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Sample text
An important property of the multivariate nOllllal distribution is that a linear transfOlIllation of a multivariate normal vector yields a multivariate normal vector; that is, if x - Nm eJ1, 0) and A is a px m matrix of constants, then y = Ax • has a p-variate normal distribution. 9) we know that y - N"eAJ1, AOA'). One of the most widely used procedures in statistics is regression analysis. We will briefly describe this analysis here and subsequently use regression analysis to illustrate some of the matrix methods developed in this text.
S , is t a th ; S in r orthogonal to every vecto YES}. 15. I f . m R f o e c a p s b u s r to c e v a o ls ment S1. is a y n a r fo 0 ::: y ; x ::: y ~ x t a th o s 1. S e 2 X d n a 1. S e I X t Proof Suppose tha e v a h e w , i2 C d n a il C rs la a c s y n a d n a S e y y n a r fo , y Y E S . ,. , , , , I, , • and so (C iI X I + C i2 X 2 ) E o . e c a p s r to c e v a is . 1 S s S1. and thu , I · ,,• , , f o e c a p s b u s r to c e v a is S if t a th is m re o e th g in w o ll fo A consequence o f the r.
G( dia = G d an 2 = III if e. pl am ex r Fo 1. 1. \ thell a large value of (x n tha er all sm is x of nt ne po m co st fir e th of e nc ria va of (X2 - 1-'2)2 because the g in fin de in le ab on as re s em se it is, t tha ; nt ne po m co the variance of the second te ria op pr ap e or m A )2. 1-'2 (X2 on an th )2 1 1-' I (X on distance to put more weight distance function is given by . , •. I.. I. d an x n ee tw be also referred to as the distance sis aly an t an in rim sc di as n ow kn e ur ed oc pr al tic tis sta e iat ar useful in a multiv e nc sta di s thi I = {} if at th te No ].
