Problem Set 7
Sneha Nimmagadda
26 October 2018
library(plotrix)
library(faraway)## Warning: package 'faraway' was built under R version 3.6.2data("kanga")
KANGA<-data("kanga")
kangaSet <- kanga[!is.na(rowSums(kanga[,3:20])),]
print(kangaSet)## species sex basilar.length occipitonasal.length palate.length
## 2 giganteus Male 1439 1503 985
## 4 giganteus Male 1315 1367 895
## 7 giganteus Male 1294 1421 872
## 8 giganteus Male 1377 1504 954
## 10 giganteus Male 1470 1563 987
## 11 giganteus Male 1612 1699 1119
## 12 giganteus Male 1388 1500 936
## 13 giganteus Male 1575 1655 1100
## 14 giganteus Male 1717 1821 1184
## 15 giganteus Male 1587 1711 1115
## 16 giganteus Male 1604 1770 1132
## 17 giganteus Male 1630 1703 1122
## 18 giganteus Male 1490 1599 1007
## 19 giganteus Male 1552 1540 1031
## 21 giganteus Male 1840 1907 1279
## 24 giganteus Male 1702 1860 1270
## 27 giganteus Female 1262 1367 855
## 28 giganteus Female 1423 1490 971
## 29 giganteus Female 1373 1494 952
## 30 giganteus Female 1414 1517 971
## 31 giganteus Female 1415 1523 973
## 32 giganteus Female 1374 1463 927
## 33 giganteus Female 1427 1487 978
## 34 giganteus Female 1382 1494 942
## 35 giganteus Female 1440 1557 985
## 36 giganteus Female 1575 1667 1105
## 37 giganteus Female 1462 1516 1016
## 38 giganteus Female 1559 1650 1087
## 40 giganteus Female 1546 1621 1072
## 41 giganteus Female 1512 1567 1052
## 42 giganteus Female 1400 1501 1041
## 43 giganteus Female 1464 1573 1037
## 44 giganteus Female 1491 1578 1028
## 46 giganteus Female 1570 1618 1064
## 47 giganteus Female 1607 1647 1118
## 49 giganteus Female 1589 1750 1128
## 50 giganteus Female 1548 1663 1079
## 52 melanops Male 1299 1345 895
## 53 melanops Male 1337 1395 910
## 55 melanops Male 1336 1441 903
## 56 melanops Male 1301 1387 888
## 62 melanops Male 1440 1580 972
## 63 melanops Male 1474 1555 989
## 64 melanops Male 1503 1603 1031
## 69 melanops Male 1568 1689 1086
## 71 melanops Male 1774 1838 1210
## 72 melanops Male 1893 1945 1315
## 73 melanops Male 1765 1781 1240
## 75 melanops Female 1389 1486 931
## 76 melanops Female 1263 1372 857
## 81 melanops Female 1413 1490 962
## 82 melanops Female 1470 1583 1000
## 84 melanops Female 1464 1539 971
## 85 melanops Female 1452 1592 973
## 86 melanops Female 1444 1552 972
## 87 melanops Female 1487 1586 1002
## 89 melanops Female 1536 1620 1070
## 90 melanops Female 1499 1606 1028
## 91 melanops Female 1505 1569 1042
## 92 melanops Female 1519 1594 1066
## 93 melanops Female 1566 1606 1046
## 94 melanops Female 1509 1601 1023
## 95 melanops Female 1553 1607 1059
## 96 melanops Female 1660 1701 1171
## 97 melanops Female 1719 1757 1190
## 99 fuliginosus Male 1382 1493 928
## 100 fuliginosus Male 1438 1481 976
## 102 fuliginosus Male 1391 1430 950
## 103 fuliginosus Male 1716 1688 1158
## 104 fuliginosus Male 1530 1578 1046
## 108 fuliginosus Male 1562 1580 1076
## 109 fuliginosus Male 1656 1640 1146
## 110 fuliginosus Male 1477 1486 1001
## 111 fuliginosus Male 1568 1601 1095
## 113 fuliginosus Male 1619 1678 1106
## 114 fuliginosus Male 1687 1692 1153
## 117 fuliginosus Male 1745 1738 1235
## 118 fuliginosus Male 1680 1668 1151
## 119 fuliginosus Male 1653 1701 1151
## 120 fuliginosus Male 1732 1702 1200
## 122 fuliginosus Male 1711 1695 1191
## 123 fuliginosus Male 1834 1823 1247
## 124 fuliginosus Female 1271 1334 859
## 125 fuliginosus Female 1329 1375 885
## 126 fuliginosus Female 1248 1286 827
## 127 fuliginosus Female 1271 1355 855
## 128 fuliginosus Female 1317 1311 891
## 129 fuliginosus Female 1356 1387 926
## 132 fuliginosus Female 1363 1430 926
## 133 fuliginosus Female 1389 1415 944
## 134 fuliginosus Female 1370 1424 934
## 136 fuliginosus Female 1428 1430 977
## 138 fuliginosus Female 1395 1426 942
## 139 fuliginosus Female 1385 1399 945
## 141 fuliginosus Female 1464 1496 1008
## 142 fuliginosus Female 1486 1483 1019
## 144 fuliginosus Female 1485 1500 1016
## 145 fuliginosus Female 1468 1536 996
## 146 fuliginosus Female 1510 1546 1043
## 147 fuliginosus Female 1526 1512 1052
## 148 fuliginosus Female 1570 1583 987
## palate.width nasal.length nasal.width squamosal.depth lacrymal.width
## 2 230 629 222 150 416
## 4 230 564 207 158 394
## 7 239 606 226 155 396
## 8 248 660 240 159 417
## 10 236 672 231 185 429
## 11 281 778 263 185 441
## 12 227 616 220 150 412
## 13 295 727 271 178 461
## 14 307 810 284 185 490
## 15 293 778 279 184 461
## 16 268 823 272 173 474
## 17 294 755 268 190 467
## 18 289 710 278 179 483
## 19 234 701 238 192 447
## 21 297 855 308 225 536
## 24 332 864 306 221 513
## 27 211 575 200 145 386
## 28 229 626 226 159 441
## 29 247 664 238 171 428
## 30 256 659 229 197 433
## 31 257 671 247 181 443
## 32 241 629 205 169 393
## 33 221 646 210 173 402
## 34 229 674 221 170 407
## 35 233 687 225 175 413
## 36 285 756 249 185 467
## 37 255 687 223 190 432
## 38 282 734 245 182 462
## 40 275 729 238 180 445
## 41 287 695 251 183 439
## 42 267 731 242 167 440
## 43 286 717 258 182 450
## 44 259 682 253 177 455
## 46 294 725 261 160 455
## 47 276 741 261 184 475
## 49 311 811 289 187 479
## 50 265 784 251 206 457
## 52 219 565 204 163 385
## 53 234 562 216 145 404
## 55 185 596 220 151 414
## 56 225 579 219 157 411
## 62 248 675 217 158 399
## 63 239 629 211 170 433
## 64 259 692 238 152 454
## 69 290 717 231 183 450
## 71 281 816 275 198 547
## 72 267 893 260 213 499
## 73 295 766 261 192 476
## 75 245 625 203 152 411
## 76 225 587 203 146 400
## 81 244 630 235 170 430
## 82 211 690 242 166 451
## 84 246 663 196 165 411
## 85 236 694 236 176 461
## 86 217 667 261 156 467
## 87 242 681 240 171 439
## 89 255 716 242 165 455
## 90 275 699 254 177 439
## 91 220 703 207 164 433
## 92 259 704 