this is multivariate analysis

'5. We use discriminant analysis on data for two variables X1 and X3 from three groups Cl, C2 and C3. The number of observations for each of the three groups isI respectively: 1:1 2 25., 212 = 35 and 113 = 25. The sample means and comriance matrices for the different groups are.' 91 I33 1 [)3 X1 = (1.l18)* X2 = (41?) IE 2 (1:12) .2 = 25.2 22.5 s = 52.2 52.2 s = 22.2 15.2 1 22.5 12.5 ' 1 52.2 41.2 * 3 15.2 21.5 ' We also have a new observation X = {Ill1 UT. [i] {4 pts] Determine the betweengroup sum of squares matrix B and the pooled sample covariance matrix Spud used for the discriminant analysis. {11) {4 p25} Determine the rst two 11125225155515 51 f1, f5. f3 and Jr and plot them. {iii} [3 ptsj To which of the three groups would you allocate X? Justify your answer. {iv} [2 pts) In general. for a discriminant analysis with (3' groups and u observations on 1: variables, what is the maidmum number of discriminants you can use? {iv} {4 pts] In general. what is the difference between making a plot of the rst two principal components, and a plot of the rst two discriminants? W'hen would you use each