By Richard Arnold Johnson, Dean W. Wichern

This market-leading e-book bargains a readable creation to the statistical research of multivariate observations. Its overarching target is to supply readers with the data essential to make right interpretations and choose applicable recommendations for studying multivariate information. bankruptcy themes contain points of multivariate research, matrix algebra and random vectors, pattern geometry and random sampling, the multivariate basic distribution, inferences a couple of suggest vector, comparisons of numerous multivariate capability, multivariate linear regression types, important parts, issue research and inference for dependent covariance matrices, canonical correlation research, and discrimination and category. For experimental scientists in quite a few disciplines.

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**Example text**

1 1 Mod ified scatter p l ots with (a) g ro u p of poi nts sel ected a n d (b) poi nts, i n c l u d i n g s peci m e n 2 5, deleted a n d the scatter plots resca led. 16 . . . . . . . . . • :... . . . . . . . 9 x (a) 16 . • • . • . . . (b) Outliers masked. Outliers clear. � l . . • . . • • • . . • • . • . �3 • . 12 Specimen 9 large. (d ) 9 Good view of space. x2 , x3 , x4 Th ree-d imensional perspectives fo r the l u mber stiffness data. Graphs of G rowth Cu rves When the height of a young child is measured at each birthday, the points can be plotted and then connected by lines to produce a graph.

1 04 . .. , . · . : .. , • I I • ... ' �· . 97 1 (xi ) Density . 758 . ' . •• 1 . .. . . . . ' . •••,.. I . ;·· (b) . .. �· . ·.. ·. \ . . Figure 1 . 1 0 Mod ified scatter pl ots for the paper-q u a l ity d ata with outl ier (25) (a) sel ected and (b) deleted. 22 Chapter 1 Aspects of M u ltiva riate Ana lysis points, using the (dashed) rectangle (see page 23 ) , highlights the selected points in all of the other scatter plots and leads to the display in Figure 1 . 1 1 (a) . Further checking revealed that specimens 1 6-2 1 , specimen 34, and specimens 38-41 were actually specimens from an older roll of paper that was included in order to have enough plies in the cardboard being manufactured.

Figure 1 . 14 gives the array of seven curves for weight. Some growth curves look linear and others quadratic. 15 gives a growth curve array for length. One bear seemed to get shorter from 2 to 3 years old, but the researcher knows that the steel tape mea • surement of length can be thrown off by the bear ' s posture when sedated. We now turn to two popular pictorial representations of multivariate data in two dimensions: stars and Chernoff faces. Sta rs Suppose each data unit consists of nonnegative observations on p 2 variables.