238 184 430
## 93 227 669 238 198 450
## 94 256 693 228 183 434
## 95 235 675 259 203 484
## 96 300 769 253 188 482
## 97 275 800 245 194 492
## 99 230 573 231 169 427
## 100 250 566 218 173 428
## 102 256 551 202 176 421
## 103 249 698 247 192 471
## 104 259 638 208 185 452
## 108 295 638 240 177 455
## 109 280 624 226 194 500
## 110 244 590 206 155 402
## 111 262 628 250 205 504
## 113 256 719 253 193 473
## 114 260 687 263 204 491
## 117 304 715 246 237 513
## 118 293 685 255 224 479
## 119 299 734 239 215 490
## 120 328 708 255 230 496
## 122 291 699 233 221 461
## 123 320 737 278 280 535
## 124 211 503 171 152 381
## 125 229 549 197 172 396
## 126 236 494 196 154 380
## 127 212 522 190 138 374
## 128 198 497 167 152 390
## 129 214 554 195 160 392
## 132 227 578 217 167 408
## 133 230 574 212 172 405
## 134 248 571 205 171 408
## 136 252 570 214 162 437
## 138 240 571 222 182 430
## 139 215 553 191 156 386
## 141 226 636 230 183 436
## 142 287 603 213 180 442
## 144 277 552 205 203 454
## 145 264 667 222 190 431
## 146 264 656 218 197 423
## 147 281 625 250 201 470
## 148 285 646 244 198 482
## zygomatic.width orbital.width .rostral.width occipital.depth crest.width
## 2 824 233 248 632 141
## 4 801 224 242 568 116
## 7 780 237 238 577 149
## 8 812 240 245 614 128
## 10 856 227 268 659 103
## 11 921 251 284 699 86
## 12 805 236 249 628 107
## 13 905 251 281 692 82
## 14 960 258 288 764 104
## 15 910 234 282 673 81
## 16 880 249 258 702 57
## 17 902 261 314 710 81
## 18 897 250 299 674 115
## 19 852 246 287 691 82
## 21 984 277 350 780 84
## 24 947 239 315 765 39
## 27 760 226 220 569 164
## 28 839 256 234 613 148
## 29 828 249 228 605 147
## 30 853 233 264 664 131
## 31 859 240 288 665 125
## 32 833 235 247 615 129
## 33 823 238 242 589 125
## 34 803 210 222 599 101
## 35 832 229 265 646 121
## 36 903 233 301 722 104
## 37 873 222 286 663 135
## 38 920 248 258 699 103
## 40 914 251 272 672 80
## 41 885 235 271 646 82
## 42 878 234 259 688 123
## 43 848 205 262 625 70
## 44 875 244 288 647 114
## 46 894 212 302 684 74
## 47 911 222 306 699 95
## 49 911 238 326 716 122
## 50 907 244 282 687 100
## 52 764 235 215 542 153
## 53 794 272 236 577 154
## 55 788 245 240 574 156
## 56 787 231 229 582 113
## 62 815 227 234 647 129
## 63 888 251 253 662 134
## 64 825 220 268 638 83
## 69 900 252 318 694 18
## 71 994 275 368 753 56
## 72 994 234 345 754 13
## 73 978 220 313 726 38
## 75 801 245 242 587 125
## 76 782 232 237 554 170
## 81 834 240 271 626 88
## 82 855 249 271 634 129
## 84 821 236 237 645 138
## 85 855 261 240 656 140
## 86 869 262 251 650 176
## 87 822 245 290 656 112
## 89 894 222 326 625 87
## 90 835 254 264 650 112
## 91 843 230 266 629 127
## 92 865 238 273 645 70
## 93 882 268 267 656 135
## 94 828 240 256 638 120
## 95 882 239 294 698 140
## 96 960 247 320 695 86
## 97 939 270 333 705 65
## 99 861 261 250 618 151
## 100 912 249 261 619 172
## 102 886 260 252 646 140
## 103 972 290 300 687 189
## 104 929 243 265 667 134
## 108 925 243 272 675 118
## 109 969 235 314 738 114
## 110 867 242 268 639 160
## 111 932 265 290 719 115
## 113 946 242 276 689 119
## 114 986 240 288 735 111
## 117 1070 258 328 744 149
## 118 1032 213 337 728 78
## 119 1004 239 319 742 126
## 120 990 233 312 703 106
## 122 989 210 308 751 60
## 123 1090 262 371 770 151
## 124 824 240 216 563 199
## 125 838 214 239 587 153
## 126 804 230 227 574 169
## 127 799 247 215 585 167
## 128 807 226 237 609 155
## 129 837 220 245 611 181
## 132 844 234 249 603 153
## 133 822 241 241 612 170
## 134 859 246 235 623 154
## 136 880 248 263 620 170
## 138 853 228 259 650 138
## 139 827 217 247 585 137
## 141 897 234 264 646 172
## 142 927 230 274 649 139
## 144 919 225 278 676 122
## 145 951 217 305 650 178
## 146 891 190 270 651 78
## 147 934 236 289 680 145
## 148 984 253 291 699 188
## foramina.length mandible.length mandible.width mandible.depth ramus.height
## 2 100 1158 148 181 643
## 4 79 1090 132 189 594
## 7 101 1084 124 168 578
## 8 91 1149 129 175 628
## 10 94 1240 132 196 683
## 11 79 1345 148 232 772
## 12 85 1179 132 180 652
## 13 125 1309 145 210 712
## 14 81 1443 157 222 731
## 15 75 1339 135 207 692
## 16 109 1361 140 208 713
## 17 104 1377 137 206 754
## 18 107 1253 142 194 688
## 19 89 1293 137 213 722
## 21 116 1539 163 238 795
## 24 137 1526 138 218 776
## 27 72 1059 113 164 578
## 28 106 1197 129 173 651
## 29 99 1131 126 167 621
## 30 94 1215 139 200 660
## 31 104 1202 147 192 676
## 32 100 1176 128 171 638
## 33 99 1198 128 169 649
## 34 106 1151 122 176 629
## 35 88 1214 130 195 668
## 36 117 1324 147 198 731
## 37 105 1258 131 205 688
## 38 70 1355 149 193 724
## 40 93 1344 137 204 735
## 41 67 1297 135 203 709
## 42 130 1265 137 175 684
## 43 118 1235 124 180 659
## 44 111 1290 148 194 706
## 46 103 1355 141 206 706
## 47 97 1370 139 218 733
## 49 90 1366 129 174 715
## 50 119 1314 126 198 706
## 52 93 1054 118 156 556
## 53 102 1094 122 158 625
## 55 95 1083 133 178 623
## 56 78 1115 123 164 616
## 62 84 1213 131 186 634
## 63 91 1225 144 205 716
## 64 95 1264 141 203 712
## 69 98 1337 140 194 759
## 71 80 1482 146 227 794
## 72 92 1568 163 216 824
## 73 95 1503 159 211 775
## 75 114 1164 123 166 645
## 76 113 1055 120 166 580
## 81 96 1198 132 191 665
## 82 80 1209 138 210 708
## 84 83 1219 143 188 702
## 85 87 1210 143 194 695
## 86 105 1194 138 197 704
## 87 108 1237 127 187 679
## 89 85 1287 135 196 692
## 90 91 1243 125 200 668
## 91 88 1228 136 194 709
## 92 121 1275 131 192 689
## 93 114 1296 142 219 699
## 94 107 1248 129 198 692
## 95 117 1314 135 212 722
## 96 126 1430 154 205 770
## 97 97 1450 154 240 813
## 99 98 1162 133 186 640
## 100 86 1220 147 193 655
## 102 106 1187 146 202 688
## 103 88 