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

Least squares regression


In the previous section, we saw an example of simple linear regression, built the model, and now have a brief description of it. Next, we will explain the results in detail. We will get started by introducing the key concepts, with another simple linear regression example; we will just use data in the form of a spreadsheet containing the number of vehicles registered in Italy and the population of the different regions. Using this data we will try to determine the line that best estimates the relationship between the population and number of registered vehicles. We can do this in various different ways; we will begin with the simplest. Previously, we said that a linear relationship is represented by the following formula:

If we have a set of observations in the form (x1, y1), (x2, y2), ... (xn, yn), for each of these pairs we can write an equation of the type just seen. In this way, we get a system of linear equations. Represent this equation in matrix form as follows...