The correlation matrix can be obtained from the covariance matrix and vice versa. Define D. = diag( $11, VS22, . . . ; Spp = diag ($1, $2, . . .,8p) 0 . . 0 0 = (3.36) Then by (2.57) R = D 'SD', (3.37)3.17 Define the following linear combinations for the variables in Table 3.4: 21 = y1 + 92 + 93 22 = 2y1 - 3y2 + 2y3 23 = -y1 - 212 - 313 (a) Find z and Sz using (3.62) and (3.64). (b) Find R, from S, using (3.37). Z y = Ay. (3.62) By an extension of (3.60), the sample covariance matrix of the z's becomes a; San a, Say a, Sak a;Sai a,Say asSax S. = (3.63) a Say a Saz ... aSak a'; (Sal. Saz. Sax) as (Sai, Say, Sax) a (Sa1, Say, .. . ; Sak) (San, Saz, . .., Sax) [by (2.47)] S(a1, az, . .., ax) [by (2.48)] P. . .. = ASA' (3.64)