1450 160 236 799
## 104 104 1315 144 201 750
## 108 80 1320 154 217 753
## 109 92 1422 166 227 805
## 110 88 1245 147 185 672
## 111 96 1367 159 223 777
## 113 94 1369 159 215 765
## 114 104 1412 157 227 823
## 117 96 1502 167 239 853
## 118 76 1466 158 214 835
## 119 94 1408 169 209 836
## 120 87 1474 158 239 822
## 122 73 1452 154 215 815
## 123 100 1555 156 271 880
## 124 70 1078 130 181 634
## 125 79 1103 133 182 666
## 126 72 1046 131 170 616
## 127 90 1058 132 179 629
## 128 93 1073 130 178 648
## 129 85 1140 135 188 657
## 132 73 1163 129 194 654
## 133 73 1163 139 191 641
## 134 98 1152 143 194 689
## 136 83 1179 140 189 650
## 138 79 1199 148 202 700
## 139 98 1156 134 190 642
## 141 78 1263 150 216 715
## 142 97 1291 157 217 737
## 144 74 1260 148 194 751
## 145 82 1287 141 199 736
## 146 87 1337 158 210 747
## 147 106 1334 153 211 739
## 148 103 1354 153 223 807Type_kanga<-as.numeric(kangaSet$sex)
KangaMaleSet<-subset(kangaSet, kangaSet$sex == "Male")
KangaFemaleSet<-subset(kangaSet, kangaSet$sex == "Female")
SumofAll<-kangaSet$basilar.length+kangaSet$occipitonasal.length+kangaSet$palate.length+kangaSet$palate.width+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$squamosal.depth+kangaSet$lacrymal.width+kangaSet$zygomatic.width+kangaSet$orbital.width+kangaSet$occipital.depth+kangaSet$crest.width+kangaSet$foramina.length+kangaSet$mandible.length+kangaSet$mandible.width+kangaSet$mandible.depth+kangaSet$ramus.height+kangaSet$.rostral.width
Reg_Kanga <- lm(Type_kanga ~ SumofAll, data=kangaSet)
Sum_Kanga<-summary(Reg_Kanga)
Sum_Kanga##
## Call:
## lm(formula = Type_kanga ~ SumofAll, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6842 -0.4075 -0.2155 0.4260 0.8555
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.971e-01 5.566e-01 -1.073 0.2860
## SumofAll 1.944e-04 5.303e-05 3.665 0.0004 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.47 on 99 degrees of freedom
## Multiple R-squared: 0.1195, Adjusted R-squared: 0.1106
## F-statistic: 13.43 on 1 and 99 DF, p-value: 4e-04plot(SumofAll,Type_kanga,xlab="", ylab="Sum of Linear Variables", pch=19, col="blue")
abline(lm(Type_kanga ~ SumofAll, data=kangaSet), col="red")
Predicted_Values<-round(predict(Reg_Kanga))
Predicted_Values## 2 4 7 8 10 11 12 13 14 15 16 17 18 19 21 24 27 28 29 30
## 1 1 1 1 1 2 1 2 2 2 2 2 1 1 2 2 1 1 1 1
## 31 32 33 34 35 36 37 38 40 41 42 43 44 46 47 49 50 52 53 55
## 1 1 1 1 1 2 1 2 2 1 1 1 1 2 2 2 2 1 1 1
## 56 62 63 64 69 71 72 73 75 76 81 82 84 85 86 87 89 90 91 92
## 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1
## 93 94 95 96 97 99 100 102 103 104 108 109 110 111 113 114 117 118 119 120
## 1 1 2 2 2 1 1 1 2 1 1 2 1 2 2 2 2 2 2 2
## 122 123 124 125 126 127 128 129 132 133 134 136 138 139 141 142 144 145 146 147
## 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 148
## 2Type_kanga## [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [38] 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
## [75] 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1model <- lm(Type_kanga~SumofAll )
model##
## Call:
## lm(formula = Type_kanga ~ SumofAll)
##
## Coefficients:
## (Intercept) SumofAll
## -0.5970735 0.0001944plot (model$fit~kangaSet$sex, xlab="Gender",ylab =" Gender coefficient ")
points (Type_kanga,model$fit )
abline (1.5 ,0 , lwd =3)
predictedgender <- model $ fit > 1.5
table (Type_kanga ,c("Female","Male")[( predictedgender +1) ])##
## Type_kanga Female Male
## 1 46 11
## 2 21 23print("Accuracy = 69/101 = 68.31%")## [1] "Accuracy = 69/101 = 68.31%"Problem 2:
##Fit a model predicting academic by everything else:
library(faraway)
data("kanga")
lm1 <-lm(Type_kanga~kangaSet$basilar.length+kangaSet$occipitonasal.length+kangaSet$palate.length+kangaSet$palate.width+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$squamosal.depth+kangaSet$lacrymal.width+kangaSet$zygomatic.width+kangaSet$orbital.width+kangaSet$occipital.depth+kangaSet$crest.width+kangaSet$foramina.length+kangaSet$mandible.length+kangaSet$mandible.width+kangaSet$mandible.depth+kangaSet$ramus.height+kangaSet$.rostral.width,data=kangaSet)
summary(lm1)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.71675 -0.31868 -0.09668 0.30148 0.91041
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.9801219 0.9848991 -2.010 0.047667 *
## kangaSet$basilar.length 0.0010878 0.0026435 0.412 0.681779
## kangaSet$occipitonasal.length 0.0051656 0.0021280 2.427 0.017394 *
## kangaSet$palate.length 0.0021677 0.0026806 0.809 0.421046
## kangaSet$palate.width -0.0008720 0.0028873 -0.302 0.763400
## kangaSet$nasal.length -0.0081358 0.0020655 -3.939 0.000171 ***
## kangaSet$nasal.width 0.0080635 0.0044446 1.814 0.073301 .
## kangaSet$squamosal.depth 0.0001512 0.0041188 0.037 0.970808
## kangaSet$lacrymal.width -0.0061008 0.0040909 -1.491 0.139718
## kangaSet$zygomatic.width 0.0027272 0.0027402 0.995 0.322539
## kangaSet$orbital.width 0.0054834 0.0034168 1.605 0.112368
## kangaSet$occipital.depth 0.0016855 0.0026351 0.640 0.524196
## kangaSet$crest.width -0.0049138 0.0020774 -2.365 0.020371 *
## kangaSet$foramina.length -0.0020106 0.0033836 -0.594 0.553991
## kangaSet$mandible.length -0.0033901 0.0025522 -1.328 0.187762
## kangaSet$mandible.width 0.0100053 0.0078866 1.269 0.208155
## kangaSet$mandible.depth -0.0026807 0.0049569 -0.541 0.590114
## kangaSet$ramus.height -0.0031911 0.0026440 -1.207 0.230935
## kangaSet$.rostral.width -0.0017068 0.0030700 -0.556 0.579753
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4166 on 82 degrees of freedom
## Multiple R-squared: 0.4269, Adjusted R-squared: 0.3011
## F-statistic: 3.394 on 18 and 82 DF, p-value: 8.044e-05drop1(lm1,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 14.231 -159.93
