zoom 30 x 200 matrix for red: r(red) g(green) b(blue) frequency for red: 0 0 1

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30 x 200 Matrix for Red:

R(red) G(green) B(blue)

Frequency for red:pixel freq %

254 3967 66.117216 718 11.967247 293 4.8833157 157 2.6167253 73 1.2167

00

1254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 254 216 254 254 254 254 254 254 254 254 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30 x 200 Matrix

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 00 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 00 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 00 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 00 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 00 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 00 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

CUT

0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 00 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 10 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 10 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 00 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 00 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 00 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 00 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 00 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 00 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 01 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 01 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 00 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 00 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0

CUT

0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 00 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 10 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 10 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 00 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 00 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 00 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 00 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 00 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 00 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 01 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 01 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 00 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 00 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0

for i=1:n for j=1:m if x(i,j)==1 for i1=(i+1):n k=abs(i-i1); for j1=(j+1):m if x(i1,j1)==1 dist(k+abs(j-j1)) =dist(k+abs(j-j1))+1; end end end end endend

n x m matrix:Calculate distance distribution:into array dist(100)

0 01 1382 2403 3164 3715 4176 4507 4698 4849 494

10 49411 48412 46713 43914 40115 34916 29117 23418 18019 13020 8321 4922 2523 1124 325 0

Z 138 240 316 371 417 450 469 484 494 494 484 467 439 401 349 291 234 180 130 83 49 25 11 3 0 0

Dataset ccc cccc x25 x26 x27 x28 x29 x30 x31 x32 x33 x34 x35 x36 x37 x38 x39 x40 x41 x42 x43 x44 x45 x46 x47 x48 x49 x50 x51 x52

I 9 115 205 280 333 370 391 397 397 386 374 355 341 319 298 274 252 227 200 168 135 100 70 48 31 19 11 6 21 28 111 193 253 287 297 285 253 221 188 157 130 107 86 69 55 45 38 31 22 13 8 5 4 2 1 0 0 0Y 25 132 236 316 378 424 456 476 487 489 483 468 447 422 395 367 336 306 268 226 183 147 114 87 66 48 34 24 165 32 141 244 316 369 405 430 453 472 480 479 470 456 425 384 333 277 219 161 109 70 39 17 6 0 0 0 0 0F 6 158 274 364 442 501 538 560 572 576 568 541 505 466 421 376 335 294 250 198 151 111 79 55 36 23 14 8 4O 15 190 331 432 494 530 552 569 588 614 646 676 711 729 734 724 705 674 616 543 462 366 262 172 100 48 16 0 00 27 165 281 355 408 448 475 502 543 599 658 699 715 710 683 633 556 454 348 253 170 102 51 16 2 0 0 0 0Y 25 134 232 316 381 425 455 475 485 486 476 462 444 420 390 361 333 307 266 224 186 155 127 100 77 58 43 31 22R 18 218 397 548 673 774 852 909 968 1027 1065 1079 1071 1040 986 912 825 731 633 542 461 389 326 272 221 179 140 107 80S 19 150 254 331 395 448 498 537 564 583 586 583 564 524 467 405 343 296 256 215 172 128 89 50 22 6 0 0 08 35 139 234 308 368 422 476 514 550 573 584 567 526 463 400 348 302 275 242 207 164 120 75 38 12 0 0 0 0A 1 126 225 303 366 415 452 474 480 475 464 443 418 386 351 316 280 241 203 165 130 101 75 56 40 27 17 9 46 33 176 307 417 501 567 619 667 712 742 748 731 694 644 584 518 452 385 313 240 166 104 57 25 6 0 0 0 05 32 142 250 329 387 426 454 475 490 499 504 502 496 486 463 434 385 320 252 187 133 91 57 31 14 4 0 0 0B 2 226 401 540 651 740 808 864 926 988 1037 1064 1065 1041 994 928 851 770 680 589 507 428 353 285 224 172 129 93 65N 14 147 261 350 426 488 523 550 567 579 589 599 595 581 568 552 517 472 419 362 309 261 216 175 139 106 79 58 435 32 136 235 309 362 402 433 457 478 485 479 460 437 408 367 320 264 217 162 116 77 44 23 9 4 0 0 0 01 28 108 195 262 308 335 345 337 325 310 293 274 253 232 209 186 163 140 114 89 67 48 33 22 15 9 6 4 24 31 113 193 269 336 384 411 422 422 417 405 382 353 316 269 217 170 128 88 54 32 18 8 2 0 0 0 0 0U 21 128 212 276 311 326 322 310 307 321 343 367 382 395 404 401 381 341 304 252 203 158 123 91 65 42 33 23 16E 5 162 271 352 421 480 522 536 566 602 631 634 623 609 582 556 529 493 436 373 311 248 201 161 122 87 66 47 35

