Quadratic Polynomial Regression Model Solved Example

 
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Quadratic Polynomial Regression Model Solved Example in Machine Learning

Regression modeling is a process of determining a relationship between one or more independent variables and one dependent or output variable.

Example:

1. Predicting the price of the car given the car model, year of manufacturing, mileage, engine capacity.

2. Predicting the height of a person given the age of the person.

Polynomial Regression

Let there be only one independent variable x and the relationship between x, and dependent variable y, be modeled as,

y=a+a1*x+a2*x2 +………+ +an*xn

for some positive integer n >1, then we have a polynomial regression.

Problem Deninition:

Find a quadratic regression model for the following data:

XY
32.5
43.2
53.8
66.5
711.5

Solution:

Let the quadratic polynomial regression model be

y=a+a1*x+a2*x2

The values of a, a1, and a2 are calculated using the following system of equations:

Quadratic Polynomial Regression Model

First, we calculate the required variables and note them in the following table.

xyx2x3x4y*xy*x2
32.5927817.522.5
43.2166425612.851.2
53.8251256251995
66.536216129639234
71249343240180.5563.5
Σ2527.51357754659158.8966.2

Using the given data we,

 Quadratic Polynomial Regression

Solving this system of equations we get

a=12.4285714

a1=-5.5128571

a2=0.7642857

The required quadratic polynomial model is

y=12.4285714 -5.5128571 * x +0.7642857 * x2

Now, given the value of x (independent variable), we can calculate the value of y (dependent or output variable).

Video Tutorial of Quadratic Polynomial Regression Model

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