Book Image

Regression Analysis with R

By : Giuseppe Ciaburro
Book Image

Regression Analysis with R

By: Giuseppe Ciaburro

Overview of this book

Regression analysis is a statistical process which enables prediction of relationships between variables. The predictions are based on the casual effect of one variable upon another. Regression techniques for modeling and analyzing are employed on large set of data in order to reveal hidden relationship among the variables. This book will give you a rundown explaining what regression analysis is, explaining you the process from scratch. The first few chapters give an understanding of what the different types of learning are – supervised and unsupervised, how these learnings differ from each other. We then move to covering the supervised learning in details covering the various aspects of regression analysis. The outline of chapters are arranged in a way that gives a feel of all the steps covered in a data science process – loading the training dataset, handling missing values, EDA on the dataset, transformations and feature engineering, model building, assessing the model fitting and performance, and finally making predictions on unseen datasets. Each chapter starts with explaining the theoretical concepts and once the reader gets comfortable with the theory, we move to the practical examples to support the understanding. The practical examples are illustrated using R code including the different packages in R such as R Stats, Caret and so on. Each chapter is a mix of theory and practical examples. By the end of this book you will know all the concepts and pain-points related to regression analysis, and you will be able to implement your learning in your projects.
Table of Contents (15 chapters)
Title Page
Packt Upsell
Contributors
Preface
Index

Understanding logistic regression


In linear regression, the dependent variable y (response variable) is continuous and its estimated value can be thought of as a conditional mean estimation for each value of x. In this case, it is assumed that the variable y is distributed according to normal distribution. When the dependent variable is dichotomous, and can be coded as having two values, zero or one (such as on = one, off = zero), the theoretical distribution of reference should not be normal but binomial distribution.

In fact, as we have seen in Chapter 2Basic Concepts – Simple Linear Regression, the linear model is based on the following regression equation:

Here, the values of the dependent variable can go from -∞ to +∞. All this does not agree with the expected values for a dichotomous variable, which as we have said, assumes only two values (0;1).

Let's try to understand this concept better by analyzing a simple example. Let's suppose we've put the data of a certain observation on a...