By Theodore W. Anderson
Perfected over 3 variations and greater than 40 years, this box- and classroom-tested reference:* makes use of the tactic of extreme chance to a wide volume to make sure average, and in certain cases optimum procedures.* Treats all of the uncomplicated and critical subject matters in multivariate statistics.* provides new chapters, in addition to a few new sections.* offers the main methodical, up to date info on MV information on hand.
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Extra resources for An Introduction to Multivariate Statistical Analysis (Wiley Series in Probability and Statistics)
Consists of p - q numbers. 2 = l:1l -l: 12 l: Z21l:21' (6) It should be noted that the mean of X(I) given x(2) is simply a linear function of X(2), and the covariance matrix of X(I) given X(2) does not depend on X(2) at all. 1. The matrix ~ ficients of X(ll on X(2). = l: 12l:Z21 is the matrix of regression coef- The element in the ith row and (k - q )th column of ~ = l: 12 l:Z21 is often denoted by (7) i=l, .. q+ I ..... k+ I ..... p' k=q+l, ... ,p. LII) + ~(x(2) - 1-1-(2») is called the regression function.
Q+1, .. = , cr.. ll·q+I ..... 2 "q+I" .. ,p ) a:II' .. This shows incidentally that any partial variance of a component of X cannot be greater than the variance. 5 CONDmONAL DISTRIBUTIONS; MULTIPLE CORRELATION 39 reduction in variance on going to the conditional distribution. This fact is another reason for considering tiIe multiple correlation coefficient a measure of association between Xi and X(2). That ~(i)X(2) is the best linear predictor of Xi and has the maximum correlation between Xi and linear functions of X(2) depends only on the covariance structure, without regard to normality.
Cra r( a' X (2) - . 4. The maximum co"elation between Xi and the linear combination a' X(2) is called the multiple correlation coefficient between Xi and X(2). 'Q+1, .. = , cr.. ll·q+I ..... 2 "q+I" .. ,p ) a:II' .. This shows incidentally that any partial variance of a component of X cannot be greater than the variance. 5 CONDmONAL DISTRIBUTIONS; MULTIPLE CORRELATION 39 reduction in variance on going to the conditional distribution. This fact is another reason for considering tiIe multiple correlation coefficient a measure of association between Xi and X(2).