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  3. Multivariate Probability Distributions in R
  • 1

    Reading and plotting multivariate data

    Gratuito

    In this introduction to multivariate data, you will learn how to read and summarize it. You will learn how to summarize multivariate data using descriptive statistics, such as the mean vector, variance-covariance, and correlation matrices. You'll then explore plotting techniques to provide insights into multivariate data.

  • 2

    Multivariate Normal Distribution

    This chapter will introduce you to the most important and widely used multivariate probability distribution, the multivariate normal. You will learn how to generate random samples from a multivariate normal distribution and how to calculate and plot the densities and probabilities under this distribution. You will also learn how to test if a dataset follows multivariate normality.

  • 3

    Other Multivariate Distributions

    This chapter introduces a host of probability distributions to model non-normal data. In particular, you will be introduced to multivariate t-distributions, which can model heavier tails and are a generalization of the univariate Student's t-distribution. You will be introduced to various skew distributions, which are specifically designed to model data that are right or left skewed.

  • 4

    Principal Component Analysis and Multidimensional Scaling

    In the final chapter, you will be introduced to techniques for analyzing high dimensional data, including principal component analysis (PCA) and multidimensional scaling (MDS). You will also learn to implement these techniques by analyzing data.

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Exercicio

Visualizing PCA using the factoextra library

The factoextra library provides a number of functions which make it easy to extract and visualize the output of many exploratory multivariate data analyses, including PCA. In this exercise, you will use several functions to visualize the scores and PC loadings of the state.x77 dataset.

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  • Using the fviz_pca_ind() function, plot the scores of the first two components of the state.x77 dataset.