Basics of Multivariate Analysis I (Regression Analysis): Theory and Exercise using R

Many introductory books about regression analysis using R have been published. Those books describe how to use, for example, the lm() function of R. The unique feature of this book is that step-by-step it explains the background theory of lm() function of R and helps readers carry out the identification of regression models from simple examples to complex ones.

The prerequisites for readers to read this book are: the basics of differentiation; the basics of vector; i.e. inner product of vectors; the basics of matrix, including product, transpose, inverse, and Eigen values of matrices.

Scripts used in this book can be downloaded from http://www.mybook-pub-site.sakura.ne.jp/multi_variate_analysis/reg_analysis/index.html. This book uses R 3.0.2 for Windows. The software can be downloaded from http://cran.r-project.org/ for free. This book uses the Windows versions of scripts. Mac users only have to change the file path to load data files.


1. Introduction

2. Simple Linear Regression
2.1 Basic Theory
2.2 Calculation Using R
2.3 Matrix Expression
2.4 Matrix Calculation using R
2.5 Calculation using R Function lm()
2.6 Correlation Coefficient
2.7 Coefficient of Determination}
2.8 Calculation of Correlation Coefficient and Coefficient of Determination

3. Multiple Linear Regression
3.1 Basic Theory (two Regressors)
3.2 Calculation using R
3.3 Matrix Expression (m Regressors)
3.4 Matrix Calculation using R
3.5 Calculation using R Function (lm())
3.6 Partial Regression Coefficient
3.7 Calculation of Partial Regression Coefficient using R
3.8 Multiple Coefficient of Determination
3.9 Calculation of Multiple Coefficient of Determination using R
3.10 Multicollinearity

4. Concluding Remarks

About the Author
Professor, Dept. of Computational Science and Eng., Nagoya University