fundamentals of statistical learnin

A discriminant analysis was carried out on a data set of size 80 in order to classify observa- tions of the form (X1, X2, X3, X4, X5) into three groups. i) The table below gives the average of each of the 5 variables within each group. Looking at these values, is there any hope that a discriminant analysis can be successful? Provide a short justification. K Xkl X K2 X k3 XKA Xk5 -0.155 0.202 -0.003 -0.909 -0.952 2 0.227 0.050 0.091 0.067 0.084 3 0.505 -0.313 -0.092 0.475 0.776 ii) The matrices S, W and B described in the course notes are given below. Three values are missing, denoted AAAAA, BBBBB, and CCCCC. What are they? Matrix S: [, 1] [, 2] [,3] [, 4] [, 5] [1,] 62. 8029695 AAAAA -4. 471622 -0. 3359447 10.369236 [2,] AAAAA 81 . 038586 26.437970 -4. 6206012 7. 087506 [3, ] -4. 4716215 26. 437970 80.626818 12. 6439431 -6. 670094 [4, ] -0. 3359447 -4.620601 12. 643943 85.5572762 30. 720944 [5,] 10.3692360 7. 087506 -6.670094 30. 7209436 88. 442644 Matrix W: [, 1] [, 2] [,3] [,4] [,5] [1,] 56. 401092 10.81546 -3. -13. 814659 -6. [2,] 10.815459 76.90362 25. 490769 5. 371660 19. 919442 [3,] -3.671480 25.49077 80. 197630 13.933547 -4. 655554 -13. 814659 5.37166 13.933547 56. 704695 BBBBB [5,] -6.382273 19.91944 -4. 655554 BBBBB 44. 590677 Matrix B: [, 1] [,2] [, 3] [, 4] [, 5 [1,] 6. 4018771 -4. 934314 -0. 8001411 13. 478714 16.75151 [2,] -4.9343145 4. 134966 0. 9472010 CCCcc -12. 83194 [3,] -0. 8001411 0. 947201 0. 4291877 -1.289604 -2. 01454 [4,] 13. 4787145 CCCCC -1. 2896044 28. 852581 35. 36415 [5,] 16. 7515092 -12.831936 -2. 0145400 35.364146 43. 85197iii) The two largest eigenvalues of the matrix S*1B are A1 = 0.751 and A2 = 0.011. The corresponding normed eigenvectors are 0.40 0.08 0.37 0.65 31 = 0.09 , a2 = U.28 0.44 0.64 0.71 0.29 a) What is the discriminating power of Fisher's discriminating function? b) In which group would this function classify the observation (X 1, X2, X3, X4, X 5) = (0.5, 0.5, 0,1,1)