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Chapter 14Multivariate Statistical Analysis - I

Package(s): `ICSNP`, `scatterplot3d`, `aplpack`, `mvtnorm`, `foreign`

Dataset(s): `cardata`, `stiff`, `iris`, `hw`, `calcium`, `mfp`, `rootstock`, `waterquality`, `pw`, `sheishu`

14.1 Introduction

In many real-world problems, data is seldom univariate. We have more than one variable, which needs a good understanding of the underlying uncertain phenomenons. Thus, we need a set of tools to handle this type of data, and this is provided by Multivariate Statistical Analysis (MSA), a branch of the subject. We saw in the previous chapters on regression, that multiple regressors explain the regressand. Sometimes experiments may need a deeper study of the covariates themselve. In particular, we are now concerned with a random vector, the characteristics of which form the crux of this and the next chapter.

In Section 14.2 we look at graphical plots, which give a deeper insight into the structure of the dataset. The core concepts of MSA are introduced in Section 14.3. Sections 14.4 and 14.5 deal with the inference problem related to the mean vectors of multivariate data, whereas inference related with the variance-covariance matrix are performed in Sections 14.7 and 14.8. Multivariate Analysis of Variance, abbreviated as MANOVA, tools are introduced and illustrated in Section 14.6 and some tests for independence of sub-vectors are addressed in Section 14.9. Advanced topics of multivariate statistical analysis are carried over to the next chapter.

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