Polynomial regression

Polynomial regression, also known as nonlinear regression, is an advanced machine learning technique used to predict continuous output from given input data. It is a type of regression analysis in which the dependent variable (the one being predicted) is a polynomial of an independent variable (the one being used to make predictions). Unlike linear regression, which models data using a straight line, polynomial regression curves data instead. This means that polynomial regression can capture more complex relationships between variables compared to linear regression.

Polynomial regression models are used in various applications, including prediction, forecasting, optimization and uncertainty quantification. It is a particularly useful tool for predicting values beyond the range of collected data, and can be used to model non-linear relationships in data.

In order to fit a polynomial regression model, the user will first need to define the degree of the polynomial (the highest power of the independent variable), and then generate a set of curves that each model the data with varying degrees of complexity. The user will then select the model that best fits the data, using metrics such as Mean Squared Error (MSE) and R². Once the degree of the best-fitting polynomial is known, the coefficients for each term in the equation can be estimated.

Polynomial regression is an advanced tool for predicting and modeling complex relationships in data, and is commonly used in a wide range of applications, including engineering, economics, and finance. It is important to note, however, that polynomial regression models should only be used when there is sufficient data to generate reliable models; otherwise, the results may be unreliable.