## kangaSet$basilar.length 1 0.02939 14.260 -161.72 0.1693 0.6817792
## kangaSet$occipitonasal.length 1 1.02263 15.253 -154.92 5.8927 0.0173942 *
## kangaSet$palate.length 1 0.11349 14.344 -161.13 0.6539 0.4210458
## kangaSet$palate.width 1 0.01583 14.246 -161.82 0.0912 0.7633996
## kangaSet$nasal.length 1 2.69254 16.923 -144.43 15.5151 0.0001711 ***
## kangaSet$nasal.width 1 0.57120 14.802 -157.96 3.2914 0.0733011 .
## kangaSet$squamosal.depth 1 0.00023 14.231 -161.93 0.0013 0.9708081
## kangaSet$lacrymal.width 1 0.38596 14.617 -159.23 2.2240 0.1397179
## kangaSet$zygomatic.width 1 0.17190 14.402 -160.72 0.9905 0.3225386
## kangaSet$orbital.width 1 0.44698 14.678 -158.81 2.5756 0.1123676
## kangaSet$occipital.depth 1 0.07100 14.302 -161.43 0.4091 0.5241957
## kangaSet$crest.width 1 0.97100 15.202 -155.27 5.5952 0.0203712 *
## kangaSet$foramina.length 1 0.06128 14.292 -161.50 0.3531 0.5539914
## kangaSet$mandible.length 1 0.30620 14.537 -159.78 1.7644 0.1877625
## kangaSet$mandible.width 1 0.27931 14.510 -159.97 1.6095 0.2081553
## kangaSet$mandible.depth 1 0.05075 14.281 -161.57 0.2925 0.5901143
## kangaSet$ramus.height 1 0.25279 14.483 -160.15 1.4566 0.2309345
## kangaSet$.rostral.width 1 0.05364 14.284 -161.55 0.3091 0.5797527
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lm2 <- lm(Type_kanga~kangaSet$basilar.length+kangaSet$occipitonasal.length+kangaSet$palate.length+kangaSet$palate.width+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$zygomatic.width+kangaSet$orbital.width+kangaSet$occipital.depth+kangaSet$crest.width+kangaSet$foramina.length+kangaSet$mandible.length+kangaSet$mandible.width+kangaSet$mandible.depth+kangaSet$ramus.height+kangaSet$.rostral.width,data=kangaSet)
summary(lm2)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$zygomatic.width +
## kangaSet$orbital.width + kangaSet$occipital.depth + kangaSet$crest.width +
## kangaSet$foramina.length + kangaSet$mandible.length + kangaSet$mandible.width +
## kangaSet$mandible.depth + kangaSet$ramus.height + kangaSet$.rostral.width,
## data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.71477 -0.31716 -0.09491 0.30268 0.91194
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.9852723 0.9689706 -2.049 0.043636 *
## kangaSet$basilar.length 0.0010889 0.0026274 0.414 0.679634
## kangaSet$occipitonasal.length 0.0051628 0.0021138 2.442 0.016710 *
## kangaSet$palate.length 0.0021727 0.0026610 0.817 0.416548
## kangaSet$palate.width -0.0008693 0.0028689 -0.303 0.762644
## kangaSet$nasal.length -0.0081426 0.0020449 -3.982 0.000146 ***
## kangaSet$nasal.width 0.0080659 0.0044173 1.826 0.071449 .
## kangaSet$lacrymal.width -0.0060927 0.0040603 -1.501 0.137264
## kangaSet$zygomatic.width 0.0027530 0.0026322 1.046 0.298648
## kangaSet$orbital.width 0.0054596 0.0033345 1.637 0.105346
## kangaSet$occipital.depth 0.0017000 0.0025897 0.656 0.513364
## kangaSet$crest.width -0.0049086 0.0020600 -2.383 0.019464 *
## kangaSet$foramina.length -0.0019962 0.0033402 -0.598 0.551727
## kangaSet$mandible.length -0.0033884 0.0025364 -1.336 0.185228
## kangaSet$mandible.width 0.0098992 0.0072934 1.357 0.178368
## kangaSet$mandible.depth -0.0026349 0.0047682 -0.553 0.582030
## kangaSet$ramus.height -0.0031836 0.0026202 -1.215 0.227802
## kangaSet$.rostral.width -0.0017092 0.0030508 -0.560 0.576821
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4141 on 83 degrees of freedom
## Multiple R-squared: 0.4269, Adjusted R-squared: 0.3095
## F-statistic: 3.637 on 17 and 83 DF, p-value: 4.052e-05drop1(lm2,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$zygomatic.width +
## kangaSet$orbital.width + kangaSet$occipital.depth + kangaSet$crest.width +
## kangaSet$foramina.length + kangaSet$mandible.length + kangaSet$mandible.width +
## kangaSet$mandible.depth + kangaSet$ramus.height + kangaSet$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 14.231 -161.93
## kangaSet$basilar.length 1 0.02945 14.260 -163.72 0.1717 0.6796345
## kangaSet$occipitonasal.length 1 1.02284 15.254 -156.92 5.9656 0.0167100 *
## kangaSet$palate.length 1 0.11431 14.345 -163.12 0.6667 0.4165481
## kangaSet$palate.width 1 0.01574 14.246 -163.82 0.0918 0.7626443
## kangaSet$nasal.length 1 2.71850 16.949 -146.27 15.8554 0.0001459 ***
## kangaSet$nasal.width 1 0.57167 14.803 -159.95 3.3342 0.0714489 .
## kangaSet$lacrymal.width 1 0.38606 14.617 -161.23 2.2517 0.1372640
## kangaSet$zygomatic.width 1 0.18755 14.418 -162.61 1.0939 0.2986480
## kangaSet$orbital.width 1 0.45965 14.690 -160.72 2.6809 0.1053464
## kangaSet$occipital.depth 1 0.07388 14.305 -163.41 0.4309 0.5133643
## kangaSet$crest.width 1 0.97352 15.204 -157.25 5.6780 0.0194637 *
## kangaSet$foramina.length 1 0.06123 14.292 -163.50 0.3571 0.5517273
## kangaSet$mandible.length 1 0.30599 14.537 -161.78 1.7847 0.1852284
## kangaSet$mandible.width 1 0.31586 14.547 -161.71 1.8422 0.1783682
## kangaSet$mandible.depth 1 0.05235 14.283 -163.56 0.3054 0.5820305
## kangaSet$ramus.height 1 0.25312 14.484 -162.15 1.4763 0.2278023
## kangaSet$.rostral.width 1 0.05382 14.285 -163.55 0.3139 0.5768213
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm2)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$zygomatic.width +
## kangaSet$orbital.width + kangaSet$occipital.depth + kangaSet$crest.width +
## kangaSet$foramina.length + kangaSet$mandible.length + kangaSet$mandible.width +
## kangaSet$mandible.depth + kangaSet$ramus.height + kangaSet$.rostral.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 83 14.231 -1 -0.00023383 0.0013 0.9708lm3 <- lm(Type_kanga~kangaSet$basilar.length+kangaSet$occipitonasal.length+kangaSet$palate.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$zygomatic.width+kangaSet$orbital.width+kangaSet$occipital.depth+kangaSet$crest.width+kangaSet$foramina.length+kangaSet$mandible.length+kangaSet$mandible.width+kangaSet$mandible.depth+kangaSet$ramus.height+kangaSet$.rostral.width,data=kangaSet)
summary(lm3)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$nasal.length + kangaSet$nasal.width +
## kangaSet$lacrymal.width + kangaSet$zygomatic.width + kangaSet$orbital.width +
## kangaSet$occipital.depth + kangaSet$crest.width + kangaSet$foramina.length +
## kangaSet$mandible.length + kangaSet$mandible.width + kangaSet$mandible.depth +
## kangaSet$ramus.height + kangaSet$.rostral.width, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.73048 -0.31253 -0.07762 0.30076 0.92284
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.002652 0.962028 -2.082 0.04041 *
