
  • Click on the “Show Steps” button to see the step-by-step solution
  • You can erase all the data by clicking on the “Reset” button
  • No. of observations both in X and Y should be equal

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Quadratic Regression


Quadratic Regression Calculator


The Quadratic regression calculator helps you evaluate the quadratic regression equation using data sets X and Y. It also shows a graph with a step-by-step solution.


Formula of quadratic regression:


The quadratic regression equation is

Y = a + b(x) + c(x2)   where a

Here,

b = (Sxy Sx2x2 – Sx2y Sxx2 ) / Sxy Sx2x2 – (Sxx2)2

c = (Sx2y Sxx – Sxy Sxx2 ) / Sxy Sx2x2 – (Sxx2)2

a = y - bx - cx2


Method to calculate the quadratic regression:


In the following example, the procedure to calculate the quadratic regression is explained briefly.  

Example 1:

Determine a quadratic regression equation for the following data set of points.

(4,5),(3,6),(2,4),(1,8)

Solution:

Step 1: Separate the values

X= 4, 3, 2, 1

Y= 5, 6, 4, 8

Step 2: Calculate the mean of the datasets

Mean X = (4 + 3 + 2 + 1) / 4 = 5 / 2 = 2.5

Mean Y = (5 + 6 + 4 + 8) / 4 = 23 / 4 = 5.75    

Step 3: Draw a table.

Sxx

Sxy

Sxx2

Sx2x2

Sx2y

2.25

-1.125

12.75

72.25

-6.375

0.25

0.125

0.75

2.25

0.375

0.25

0.875

1.75

12.25

6.125

2.25

-3.375

9.75

42.25

-14.625

∑Sxx =5

∑Sxy = -3.5

∑Sxx2= 25

 ∑Sx2x2 = 129

∑Sx2y = - 14.5

 

Step 4: Calculate a, b, and c.  

For “b”:

b = (Sxy Sx2x2 – Sx2y Sxx2 ) / Sxy Sx2x2 – (Sxx2)2

b = {(-3.5) (129) – (-14.5) (25)} / {(5) (129) – (25)2}  

b= -4.45

For “c”:

c = (Sx2y Sxx – Sxy Sxx2 ) / Sxy Sx2x2 – (Sxx2)2

c = {(-14.5) (5) – (-3.5) (25)} / {(5) (129) – (25)2

c = 0.75

For “a”:

a = y - bx - cx2

a = 5.75 – (-4) (2.5) – (0.75) (7.5)

a = 11.25

Step 5: Put the values in the formula.

y = ax2 + b(x) + c, where a ≠ 0

y = (11.25) x2 + (-4.45) x + (0.75)


References:

Quadratic regression | Voxco

A brief introduction to Quadratic regression | Varsitytutors


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