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

Nonlinear least squares


In Chapter 3More Than Just One Predictor – MLR, we have already handled a case in which a linear regression was unable to model the relationship between the response and predictors. In that case, we solved the problem by applying polynomial regression. When the relationships between variables are not linear, three solutions are possible:

  • Linearize the relationship by transforming the data
  • Fit polynomial or complex spline models
  • Fit a nonlinear model

The first two solutions you have already faced in somemanner in the previous chapters. Now we will focus on the third solution. If the parameters of the regression function to be estimated are nonlinear, that is, they appear at a different degree from the first, the Ordinary Least Squares (OLS) can no longer be applied and other methods need to be applied.

In the multiple nonlinear regression models, the dependent variable is related to two or more independent variables as follows:

Here, the model is not linear with respect...