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describe which scale you would use to measure the following random variables state reasons for your choice and whether
prove that for a symmetric matrix with strictly positive elements 1 there exists a largest unique latent root
prove theorem 213theorem 213the multivariate normal random variablesnbspxnbspinbsp x2 xknbspare mutually independent
principal components can be used as multivariate indices for example when evaluating toxicity in phase iii clinical
using theorem 315 show that pc correlation loadings extracted from a covariance matrix are identical to those from a
the use of the rationbsplinbsptrxtx as the proportion of total variance accounted for by thenbspith sample pc has the
the following data represent averages of 10 independent measurements from the herbarius at the university of british
using eq 3103a and b prove the results of theorem 317theorem 317singular value decomposition let x be a n x p data
let s nbspnbspxtx be the sample covariance matrix where l and p are latent roots and vectors of xtx respectively prove
consider the 4 x 4 covariance correlation matrix of example 32 verify the results of theorem 38 also verify that latent
nbspconsider the latent roots of table 413 in example 414a using the chi-squared criterion eq 46 test whether the
the following correlation matrix is given by allison and ciechetti 1976 in a study of sleep in mammalswhere the random
a chemical analysis of hellenistic black-glazed wares using attic and non-attic samples yields the following data
the following data representnbsppnbsp 22 physical and chemical measurements fornbspnnbsp 8 samples of crude oil
show that the canonical correlation model of theorem 58 is equivalent to the modeltheorem 58let sigma be a p x p
prove the second part of theorem 510theorem 510krzanowski 1979 letand up1h where u is a unit vector m is a diagonal
using theorem 58 prove eq 560theorem 58let sigma be a p x p partitioned covariance matrix the coefficients that
consider eq 518b where g and btnbspare orthogonally rotated components and loadings respectively theorem 52a show that
prove that the rotated principal components vrnbspof theorem 52 no longer successively account for maximum
let xprtnbspbe the generalized inverse of a n x p matrix x theorem 51 show that the following relations holdtheorem
stroud 1953 obtains the following correlation matrix fornbsppnbsp 14 body measurements of soldier termites table 617a
following theorem 66 prove that the reciprocal proportionality model section 641 is invariant with respect to scaling
consider the criminological data of table 71 example 71a repeat the analysis using 1 the matrix yty and ii the cosine
carry out a factor analysis of the vehicle fatalities data of table 76 by replacing provinces by years that is by
core samples taken from ocean floors are at times analyzed for plankton content in order to infer approximate