Book Image

R Statistics Cookbook

By : Francisco Juretig
2 (2)
Book Image

R Statistics Cookbook

2 (2)
By: Francisco Juretig

Overview of this book

R is a popular programming language for developing statistical software. This book will be a useful guide to solving common and not-so-common challenges in statistics. With this book, you'll be equipped to confidently perform essential statistical procedures across your organization with the help of cutting-edge statistical tools. You'll start by implementing data modeling, data analysis, and machine learning to solve real-world problems. You'll then understand how to work with nonparametric methods, mixed effects models, and hidden Markov models. This book contains recipes that will guide you in performing univariate and multivariate hypothesis tests, several regression techniques, and using robust techniques to minimize the impact of outliers in data.You'll also learn how to use the caret package for performing machine learning in R. Furthermore, this book will help you understand how to interpret charts and plots to get insights for better decision making. By the end of this book, you will be able to apply your skills to statistical computations using R 3.5. You will also become well-versed with a wide array of statistical techniques in R that are extensively used in the data science industry.
Table of Contents (12 chapters)

Computing ordinary least squares estimates

Ordinary least squares estimates are derived from minimizing the sum of the squared residuals. It can be proven that this minimisation leads to . It should be noted that we need to compute an inverse, and that can only be done if the determinant is different from zero. The determinant will be zero if there is a linear dependency between the variables.

It can also be proven that the beta coefficients are distributed according to a Gaussian distribution with variances equal to the diagonal elements of where is the estimated residual standard error.

How to do it...

In this exercise, we will simulate some data, and compute the estimates using both the lm function and doing the...