# Polynomial Regression along with code

Hello World, Today we are going to discuss Polynomial regression and I will make it a very easy topic for you. It is going to be an amazing tutorial. This article contains hands-on exercise of polynomial regression which will help us understand this topic more deeply.

Without any delay, Let's get started!

First thing first,

**What is Regression?**

*Regression analysis is a form of predictive *modeling* technique *that* investigates the relationship between a dependent and independent variable.*

The above-written definition is a bookish definition. If you understood the above line, it's well and good, If you didn't, it's OK.

Finding the best-fit regression equation using the relationship between dependent variable X and independent variable y, so that we can make predictions from it is known as regression.

**Polynomial Regression**

If you have seen my __linear regression blog__, it was having data that can fit into a straight line. But what if your data is actually more complex then a simple straight line? We can fit a polynomial regression model on that depending on how the data looks like.

What does polynomial regression do under the hood to fit the non-linear data?

Surprisingly, We can use a linear model to fit non-linear data. A simple method to do this is to add powers of each feature as new features then train a linear model on this extended set of features. This technique is known as polynomial regression.

Figure 1: Linear Regression (source: Towards data science)

Figure 2: Polynomial regression (source: Towards data science)

Therefore, if we have used a simple linear regression in the above graph as shown in figure 1 then as we can see the linear regression line would not fit the data very well. It is hard to fit a linear regression line on the graph of figure 1 and receiving a low error value. Hence, it is essential to fit a polynomial regression to achieve a minimum error.

**General equation of Polynomial Function:-**

*Y*=θo + θ₁*X*+ θ₂*X*² + … + θₘXᵐ +**residual error**

**Advantages of using Polynomial Regression:**

The polynomial function gives the finest approximation of the relationship between its independent variable & dependent variable

A wide range of curvature can be fit by the polynomial function

It can fit a very broad range of functions

**Disadvantages of using Polynomial Regression:**

The results of the non-linear analysis can be seriously affected by the presence of one or two outliers in the data

There are only a few model validation tools for detecting the outliers in a Non-linear regression.

I conclude this article and take you to the coding section in Kaggle.

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