What is Multiple Polynomial Regression?

Multiple polynomial regression is a statistical method used to model the relationship between multiple independent variables and a single dependent variable. In contrast to simple linear regression, which only considers a linear relationship between variables, multiple polynomial regression allows for more complex relationships to be captured.

In multiple polynomial regression, the relationship between the dependent variable and the independent variables is represented by an equation in the form:

y = b0 + b1x1 + b2x1^2 + b3x2 + b4x2^2 + ... + bnxn + bnxn^2 + ... + error

where y is the dependent variable, b0 is the intercept term, b1, b2, …, bn are the coefficients for the independent variables x1, x2, …, xn, and error represents the residual error in the model.

By including higher-order terms, such as squared or cubed variables, in the regression equation, multiple polynomial regression can capture non-linear relationships between variables. This allows for more flexibility in modeling complex patterns in the data.

Multiple polynomial regression is often used in fields such as economics, biology, and engineering where relationships between variables are non-linear and more complex. It is a powerful tool for analyzing and predicting outcomes based on multiple factors.