## kangaSet$basilar.length 0.001271 0.002544 0.499 0.61883
## kangaSet$occipitonasal.length 0.005147 0.002102 2.449 0.01640 *
## kangaSet$palate.length 0.002100 0.002636 0.797 0.42789
## kangaSet$nasal.length -0.008087 0.002026 -3.992 0.00014 ***
## kangaSet$nasal.width 0.007686 0.004213 1.824 0.07163 .
## kangaSet$lacrymal.width -0.005944 0.004009 -1.483 0.14188
## kangaSet$zygomatic.width 0.002506 0.002489 1.007 0.31695
## kangaSet$orbital.width 0.005489 0.003315 1.656 0.10148
## kangaSet$occipital.depth 0.001627 0.002565 0.635 0.52748
## kangaSet$crest.width -0.004775 0.002001 -2.386 0.01928 *
## kangaSet$foramina.length -0.002027 0.003321 -0.610 0.54330
## kangaSet$mandible.length -0.003551 0.002465 -1.441 0.15343
## kangaSet$mandible.width 0.010015 0.007244 1.383 0.17048
## kangaSet$mandible.depth -0.002478 0.004714 -0.526 0.60057
## kangaSet$ramus.height -0.003157 0.002605 -1.212 0.22881
## kangaSet$.rostral.width -0.001732 0.003033 -0.571 0.56946
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4118 on 84 degrees of freedom
## Multiple R-squared: 0.4263, Adjusted R-squared: 0.317
## F-statistic: 3.901 on 16 and 84 DF, p-value: 2.041e-05drop1(lm3,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$nasal.length + kangaSet$nasal.width +
## kangaSet$lacrymal.width + kangaSet$zygomatic.width + kangaSet$orbital.width +
## kangaSet$occipital.depth + kangaSet$crest.width + kangaSet$foramina.length +
## kangaSet$mandible.length + kangaSet$mandible.width + kangaSet$mandible.depth +
## kangaSet$ramus.height + kangaSet$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 14.246 -163.82
## kangaSet$basilar.length 1 0.04229 14.289 -165.52 0.2494 0.6188259
## kangaSet$occipitonasal.length 1 1.01727 15.264 -158.85 5.9980 0.0164012 *
## kangaSet$palate.length 1 0.10764 14.354 -165.06 0.6347 0.4278894
## kangaSet$nasal.length 1 2.70323 16.950 -148.27 15.9387 0.0001395 ***
## kangaSet$nasal.width 1 0.56456 14.811 -161.89 3.3288 0.0716333 .
## kangaSet$lacrymal.width 1 0.37288 14.619 -163.21 2.1985 0.1418839
## kangaSet$zygomatic.width 1 0.17190 14.418 -164.61 1.0135 0.3169465
## kangaSet$orbital.width 1 0.46503 14.712 -162.57 2.7419 0.1014793
## kangaSet$occipital.depth 1 0.06828 14.315 -165.34 0.4026 0.5274759
## kangaSet$crest.width 1 0.96554 15.212 -159.20 5.6930 0.0192807 *
## kangaSet$foramina.length 1 0.06317 14.310 -165.37 0.3725 0.5433010
## kangaSet$mandible.length 1 0.35195 14.598 -163.35 2.0751 0.1534339
## kangaSet$mandible.width 1 0.32417 14.571 -163.55 1.9114 0.1704752
## kangaSet$mandible.depth 1 0.04685 14.293 -165.49 0.2762 0.6005734
## kangaSet$ramus.height 1 0.24924 14.496 -164.07 1.4696 0.2288141
## kangaSet$.rostral.width 1 0.05532 14.302 -165.43 0.3262 0.5694580
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm3)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$nasal.length + kangaSet$nasal.width +
## kangaSet$lacrymal.width + kangaSet$zygomatic.width + kangaSet$orbital.width +
## kangaSet$occipital.depth + kangaSet$crest.width + kangaSet$foramina.length +
## kangaSet$mandible.length + kangaSet$mandible.width + kangaSet$mandible.depth +
## kangaSet$ramus.height + kangaSet$.rostral.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 84 14.246 -2 -0.015976 0.046 0.955lm4 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$palate.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$zygomatic.width+kangaSet$orbital.width+kangaSet$occipital.depth+kangaSet$crest.width+kangaSet$foramina.length+kangaSet$mandible.length+kangaSet$mandible.width+kangaSet$mandible.depth+kangaSet$ramus.height+kangaSet$.rostral.width,data=kangaSet)
summary(lm4)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.73940 -0.30973 -0.08863 0.29273 0.99085
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.012083 0.957586 -2.101 0.0386 *
## kangaSet$occipitonasal.length 0.005707 0.001770 3.224 0.0018 **
## kangaSet$palate.length 0.002786 0.002239 1.245 0.2167
## kangaSet$nasal.length -0.008375 0.001933 -4.332 4.03e-05 ***
## kangaSet$nasal.width 0.007392 0.004153 1.780 0.0787 .
## kangaSet$lacrymal.width -0.005974 0.003990 -1.497 0.1380
## kangaSet$zygomatic.width 0.002306 0.002446 0.943 0.3483
## kangaSet$orbital.width 0.005698 0.003274 1.741 0.0854 .
## kangaSet$occipital.depth 0.001407 0.002515 0.559 0.5773
## kangaSet$crest.width -0.004655 0.001978 -2.353 0.0209 *
## kangaSet$foramina.length -0.002243 0.003278 -0.684 0.4955
## kangaSet$mandible.length -0.003127 0.002304 -1.357 0.1783
## kangaSet$mandible.width 0.010289 0.007191 1.431 0.1561
## kangaSet$mandible.depth -0.001884 0.004542 -0.415 0.6793
## kangaSet$ramus.height -0.003024 0.002579 -1.172 0.2444
## kangaSet$.rostral.width -0.001384 0.002939 -0.471 0.6389
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.41 on 85 degrees of freedom
## Multiple R-squared: 0.4246, Adjusted R-squared: 0.323
## F-statistic: 4.181 on 15 and 85 DF, p-value: 1.057e-05drop1(lm4,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 14.289 -165.52
## kangaSet$occipitonasal.length 1 1.74679 16.036 -155.87 10.3911 0.001797 **
## kangaSet$palate.length 1 0.26041 14.549 -165.70 1.5491 0.216690
## kangaSet$nasal.length 1 3.15458 17.443 -147.37 18.7656 4.028e-05 ***
## kangaSet$nasal.width 1 0.53260 14.821 -163.82 3.1683 0.078654 .
## kangaSet$lacrymal.width 1 0.37682 14.666 -164.89 2.2416 0.138045
## kangaSet$zygomatic.width 1 0.14949 14.438 -166.47 0.8893 0.348346
## kangaSet$orbital.width 1 0.50927 14.798 -163.98 3.0295 0.085384 .
## kangaSet$occipital.depth 1 0.05262 14.341 -167.15 0.3130 0.577293
## kangaSet$crest.width 1 0.93102 15.220 -161.15 5.5384 0.020912 *
## kangaSet$foramina.length 1 0.07876 14.368 -166.97 0.4685 0.495525
## kangaSet$mandible.length 1 0.30965 14.598 -165.35 1.8420 0.178305
## kangaSet$mandible.width 1 0.34415 14.633 -165.12 2.0473 0.156148
## kangaSet$mandible.depth 1 0.02892 14.318 -167.32 0.1721 0.679340
## kangaSet$ramus.height 1 0.23101 14.520 -165.90 1.3742 0.244362
## kangaSet$.rostral.width 1 0.03728 14.326 -167.26 0.2218 0.638883
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm4)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 85 14.289 -3 -0.058269 0.1119 0.9529lm5 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$palate.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$zygomatic.width+kangaSet$orbital.width+kangaSet$occipital.depth+kangaSet$crest.width+kangaSet$foramina.length+kangaSet$mandible.length+kangaSet$mandible.width+kangaSet$ramus.height+kangaSet$.rostral.width,data=kangaSet)
summary(lm5)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height + kangaSet$.rostral.width,
## data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.71649 -0.31588 -0.07563 0.29618 0.97096
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.988982 0.951353 -2.091 0.0395 *