Consider only two letters for nowdata bb; set aa; if ccc in ("1","O"); run;

proc princomp out=pred; var x25-x66; run;

proc gplot; plot prin1*prin2=ccc; run;

1 and O

1 and A

1 and I

Logistic regression distance distribution

proc logistic data=bb; model ccc=x25-x66; output out=pred1 p=p;run;data pred2; set pred1; if p>0.5 then a="1"; else a="A";

run;proc freq; table ccc*a; run;

Using distance distribution

Predicted by logistic model

True:

Using distance distribution

Predicted by logistic model

True:

More statistics0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 00 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 10 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 10 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 00 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 00 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 00 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 00 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 00 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 00 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 00 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 01 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 01 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 00 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 00 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0

n x m matrix:

•Block Sums (4 sums)

2 3 4 5 10 13 16 16 14 14 15 13 12 14 14 15 15 14 14 11 6 3 3 2

49 6970 49

•Column Sums (use first 20 sums)

x1-x4

x5-x24

Using sums and distance

%macro testtwo(char1, char2);data bb; set aa; if ccc in ("&char1","&char2"); run;proc princomp out=pred; var x&start-x66; run;proc gplot; plot prin1*prin2=ccc; run;proc logistic data=bb; model ccc=x&start-x66; output out=pred1 p=p;run;data pred2; set pred1; if p>0.5 then a="&char1"; else a="&char2";

run;proc freq; table ccc*a; run;%mend;%let start=1; %testtwo(1,I);

Using distance distribution

True:

Using both

More than two letters

• 26 letters + 10 digits = 36 categories

• Two stages: • Stage 1 - Nominal Responses: Baseline-

Category Logit Model• Stage 2 – if predicted value belong to, for

example, 1 or I, then using two-level logistic regression to further classify it.

Stage 2: based on the error transition probability

• 1 and I• 4, A, and V• D, H, M, W• S -> 8• Q -> O• 6, 9, and 0

Per 0 1 2 3 4 5 6 7 8 9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Total

0 2.63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.63

1 0 2.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.74

2 0 0 2.87 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.87

3 0 0 0 2.63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.63

4 0 0 0 0 2.43 0 0 0 0 0 0.04 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.47

5 0 0 0 0 0 2.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.8

6 0.17 0 0 0 0 0 2.86 0 0 0.11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.13

7 0 0 0 0 0 0 0 2.86 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.86

8 0 0 0 0 0 0 0 0 2.82 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.82

9 0 0 0 0 0 0 0.44 0 0 2.32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.76

A 0 0 0 0 0.07 0 0 0 0 0 2.63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.22 0 0 0 0 2.93

B 0 0 0 0 0 0 0 0 0 0 0 2.98 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.98

C 0 0 0 0 0 0 0 0 0 0 0 0 3.02 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.02

D 0 0 0 0 0 0 0 0 0 0 0 0 0 2.98 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.98

E 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.73 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.73

F 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.52 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.04 0 2.56

G 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.82 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.82

H 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3 0 0 0 2.34 0 0 0 0 0 0 0 0 0 0.02 0 0 0 0 0 0 0 0 2.65

I 0 0.57 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.02

J 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.91 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.91

K 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.91 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.91

L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.89 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.89

M 0 0 0 0 0 0 0 0 0 0 0 0 0 0.07 0 0 0 0.04 0 0 0 0 2.54 0 0 0 0 0 0 0 0 0 0.13 0 0 0 2.78

N 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.69 0 0 0 0 0 0 0 0 0 0 0 0 2.69

O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.54 0 0 0 0 0 0 0 0 0 0 0 2.54

P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.1 0 0 0 0 0 0 0 0 0 0 3.1

Q 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.13 0 2.43 0 0 0 0 0 0 0 0 0 2.56

R 0 0 0 0 0 0 0 0 0 0 0 0.07 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.47 0 0 0 0 0 0 0 0 2.54

S 0 0 0 0 0 0 0 0 0.2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.52 0 0 0 0 0 0 0 2.73

