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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
• You can erase all the data by clicking on the “Reset” button
• No. of observations both in X and Y should be equal

## Other Calculators

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. This quadratic equation models the relationship between two variables in the form of a parabola which is U shaped curve. This equation is used to make predictions or analyze trends.

Quadratic regression is a statistical method used to model the relationship between a dependent variable (y) and an independent variable (x) by fitting a quadratic (parabolic) equation. This technique is useful when the data follows a curved rather than a straight line.

A quadratic equation is a mathematical expression that describes a parabolic relationship between two variables. The quadratic equation takes the form:

Y = a + b(x) + c(x2)

Where:

• Y is the dependent variable.
• X is the independent variable.
• a, b, and c are the coefficients determined by the regression analysis.

The coefficients a, b, and can be calculated using the following formulas:

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

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

a = y - bx - cx2

• is the sum of the product of x and y values.
• Sx2 is the sum of the squared values.
• Sx2x2 is the sum of the fourth power of x values.
• Sx2y is the sum of the product of squared x and y values.
• Sxx2 is the sum of the product of and squared x values.
•  is the mean of the x values.
• ȳ is the mean of the y values.
• 2 is the mean of the squared x values.

## 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:

A brief introduction to Quadratic regression | Varsitytutors

10 months ago