## kangaSet$occipitonasal.length 0.005709 0.001762 3.240 0.0017 **
## kangaSet$palate.length 0.002771 0.002228 1.244 0.2169
## kangaSet$nasal.length -0.008285 0.001912 -4.334 3.96e-05 ***
## kangaSet$nasal.width 0.007036 0.004044 1.740 0.0854 .
## kangaSet$lacrymal.width -0.005920 0.003969 -1.491 0.1395
## kangaSet$zygomatic.width 0.002461 0.002405 1.023 0.3091
## kangaSet$orbital.width 0.005546 0.003238 1.713 0.0903 .
## kangaSet$occipital.depth 0.001454 0.002501 0.581 0.5626
## kangaSet$crest.width -0.004793 0.001940 -2.470 0.0155 *
## kangaSet$foramina.length -0.002056 0.003231 -0.636 0.5262
## kangaSet$mandible.length -0.003270 0.002267 -1.442 0.1528
## kangaSet$mandible.width 0.009844 0.007076 1.391 0.1678
## kangaSet$ramus.height -0.003391 0.002411 -1.407 0.1631
## kangaSet$.rostral.width -0.001439 0.002922 -0.492 0.6237
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.408 on 86 degrees of freedom
## Multiple R-squared: 0.4234, Adjusted R-squared: 0.3295
## F-statistic: 4.511 on 14 and 86 DF, p-value: 5.117e-06drop1(lm5,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height + kangaSet$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 14.318 -167.32
## kangaSet$occipitonasal.length 1 1.74817 16.066 -157.68 10.5004 0.001698 **
## kangaSet$palate.length 1 0.25761 14.575 -167.51 1.5473 0.216912
## kangaSet$nasal.length 1 3.12657 17.444 -149.37 18.7798 3.962e-05 ***
## kangaSet$nasal.width 1 0.50407 14.822 -165.82 3.0277 0.085431 .
## kangaSet$lacrymal.width 1 0.37035 14.688 -166.74 2.2245 0.139493
## kangaSet$zygomatic.width 1 0.17426 14.492 -168.09 1.0467 0.309132
## kangaSet$orbital.width 1 0.48856 14.806 -165.93 2.9346 0.090305 .
## kangaSet$occipital.depth 1 0.05625 14.374 -168.92 0.3378 0.562599
## kangaSet$crest.width 1 1.01590 15.334 -162.39 6.1020 0.015477 *
## kangaSet$foramina.length 1 0.06743 14.385 -168.84 0.4050 0.526190
## kangaSet$mandible.length 1 0.34635 14.664 -166.90 2.0804 0.152836
## kangaSet$mandible.width 1 0.32220 14.640 -167.07 1.9353 0.167769
## kangaSet$ramus.height 1 0.32942 14.647 -167.02 1.9787 0.163135
## kangaSet$.rostral.width 1 0.04037 14.358 -169.03 0.2425 0.623688
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm5)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height + kangaSet$.rostral.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 86 14.318 -4 -0.087191 0.1256 0.9728lm6 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$palate.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$zygomatic.width+kangaSet$orbital.width+kangaSet$occipital.depth+kangaSet$crest.width+kangaSet$foramina.length+kangaSet$mandible.length+kangaSet$mandible.width+kangaSet$ramus.height,data=kangaSet)
summary(lm6)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.70933 -0.28656 -0.06299 0.28854 0.95755
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.936576 0.941256 -2.057 0.04264 *
## kangaSet$occipitonasal.length 0.005750 0.001752 3.282 0.00149 **
## kangaSet$palate.length 0.002770 0.002218 1.249 0.21501
## kangaSet$nasal.length -0.008314 0.001903 -4.370 3.42e-05 ***
## kangaSet$nasal.width 0.007083 0.004025 1.760 0.08193 .
## kangaSet$lacrymal.width -0.006441 0.003808 -1.691 0.09438 .
## kangaSet$zygomatic.width 0.002203 0.002337 0.942 0.34858
## kangaSet$orbital.width 0.005661 0.003215 1.761 0.08176 .
## kangaSet$occipital.depth 0.001463 0.002490 0.588 0.55820
## kangaSet$crest.width -0.004652 0.001911 -2.435 0.01694 *
## kangaSet$foramina.length -0.001997 0.003214 -0.621 0.53601
## kangaSet$mandible.length -0.003395 0.002243 -1.513 0.13380
## kangaSet$mandible.width 0.010502 0.006919 1.518 0.13264
## kangaSet$ramus.height -0.003437 0.002398 -1.433 0.15545
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4062 on 87 degrees of freedom
## Multiple R-squared: 0.4218, Adjusted R-squared: 0.3354
## F-statistic: 4.882 on 13 and 87 DF, p-value: 2.452e-06drop1(lm6,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 14.358 -169.03
## kangaSet$occipitonasal.length 1 1.77733 16.135 -159.24 10.7694 0.001486 **
## kangaSet$palate.length 1 0.25746 14.616 -169.24 1.5600 0.215009
## kangaSet$nasal.length 1 3.15151 17.510 -150.99 19.0959 3.424e-05 ***
## kangaSet$nasal.width 1 0.51118 14.869 -167.50 3.0974 0.081934 .
## kangaSet$lacrymal.width 1 0.47202 14.830 -167.76 2.8601 0.094383 .
## kangaSet$zygomatic.width 1 0.14658 14.505 -170.00 0.8882 0.348575
## kangaSet$orbital.width 1 0.51176 14.870 -167.49 3.1009 0.081762 .
## kangaSet$occipital.depth 1 0.05702 14.415 -170.63 0.3455 0.558203
## kangaSet$crest.width 1 0.97837 15.336 -164.37 5.9282 0.016943 *
## kangaSet$foramina.length 1 0.06371 14.422 -170.58 0.3860 0.536014
## kangaSet$mandible.length 1 0.37801 14.736 -168.41 2.2905 0.133796
## kangaSet$mandible.width 1 0.38030 14.738 -168.39 2.3044 0.132637
## kangaSet$ramus.height 1 0.33889 14.697 -168.68 2.0534 0.155448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm6)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 87 14.358 -5 -0.12756 0.147 0.9804lm7 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$palate.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$zygomatic.width+kangaSet$orbital.width+kangaSet$crest.width+kangaSet$foramina.length+kangaSet$mandible.length+kangaSet$mandible.width+kangaSet$ramus.height,data=kangaSet)
summary(lm7)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$crest.width +
## kangaSet$foramina.length + kangaSet$mandible.length + kangaSet$mandible.width +
## kangaSet$ramus.height, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.68733 -0.29521 -0.04945 0.29848 1.00172
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.854989 0.927496 -2.000 0.04858 *
## kangaSet$occipitonasal.length 0.005873 0.001733 3.389 0.00105 **
## kangaSet$palate.length 0.002676 0.002204 1.214 0.22790
## kangaSet$nasal.length -0.008275 0.001894 -4.369 3.41e-05 ***
## kangaSet$nasal.width 0.007369 0.003981 1.851 0.06750 .
## kangaSet$lacrymal.width -0.006148 0.003762 -1.634 0.10575
## kangaSet$zygomatic.width 0.002254 0.002327 0.968 0.33550
## kangaSet$orbital.width 0.005576 0.003200 1.743 0.08487 .
## kangaSet$crest.width -0.004694 0.001902 -2.468 0.01553 *
## kangaSet$foramina.length -0.001846 0.003192 -0.578 0.56446
## kangaSet$mandible.length -0.003212 0.002213 -1.451 0.15022
## kangaSet$mandible.width 0.011272 0.006768 1.665 0.09939 .
## kangaSet$ramus.height -0.003168 0.002346 -1.351 0.18025
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4047 on 88 degrees of freedom
## Multiple R-squared: 0.4195, Adjusted R-squared: 0.3403
## F-statistic: 5.299 on 12 and 88 DF, p-value: 1.179e-06drop1(lm7,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$crest.width +
