1 - 10 of 13 Chapters
[WE ARE SURROUNDED by data. How is multivariate data analysis different from more familiar univariate methods? This chapter provides a summary of most of the major topics covered in this book. We also want to provide advocacy for the multivariate methods developed.]
[HE SOFTWARE PACKAGE “R” has become very popular over the past decade for good reason. It has open source, meaning you can examine exactly what steps the program is performing. Compare this to the “black box” approach adopted by so many other software packages that hope you will just push the...
[HERE ARE MANY GRAPHICAL METHODS that can be demonstrated with little or no explanation. You are likely familiar with histograms and scatterplots. Many options in R have improved on these in interesting and useful ways. The ability to produce statistical graphics is a clear strength of R....
[MANY OPERATIONS performed on multivariate data are facilitated using vector and matrix notation. In this chapter we introduce the basic operations and properties of these and then show how to perform them in R.]
[HE NORMAL DISTRIBUTION is central to much of statistics. In this chapter and the two following, we develop the normal model from the univariate, bivariate, and then, finally, the more general distribution with an arbitrary number of dimensions.]
[HE BIVARIATE NORMAL DISTRIBUTION helps us make the important leap from the univariate normal to the more general multivariate normal distribution. To accomplish this, we need to make the transition from the scalar univariate notation of the previous chapter to the matrix notation of the...
[IN THIS CHAPTER, we generalize the bivariate normal distribution from the previous chapter to an arbitrary number of dimensions. We also make use of the matrix notation. The mathematics is generally more dense and relies on the linear algebra notation covered in Chap. 4 In Sect. 4.5 we pointed...
[THE PREVIOUS CHAPTER described inference on the multivariate normal distribution. Sometimes this is more than we actually need. The multivariate distribution is used as a basis of modeling means and covariances. The covariances describe the multivariate relationship between pairs of individual...
[INEAR REGRESSION is probably one of the most powerful and useful tools available to the applied statistician. This method uses one or more variables to explain the values of another. Statistics alone cannot prove a cause and effect relationship, but we can show how changes in one set of...
[IF WE HAVE multivariate observations from two or more identified populations, how can we characterize them? Is there a combination of measurements that can be used to clearly distinguish between these groups? It is not good enough to simply say that the mean of one variable is statistically...
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