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

Robust linear regression


So far, we have used the Ordinary Least Squares (OLS) estimates for our linear regression models. But these models only become valid when all regression hypotheses are verified. If this is not the case, least squares regression can be problematic. In such cases we can try to locate the problems through residual diagnostics, but this procedure may be slow and requires a great deal of experience. Often, model-fitting problems are due to the presence of extreme values ​​called outliers. The following figure shows a distribution with outliers:

Outliers have a large influence on the fit, because squaring the residuals magnifies the effects of these extreme data points. Outliers tend to change the direction of the regression line by getting much more weight than they are worth. Thus, the estimate of the regression coefficients is clearly distorted. These effects are difficult to identify since their residuals are much smaller than they would be if the distortion wasn't...