Polynomial regression is a kind of linear regression in which the relationship shared between the dependent and independent variables Y and X is modeled as the nth degree of the polynomial. This is done to look for the best way of drawing a line using data points. Keep reading to know more about polynomial regression. 

What Is Polynomial Regression?

The algorithm of linear regression works only when the regression in the data is linear. Polynomial regression can be considered one of the exceptional cases of multiple linear regression models. In other words, it is a linear regression type containing dependent and independent variables, and they both share a curvilinear relationship. A polynomial relationship is fitted in the data.

Also, several linear regression equations are converted into polynomial regression equations by including numerous polynomial elements. 

Need for Polynomial Regression

Below listed are a few points that define the need for polynomial regression. 

  • A good result is provided if a linear model is applied to a linear database, as is the case with simple linear regression. However, a drastic output is produced if the same model is applied to a non-linear dataset with no modifications. These cause an increase in the loss function, high error rates, and a decrease in accuracy. 
  • For cases where the data points are arranged in a non-linear fashion, there is a need for polynomial regression. 
  • If a non-linear model is present and you try to cover it using a linear model, it will cover no data points. Hence, a polynomial model is used to ensure that the data points are covered. That said, a curve will be suitable for covering most data points using polynomial models instead of a straight line. 

Types of Polynomial Regression

Since there is no limit to the degree in a polynomial equation, and it can go up to the nth value, numerous kinds of polynomial regression exist. For instance, a quadratic equation, when spoken, generally is used for the second degree of a polynomial equation. This degree, as stated, can up to nth value, and you can derive as many equations as you want to or need. Hence, polynomial regression is usually categorized as mentioned below. 

  • Linear, when the degree is 1. 
  • Quadratic, the degree of this equation is 2. 
  • Cubic with a degree as three continues, based on the degree used. 

Equation of the Polynomial Regression Model

Any linear equation is a polynomial regression that has a degree of 1. The very common and usual equation used to define the regression is; 

y = mx+b

In this equation, m is the slope, and b is the y-intercept. One can easily write this as 

f(x) = c0 + c1 x where c1 is the slope and the c0 is the y-intercept. 

Implementation of Polynomial Regression using Python

Polynomial regression defines the non-linear phenomenons, such as:

  • Progression of disease epidemics. 
  • The growth rates of several tissues. 
  • The distribution of carbon isotopes in the lake sediments. 

The primary goal of regression analysis is to model the expected value of y, the dependent variable, in terms of the importance of an independent variable, x. 

  • Steps for Polynomial Regression

Find the steps below to use polynomial regression in machine learning and make the most of it. 

Step 1: At this step, you need to import the libraries and datasets that will.be used to perform polynomial regression. 

Step 2: The dataset needs to be divided into two components, x and y. The columns in X will be 1 and 2, and the columns in Y will be the two columns. 

Step 3: The linear regression model must be fitted into two components. 

Step 4: The polynomial regression model needs to be fitted in two components: x and y. 

Step 5: With the help of a scatter plot, one will visualize linear regression results. 

Step 6: The polynomial regression will also be viewed in this step using a scatter plot. 

Step 7: New results will now be predicted using Linear and Polynomial regression. 

Advantage – Polynomial Regression

  • The polynomial regression is flexible enough to get fitted in a vast range of curvatures. 
  • A broad range of functions can easily fit under it. 
  • The polynomial regression offers the best approximation of the relationship between the two dependent and independent variables. 

Disadvantage – Polynomial Regression

  • The presence of one or more outliers in the data can hurt the final results of the nonlinear analysis. 
  • The polynomial regression is very sensitive to the outliers. 
  • Very few model validation tools are available that help detect the outliers in nonlinear regression compared to the ones present for linear regression. 

Our Learners Also Ask

1. What is meant by polynomial regression?

Polynomial regression is a particular case of linear regression where a polynomial regression is fit into the data with the help of a curvilinear relationship shared by the independent variables and the target variable. 

2. How do you solve polynomial regression in machine learning?

With the help of predictions, polynomial regression is solved in machine learning. 

3. What is the use of polynomial regression?

Polynomial regression is only used when there is no linear correlation between the two variables. This is how it explains why it is more like the nonlinear functions. 

4. What are the advantages of polynomial regression?

The polynomial regression best approximates the relationship between the dependent and independent variables. A broad range of functions can easily fit under it. Also, it can easily fit a vast range of curvatures. 

5. What is the difference between linear regression and polynomial regression?

Polynomial regression with only one variable term is known as linear regression. That said, polynomial regressions with more than one variable term have names. 

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The concept of polynomial regression is not that tough but is not so easy as well. You will have to pay attention to the steps and every detail to clearly understand the whole concept and find the result. It is a machine learning model that helps to model the nonlinear relationships between independent and dependent variables. 

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