When doing linear regression, if we include a variable that is severely correlated with our regressors, we will be inflating our standard errors for those correlated variables. This happens because, if two variables are correlated, the model can't be sure to which one it should be assigning the effect/coefficient. Ridge Regression allows us to model highly correlated regressors, by introducing a bias. Our first thought in statistics is to avoid biased coefficients at all cost. But they might not be that bad after all: if the coefficients are biased but have a much smaller variance than our baseline method, we will be in a better situation. Unbiased coefficients with a high variance will change a lot between different model runs (unstable) but they will converge in probability to the right place. Biased coefficients with a low variance will be quite stable...
R Statistics Cookbook
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R Statistics Cookbook
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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)
Preface
Free Chapter
Getting Started with R and Statistics
Univariate and Multivariate Tests for Equality of Means
Linear Regression
Bayesian Regression
Nonparametric Methods
Robust Methods
Time Series Analysis
Mixed Effects Models
Predictive Models Using the Caret Package
Bayesian Networks and Hidden Markov Models
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