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Polynomial Regression

Polynomial Regression is a one of the types of linear regression. In this type of regression, relationship between the independent variable x and dependent variable y is graphed or represented as an nth degree polynomial. Polynomial regression can able to fit a nonlinear relationship between the value of variable x and the corresponding conditional mean of variable y, which is denoted as E (y |x).

Polynomial Regression 1 (i2tutorials)

  • It is the special case of Multiple Linear Regression as we add some polynomial terms to the Multiple Linear regression equation to transform it into Polynomial Regression.
  • It is a type of linear model with some additional changes in order to increase the accuracy of the model.
  • The dataset which is used in Polynomial regression for training is non-linear in nature.
  • This regression model makes use of a linear regression model to fit the complicated and non-linear functions and datasets.
  • In Polynomial regression, the original features are converted or transformed into Polynomial features of required degree (2, 3, …, n) and then modeled using a linear model.

Polynomial Regression 2 (i2tutorials)

The need of Polynomial Regression can be understood in the below points:

  • If we apply a linear model on a linear dataset, then it performs well and provides a good result as in Simple Linear Regression, but if we apply the same model without any additional changes on a non-linear dataset, then it will produce an extreme output. Due to this, loss function will increase, the error rate will be high, and accuracy will be reduced.
  • Hence, when the data points are arranged in a non-linear manner, we require the Polynomial Regression model.

Bias

Bias means the error due to the model’s simple assumptions in fitting the data. A high bias refers to the model which is unable to capture the patterns in the data and this leads to under-fitting of the data.

Variance

Variance means the error due to the complex model trying to fit the data. High variance refers to the model covers most of the data points and it leads to over-fitting of the data.

Polynomial Regression 3 (i2tutorials)

Merits of Polynomial Regression

  • It can able to fit Broad range of function.
  • Polynomial regression generally fits wide range of curvature.
  • Polynomial regression provides the best estimation of the relationship between dependent and independent variables.

Demerits of Polynomial Regression

  • Polynomial regression is too sensitive to the outliers.
  • If there are one or two outliers in the data, then these outliers can seriously affect the results of a nonlinear analysis.
  • There are only less model validation tools for the detection of outliers in nonlinear regression than there are for linear regression.