# Six Sigma Regression Regression analysis is one of the statistical tools used for assessing the relationship between two variables. It is a method that quantifies the association between the two variables for example X & Y by placing in a line or on an plane in such a way that all the points lie in a line or evenly distributed on a plane.

Regression analysis is used to depict the relationship between a variable with one or more other variables. There are different types of Regression analysis that can be used namely :

Ø  Simple Regression

Ø  Polynomial Regression

Ø  Calibration Models

Ø  Multiple Regression

Ø  Nonlinear Regression

Ø  Partial Least Squares, etc.

Simple Regression : This model has only two variables namely X & Y complying with each other. This is the simplest form of Regression Analysis. This model is applicable with both Linear & Nonlinear Regression analysis that has one variable. Simple regression model also includes Least Squares method.

Polynomial Regression : It is an nonlinear equation which that can include any number of data or terms in an equation. It is also said that Polynomial equations are not strictly nonlinear equations. Sometimes it can also be a linear equation when one variable is held as a Constant & compared with other variable. Polynomial regression is used for interpolation & graphing purposes.

Calibration Model : This is a model that includes two variables where large numbers of known values are measured & then a equation is drawn relating to the values. This equation is later used to know the unknown values by inversing the predicted value after the samples are measured.

Multiple Regression : This model defines one variable as a function to multiple number of variables. It is usually used to include data to a linear equation with two or more variables. In a nonlinear multiple regression, it is more complicated equation where variable Y is considered as a function of several X variables. Nonlinear Regression : It is a type of analysis where a nonlinear combination of the variables depends on one or more independent variables. Least Square regression models are developed for the models that are linear in the coefficients but when it needs to be used in an Nonlinear models, numerical methods has to be used.

Partial Least Squares : Partial Least Squares commonly known as PLS is designed to develop statistical models where multiple independent variables are related to multiple dependent variables. This method is useful when there are many values to be predicted. PLS is largely used by Chemical Engineers & Chemometricians.