# from "data" by herzberg and andrews The data from eight trees from each of six apple tree rootstocks are from table 6.2 of Rencher and Christensen ( 2012 ). Four dependent variables are recorded for each tree: trunk girth at 4 years (mm 100), extension growth at 4 years (m), trunk girth at 15 years (mm 100), and weight of tree above ground at 15 years (lb 1000). The grouping variable is rootstock , and the four dependent variables are y1 , y2 , y3 , and y4 60 1 1 I 111 2569 358 760 60 1 2 I 119 2928 375 821 60 1 3 I 109 2865 393 928 60 1 4 I 125 3844 394 1009 60 1 5 I 111 3027 360 766 60 1 6 I 108 2336 351 726 60 1 7 I 111 3211 398 1209 60 1 8 I 116 3037 362 750 60 1 9 II 105 2074 409 1036 60 1 10 II 117 2885 406 1094 60 1 11 II 111 3378 487 1635 60 1 12 II 125 3906 498 1517 60 1 13 II 117 2782 438 1197 60 1 14 II 115 3018 465 1244 60 1 15 II 117 3383 469 1495 60 1 16 II 119 3447 440 1026 60 1 17 III 107 2505 376 912 60 1 18 III 99 2315 444 1398 60 1 19 III 106 2667 438 1197 60 1 20 III 102 2390 467 1613 60 1 21 III 115 3021 448 1476 60 1 22 III 120 3085 478 1571 60 1 23 III 120 3308 457 1506 60 1 24 III 117 3231 456 1458 60 1 25 IV 122 2838 389 944 60 1 26 IV 103 2351 405 1241 60 1 27 IV 114 3001 405 1023 60 1 28 IV 101 2439 392 1067 60 1 29 IV 99 2199 327 693 60 1 30 IV 111 3318 395 1085 60 1 31 IV 120 3601 427 1242 60 1 32 IV 108 3291 385 1017 60 1 33 V 91 1532 404 1084 60 1 34 V 115 2552 416 1151 60 1 35 V 114 3083 479 1381 60 1 36 V 105 2330 442 1242 60 1 37 V 99 2079 347 673 60 1 38 V 122 3366 441 1137 60 1 39 V 105 2416 464 1455 60 1 40 V 113 3100 457 1325 60 1 41 VI 111 2813 376 800 60 1 42 VI 75 840 314 606 60 1 43 VI 105 2199 375 790 60 1 44 VI 102 2132 399 853 60 1 45 VI 105 1949 334 610 60 1 46 VI 107 2251 321 562 60 1 47 VI 113 3064 363 707 60 1 48 VI 111 2469 395 952 60 1 49 VII 96 2091 266 414 60 1 50 VII 91 1583 241 335 60 1 51 VII 120 4099 380 885 60 1 52 VII 110 3383 401 1012 60 1 53 VII 102 2785 296 489 60 1 54 VII 105 2785 315 616 60 1 55 VII 110 3387 358 788 60 1 56 VII 108 3082 343 733 60 1 57 IX 83 1344 231 375 60 1 58 IX 90 2247 250 410 60 1 59 IX 87 1426 219 335 60 1 60 IX 94 2211 275 560 60 1 61 IX 69 877 205 251 60 1 62 IX 84 1431 213 272 60 1 63 IX 90 1863 266 478 60 1 64 IX 90 2001 226 278 60 1 65 X 105 1964 299 506 60 1 66 X 117 2516 381 882 60 1 67 X 113 3016 362 737 60 1 68 X 113 3424 372 772 60 1 69 X 122 3174 369 827 60 1 70 X 109 2865 368 821 60 1 71 X 117 3634 408 1149 60 1 72 X 122 3393 410 1035 60 1 73 XII 129 4387 431 1609 60 1 74 XII 135 4166 465 1658 60 1 75 XII 138 4595 484 1789 60 1 76 XII 142 5131 527 2375 60 1 77 XII 132 4041 463 1556 60 1 78 XII 123 3848 412 1418 60 1 79 XII 142 5471 514 2266 60 1 80 XII 144 5956 522 2508 60 1 81 XIII 121 3705 387 1052 60 1 82 XIII 120 2886 414 1167 60 1 83 XIII 123 3856 387 981 60 1 84 XIII 109 2763 390 944 60 1 85 XIII 100 2223 327 737 60 1 86 XIII 116 2905 424 1392 60 1 87 XIII 117 3590 421 1326 60 1 88 XIII 105 2516 382 1052 60 1 89 XV 122 3484 448 1258 60 1 90 XV 116 2730 435 1304 60 1 91 XV 124 3924 451 1290 60 1 92 XV 122 3580 450 1288 60 1 93 XV 125 3355 428 1176 60 1 94 XV 122 3694 424 1177 60 1 95 XV 126 4698 482 1331 60 1 96 XV 119 3566 469 1490 60 1 97 XVI 126 4299 452 1499 60 1 98 XVI 113 3432 412 1412 60 1 99 XVI 113 3357 425 1488 60 1 100 XVI 138 5475 460 1751 60 1 101 XVI 127 4482 464 1937 60 1 102 XVI 115 3333 457 1823 60 1 103 XVI 120 3960 463 1838 60 1 104 XVI 119 4040 473 1817