## kangaSet$foramina.length + kangaSet$mandible.length + kangaSet$mandible.width +
## kangaSet$ramus.height
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 14.415 -170.63
## kangaSet$occipitonasal.length 1 1.88114 16.296 -160.24 11.4838 0.001052 **
## kangaSet$palate.length 1 0.24152 14.657 -170.95 1.4744 0.227903
## kangaSet$nasal.length 1 3.12616 17.541 -152.81 19.0843 3.407e-05 ***
## kangaSet$nasal.width 1 0.56135 14.976 -168.77 3.4269 0.067497 .
## kangaSet$lacrymal.width 1 0.43758 14.853 -169.61 2.6713 0.105746
## kangaSet$zygomatic.width 1 0.15362 14.569 -171.56 0.9378 0.335501
## kangaSet$orbital.width 1 0.49750 14.913 -169.20 3.0371 0.084874 .
## kangaSet$crest.width 1 0.99753 15.413 -165.87 6.0896 0.015533 *
## kangaSet$foramina.length 1 0.05481 14.470 -172.25 0.3346 0.564458
## kangaSet$mandible.length 1 0.34508 14.760 -170.24 2.1066 0.150222
## kangaSet$mandible.width 1 0.45433 14.870 -169.50 2.7735 0.099392 .
## kangaSet$ramus.height 1 0.29885 14.714 -170.56 1.8244 0.180252
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm7)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$crest.width +
## kangaSet$foramina.length + kangaSet$mandible.length + kangaSet$mandible.width +
## kangaSet$ramus.height
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 88 14.415 -6 -0.18457 0.1773 0.9823lm8 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$palate.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$zygomatic.width+kangaSet$orbital.width+kangaSet$crest.width+kangaSet$mandible.length+kangaSet$mandible.width+kangaSet$ramus.height,data=kangaSet)
summary(lm8)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$crest.width +
## kangaSet$mandible.length + kangaSet$mandible.width + kangaSet$ramus.height,
## data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.71904 -0.29061 -0.05457 0.29367 1.03338
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.014071 0.882464 -2.282 0.024854 *
## kangaSet$occipitonasal.length 0.006096 0.001683 3.622 0.000485 ***
## kangaSet$palate.length 0.002548 0.002184 1.166 0.246631
## kangaSet$nasal.length -0.008486 0.001852 -4.581 1.5e-05 ***
## kangaSet$nasal.width 0.007352 0.003966 1.854 0.067062 .
## kangaSet$lacrymal.width -0.006555 0.003681 -1.781 0.078395 .
## kangaSet$zygomatic.width 0.002387 0.002307 1.035 0.303665
## kangaSet$orbital.width 0.005338 0.003161 1.689 0.094782 .
## kangaSet$crest.width -0.004703 0.001895 -2.482 0.014955 *
## kangaSet$mandible.length -0.003248 0.002204 -1.474 0.144094
## kangaSet$mandible.width 0.011605 0.006718 1.727 0.087563 .
## kangaSet$ramus.height -0.003126 0.002336 -1.338 0.184248
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4032 on 89 degrees of freedom
## Multiple R-squared: 0.4173, Adjusted R-squared: 0.3453
## F-statistic: 5.794 on 11 and 89 DF, p-value: 5.399e-07drop1(lm8,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$crest.width +
## kangaSet$mandible.length + kangaSet$mandible.width + kangaSet$ramus.height
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 14.470 -172.25
## kangaSet$occipitonasal.length 1 2.1332 16.603 -160.36 13.1204 0.0004853 ***
## kangaSet$palate.length 1 0.2211 14.691 -172.72 1.3601 0.2466307
## kangaSet$nasal.length 1 3.4126 17.883 -152.86 20.9895 1.497e-05 ***
## kangaSet$nasal.width 1 0.5588 15.029 -170.42 3.4370 0.0670619 .
## kangaSet$lacrymal.width 1 0.5155 14.985 -170.71 3.1704 0.0783953 .
## kangaSet$zygomatic.width 1 0.1740 14.644 -173.04 1.0704 0.3036650
## kangaSet$orbital.width 1 0.4636 14.934 -171.06 2.8516 0.0947821 .
## kangaSet$crest.width 1 1.0013 15.471 -167.49 6.1587 0.0149552 *
## kangaSet$mandible.length 1 0.3531 14.823 -171.81 2.1717 0.1440945
## kangaSet$mandible.width 1 0.4851 14.955 -170.92 2.9839 0.0875634 .
## kangaSet$ramus.height 1 0.2911 14.761 -172.24 1.7907 0.1842484
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm8)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$crest.width +
## kangaSet$mandible.length + kangaSet$mandible.width + kangaSet$ramus.height
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 89 14.470 -7 -0.23938 0.1971 0.9853lm9 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$palate.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$orbital.width+kangaSet$crest.width+kangaSet$mandible.length+kangaSet$mandible.width+kangaSet$ramus.height,data=kangaSet)
summary(lm9)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$orbital.width + kangaSet$crest.width + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.74267 -0.32004 -0.08841 0.30592 0.97268
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.706293 0.831133 -2.053 0.042978 *
## kangaSet$occipitonasal.length 0.006054 0.001683 3.597 0.000526 ***
## kangaSet$palate.length 0.002775 0.002174 1.276 0.205098
## kangaSet$nasal.length -0.008870 0.001815 -4.886 4.45e-06 ***
## kangaSet$nasal.width 0.007828 0.003940 1.987 0.049991 *
## kangaSet$lacrymal.width -0.006179 0.003665 -1.686 0.095280 .
## kangaSet$orbital.width 0.004909 0.003135 1.566 0.120935
## kangaSet$crest.width -0.003901 0.001730 -2.255 0.026562 *
## kangaSet$mandible.length -0.002508 0.002086 -1.203 0.232274
## kangaSet$mandible.width 0.012374 0.006680 1.852 0.067248 .
## kangaSet$ramus.height -0.002318 0.002202 -1.053 0.295337
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4034 on 90 degrees of freedom
## Multiple R-squared: 0.4103, Adjusted R-squared: 0.3447
## F-statistic: 6.261 on 10 and 90 DF, p-value: 3.263e-07drop1(lm9,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$orbital.width + kangaSet$crest.width + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 14.644 -173.04
