Regression analysis is a statistical process of studying the relationship between a set of independent variables (explanatory variables) and the dependent variable (response variable). Through this technique, it is possible to understand how the value of the response variable changes when the explanatory variable is varied.

Consider a group of bikers about which some information has been collected: number of years of use, number of kilometers traveled in one year, and number of falls. Through these techniques, we can find that on an average, when the number of kilometers traveled increases, the number of falls also increases. By increasing the number of years of motorcycle usage and so increasing the experience, the number of falls tends to decrease.

A regression analysis can be conducted for a dual purpose:

• Explanatory, to understand and weigh the effects of the independent variable on the dependent variable according to a particular theoretical model
• Predictive, to locate a linear combination of the independent variable to predict the value assumed by the dependent variable-optimally

This chapter shows how to perform an accurate regression analysis in a MATLAB environment. In the Statistics and Machine Learning Toolbox, there are a variety of regression algorithms, including linear regression, nonlinear regression, generalized linear models, and mixed-effects models. We will explore the amazing MATLAB interface for regression analysis including fitting, prediction, and plotting.  This interface also provides native support for dataset arrays and categorical data.  These new capabilities speed up data analysis, produce more compact and readable MATLAB code, and eliminate the requirement to manually manipulate matrices. We will cover the following topics:

• Simple linear regression
• How to get a ordinary least squares (OLS) estimation
• Methods for measuring the intercept and slope of a straight line
• Discovering techniques to perform multiple linear regression and polynomial regression
• How to perform a regression analysis with a Regression Learner App

At the end of the chapter, we will be able to perform different types of regression techniques. We will see how to apply regression methods to our own data and how a regression algorithm works. We will understand the basic concepts that regression methods use to fit equations to data using MATLAB functions, and learn to prepare data for regression analysis. We’ll also cover topics such as simple linear regression, ordinary least square estimation, correlations, and multiple linear regressions.