# 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=a0+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:

### Solution:

Let the quadratic polynomial regression model be

y=a0+a1*x+a2*x2

The values of a0, a1, and a2 are calculated using the following system of equations:

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

Using the given data we,

Solving this system of equations we get

a0=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).