Source: Manly, Bryan F.J. Multivariate Statistical Methods: A Primer, Third Edition, CRC Press,07/2004.Page 1 of 1Tutorial – Week 8 (CCA)Question 1:a) What is the goal of CCA? Explain the CCA process.b) Why can’t multiple regression or MANOVA be used to do the same thing as CCA?c) Why might it be better to interpret the correlations between canonical variatesand variables as the variate loadings rather than the variates coefficients?d) What is the redundancy index?e) What three criteria should you use in deciding which canonical functions shouldbe interpreted?Question 2:Below are the loadings and plot from the week 10 lecture.Structural Correlations (Loadings):X Vars:CV 1 CV 2 CV 3 CV 4X1 0.56500103 0.1999069 0.0003682975 0.80050667X2 -0.06308064 -0.6888603 -0.7211485117 0.03791011X3 0.41898770 0.2274037 -0.1662912582 -0.86318254X4 -0.36068909 -0.5793048 0.7065760097 -0.18724236Y Vars:CV 1 CV 2 CV 3 CV 4Y1 0.79822609 0.54842546 -0.06679338 -0.24000680Y2 -0.40035051 -0.88894455 -0.22093666 -0.02615429Y3 0.03562821 -0.16627171 0.94578747 -0.27671359Y4 0.10806174 0.01343353 0.25456389 0.96090552The coordinates for each X and Y variable should be given by the loadings of theoriginal variables on the 2 dimensions (CVs). For example, variable X1 should belocated at 0.565 on CV1 and 0.2 on CV2, however this is not the case. Rememberthat this figure was produced using the CCA package and the loadings wereproduced from the yacca package.Find the loadings given by the CCA package and check that the figure makes sensegiven those loadings. Explain why they differ from the yacca results and why itdoes not make a difference to our interpretation of the analysis.Question 3:Complete the exercise at the end of Chapter 10 of Manly using the data set‘proteinemploy.dat’.Assume the assumption of MVN is not violated.Question 4:Prove that the structural correlations (Loadings) produced by the yacca packagecca function are equal to the correlation between the original variables and thecanonical variates. Think about the dimensions of the data matrices you need toperform the correlation and the dimensions of the structural correlations matrix.
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