Regression analysis

Regression analysis is a technique used to analyze a series of data that consists of a dependent variable and one or more independent variables. The purpose is to estimate a possible functional relationship between the dependent variable and the independent variables. Using this technique, we can build a model in which a continuous response variable is a function of one or more predictors.

In the Statistics and Machine Learning Toolbox, there are a variety of regression algorithms, including:

• Linear regression
• Nonlinear regression
• Generalized linear models
• Mixed-effects models

A scatter plot of the linear regression model is shown in the following figure.

To study the relationship between two variables, a scatter plot is useful, in which we show the values of the independent variable X on the horizontal axis and the values of the dependent variable Y on the vertical axis. Using a regression model, we can express the relationship between two variables with functions that are more or less complex. Simple linear regression is suitable when the values of X and Y are distributed along a straight line in the scatter plot (Figure 1.17).