T 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.8 0 0 0 0 0 0 2.8

U 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.52 0 0 0 0 0 2.52

V 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.43 0 0 0 0 3.43

W 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.74 0 0 0 1.74

X 0 0 0 0 0 0 0 0 0 0 0.02 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.78 0 0 2.8

Y 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.06 0 3.06

Z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.6 2.6151 171 155 142 135 151 178 154 163 131 145 165 163 181 147 136 152 128 140 157 157 156 137 145 144 167 131 134 136 151 136 197 101 150 167 140 5394

2.8 3.17 2.87 2.63 2.5 2.8 3.3 2.86 3.02 2.43 2.69 3.06 3.02 3.36 2.73 2.52 2.82 2.37 2.6 2.91 2.91 2.89 2.54 2.69 2.67 3.1 2.43 2.48 2.52 2.8 2.52 3.65 1.87 2.78 3.1 2.6 100

Total

proc DISCRIM data=aa out=discout method=normal outstat=distat;

class ccc; var x1-x66; run;proc freq data=discout; table

ccc*_into_/nofreq nocol norow; run;

Row P

0 1 2 3 4 5 6 7 8 9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 94.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

4 0 0 0 0 98.5 0 0 0 0 0 1.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

6 5.33 0 0 0 0 0 91.1 0 0 3.55 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

7 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

8 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 0 0 0 0 0 0 16.1 0 0 83.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

A 0 0 0 0 2.53 0 0 0 0 0 89.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7.59 0 0 0 0

B 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

C 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

D 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

E 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

F 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 98.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.45 0

G 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H 0 0 0 0 0 0 0 0 0 0 0 0 0 11.2 0 0 0 88.1 0 0 0 0 0 0 0 0 0 0.7 0 0 0 0 0 0 0 0

I 0 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 81 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

J 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

K 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0

M 0 0 0 0 0 0 0 0 0 0 0 0 0 2.67 0 0 0 1.33 0 0 0 0 91.3 0 0 0 0 0 0 0 0 0 4.67 0 0 0

N 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0

O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0

P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0

Q 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.07 0 94.9 0 0 0 0 0 0 0 0 0

R 0 0 0 0 0 0 0 0 0 0 0 2.92 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97.1 0 0 0 0 0 0 0 0

S 0 0 0 0 0 0 0 0 7.48 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 92.5 0 0 0 0 0 0 0

T 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0

U 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0

V 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0

W 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0

X 0 0 0 0 0 0 0 0 0 0 0.66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 99.3 0 0

Y 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0

Z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100

Total

151 171 155 142 135 151 178 154 163 131 145 165 163 181 147 136 152 128 140 157 157 156 137 145 144 167 131 134 136 151 136 197 101 150 167 140

Col Pct

0 1 2 3 4 5 6 7 8 9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

0 94 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 81.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5.71 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

4 0 0 0 0 97 0 0 0 0 0 1.38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

6 5.96 0 0 0 0 0 86.5 0 0 4.58 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

7 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

8 0 0 0 0 0 0 0 0 93.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 0 0 0 0 0 0 13.5 0 0 95.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

A 0 0 0 0 2.96 0 0 0 0 0 97.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6.09 0 0 0 0

B 0 0 0 0 0 0 0 0 0 0 0 97.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

C 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

D 0 0 0 0 0 0 0 0 0 0 0 0 0 89 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

E 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

F 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.2 0

G 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H 0 0 0 0 0 0 0 0 0 0 0 0 0 8.84 0 0 0 98.4 0 0 0 0 0 0 0 0 0 0.75 0 0 0 0 0 0 0 0

I 0 18.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 94.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

J 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

K 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0

M 0 0 0 0 0 0 0 0 0 0 0 0 0 2.21 0 0 0 1.56 0 0 0 0 100 0 0 0 0 0 0 0 0 0 6.93 0 0 0

N 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0

O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 95.1 0 0 0 0 0 0 0 0 0 0 0

P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 0

Q 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.86 0 100 0 0 0 0 0 0 0 0 0

R 0 0 0 0 0 0 0 0 0 0 0 2.42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 99.3 0 0 0 0 0 0 0 0

S 0 0 0 0 0 0 0 0 6.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0

T 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0

U 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 0

V 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 93.9 0 0 0 0

W 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 93.1 0 0 0

X 0 0 0 0 0 0 0 0 0 0 0.69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0

Y 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 98.8 0

Z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100

Tot 151 171 155 142 135 151 178 154 163 131 145 165 163 181 147 136 152 128 140 157 157 156 137 145 144 167 131 134 136 151 136 197 101 150 167 140