## kangaSet$occipitonasal.length 1 2.1047 16.749 -161.48 12.9355 0.0005263 ***
## kangaSet$palate.length 1 0.2651 14.909 -173.23 1.6292 0.2050984
## kangaSet$nasal.length 1 3.8842 18.528 -151.28 23.8718 4.454e-06 ***
## kangaSet$nasal.width 1 0.6423 15.286 -170.71 3.9472 0.0499910 *
## kangaSet$lacrymal.width 1 0.4625 15.106 -171.90 2.8423 0.0952796 .
## kangaSet$orbital.width 1 0.3989 15.043 -172.33 2.4513 0.1209349
## kangaSet$crest.width 1 0.8273 15.471 -169.49 5.0848 0.0265619 *
## kangaSet$mandible.length 1 0.2353 14.879 -173.43 1.4463 0.2322736
## kangaSet$mandible.width 1 0.5583 15.202 -171.26 3.4313 0.0672477 .
## kangaSet$ramus.height 1 0.1803 14.824 -173.80 1.1080 0.2953371
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm9)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$orbital.width + kangaSet$crest.width + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 90 14.644 -8 -0.4134 0.2978 0.9648lm10 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$palate.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$orbital.width+kangaSet$crest.width+kangaSet$mandible.length+kangaSet$mandible.width,data=kangaSet)
summary(lm10)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$orbital.width + kangaSet$crest.width + kangaSet$mandible.length +
## kangaSet$mandible.width, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.69878 -0.33011 -0.04539 0.30086 0.94008
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.665541 0.830723 -2.005 0.047942 *
## kangaSet$occipitonasal.length 0.005950 0.001681 3.539 0.000635 ***
## kangaSet$palate.length 0.003196 0.002138 1.495 0.138498
## kangaSet$nasal.length -0.008757 0.001813 -4.830 5.5e-06 ***
## kangaSet$nasal.width 0.009478 0.003617 2.620 0.010305 *
## kangaSet$lacrymal.width -0.007645 0.003392 -2.254 0.026606 *
## kangaSet$orbital.width 0.005034 0.003135 1.606 0.111736
## kangaSet$crest.width -0.003954 0.001730 -2.285 0.024629 *
## kangaSet$mandible.length -0.003663 0.001775 -2.063 0.041927 *
## kangaSet$mandible.width 0.010147 0.006340 1.601 0.112953
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4036 on 91 degrees of freedom
## Multiple R-squared: 0.403, Adjusted R-squared: 0.344
## F-statistic: 6.826 on 9 and 91 DF, p-value: 1.927e-07drop1(lm10,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$orbital.width + kangaSet$crest.width + kangaSet$mandible.length +
## kangaSet$mandible.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 14.824 -173.80
## kangaSet$occipitonasal.length 1 2.0400 16.864 -162.78 12.5229 0.0006354 ***
## kangaSet$palate.length 1 0.3639 15.188 -173.35 2.2336 0.1384983
## kangaSet$nasal.length 1 3.7997 18.624 -152.76 23.3250 5.504e-06 ***
## kangaSet$nasal.width 1 1.1182 15.942 -168.46 6.8640 0.0103050 *
## kangaSet$lacrymal.width 1 0.8275 15.652 -170.32 5.0799 0.0266056 *
## kangaSet$orbital.width 1 0.4202 15.244 -172.98 2.5793 0.1117362
## kangaSet$crest.width 1 0.8507 15.675 -170.17 5.2218 0.0246288 *
## kangaSet$mandible.length 1 0.6936 15.518 -171.19 4.2575 0.0419267 *
## kangaSet$mandible.width 1 0.4173 15.242 -173.00 2.5616 0.1129527
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm10)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$orbital.width + kangaSet$crest.width + kangaSet$mandible.length +
## kangaSet$mandible.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 91 14.824 -9 -0.59369 0.3801 0.9415lm11 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$orbital.width+kangaSet$crest.width+kangaSet$mandible.length+kangaSet$mandible.width,data=kangaSet)
summary(lm11)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width + kangaSet$mandible.length + kangaSet$mandible.width,
## data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.71470 -0.31695 -0.03904 0.31104 0.98461
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.773865 0.833085 -2.129 0.035902 *
## kangaSet$occipitonasal.length 0.006527 0.001647 3.962 0.000147 ***
## kangaSet$nasal.length -0.008521 0.001818 -4.686 9.61e-06 ***
## kangaSet$nasal.width 0.009086 0.003632 2.502 0.014132 *
## kangaSet$lacrymal.width -0.007386 0.003410 -2.166 0.032897 *
## kangaSet$orbital.width 0.005089 0.003155 1.613 0.110198
## kangaSet$crest.width -0.004435 0.001712 -2.591 0.011126 *
## kangaSet$mandible.length -0.001875 0.001320 -1.420 0.158972
## kangaSet$mandible.width 0.010794 0.006367 1.695 0.093406 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4063 on 92 degrees of freedom
## Multiple R-squared: 0.3884, Adjusted R-squared: 0.3352
## F-statistic: 7.302 on 8 and 92 DF, p-value: 1.804e-07drop1(lm11,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width + kangaSet$mandible.length + kangaSet$mandible.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 15.188 -173.35
## kangaSet$occipitonasal.length 1 2.5914 17.779 -159.44 15.6972 0.0001466 ***
## kangaSet$nasal.length 1 3.6249 18.813 -153.74 21.9575 9.614e-06 ***
## kangaSet$nasal.width 1 1.0331 16.221 -168.71 6.2578 0.0141321 *
## kangaSet$lacrymal.width 1 0.7745 15.963 -170.33 4.6915 0.0328969 *
## kangaSet$orbital.width 1 0.4295 15.618 -172.54 2.6013 0.1101980
## kangaSet$crest.width 1 1.1084 16.297 -168.24 6.7137 0.0111257 *
## kangaSet$mandible.length 1 0.3329 15.521 -173.16 2.0166 0.1589722
## kangaSet$mandible.width 1 0.4745 15.663 -172.25 2.8739 0.0934060 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm11)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width + kangaSet$mandible.length + kangaSet$mandible.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 92 15.188 -10 -0.95755 0.5518 0.848lm12 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$orbital.width+kangaSet$crest.width+kangaSet$mandible.width,data=kangaSet)
summary(lm12)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width + kangaSet$mandible.width, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.74332 -0.33268 -0.06351 0.32789 0.95860
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.488127 0.812826 -1.831 0.070332 .
## kangaSet$occipitonasal.length 0.005276 0.001400 3.769 0.000287 ***
## kangaSet$nasal.length -0.008280 0.001820 -4.549 1.63e-05 ***
## kangaSet$nasal.width 0.009707 0.003625 2.677 0.008770 **
## kangaSet$lacrymal.width -0.009129 0.003199 -2.854 0.005327 **
## kangaSet$orbital.width 0.006537 0.003003 2.177 0.032008 *
## kangaSet$crest.width -0.004302 0.001718 -2.503 0.014047 *
## kangaSet$mandible.width 0.006512 0.005639 1.155 0.251068
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4085 on 93 degrees of freedom
## Multiple R-squared: 0.375, Adjusted R-squared: 0.3279
## F-statistic: 7.97 on 7 and 93 DF, p-value: 1.48e-07drop1(lm12,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width + kangaSet$mandible.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 15.521 -173.16
## kangaSet$occipitonasal.length 1 2.3714 17.892 -160.81 14.2089 0.0002871 ***
## kangaSet$nasal.length 1 3.4529 18.974 -154.88 20.6896 1.627e-05 ***
## kangaSet$nasal.width 1 1.1964 16.717 -167.67 7.1687 0.0087704 **
## kangaSet$lacrymal.width 1 1.3591 16.880 -166.69 8.1437 0.0053266 **
## kangaSet$orbital.width 1 0.7910 16.312 -170.15 4.7396 0.0320080 *
## kangaSet$crest.width 1 1.0459 16.567 -168.58 6.2667 0.0140465 *
## kangaSet$mandible.width 1 0.2226 15.744 -173.73 1.3339 0.2510675
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm12)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width + kangaSet$mandible.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 93 15.521 -11 -1.2905 0.676 0.7572lm13 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$orbital.width+kangaSet$crest.width,data=kangaSet)
summary(lm13)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.74904 -0.31904 -0.06804 0.32100 0.92466
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.386704 0.809503 -1.713 0.0900 .
## kangaSet$occipitonasal.length 0.005976 0.001264 4.729 7.92e-06 ***
## kangaSet$nasal.length -0.009071 0.001690 -5.369 5.70e-07 ***
## kangaSet$nasal.width 0.008703 0.003526 2.468 0.0154 *
## kangaSet$lacrymal.width -0.007730 0.002966 -2.606 0.0106 *
## kangaSet$orbital.width 0.005807 0.002940 1.975 0.0512 .
## kangaSet$crest.width -0.004016 0.001704 -2.357 0.0205 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4092 on 94 degrees of freedom
## Multiple R-squared: 0.366, Adjusted R-squared: 0.3255
## F-statistic: 9.044 on 6 and 94 DF, p-value: 8.458e-08drop1(lm13,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 15.744 -173.73
## kangaSet$occipitonasal.length 1 3.7454 19.489 -154.17 22.3623 7.923e-06 ***
## kangaSet$nasal.length 1 4.8274 20.571 -148.72 28.8226 5.705e-07 ***
## kangaSet$nasal.width 1 1.0204 16.764 -169.38 6.0926 0.01538 *
## kangaSet$lacrymal.width 1 1.1376 16.881 -168.68 6.7921 0.01065 *
## kangaSet$orbital.width 1 0.6531 16.397 -171.62 3.8995 0.05123 .
## kangaSet$crest.width 1 0.9308 16.674 -169.93 5.5575 0.02048 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm13)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 94 15.744 -12 -1.5131 0.7266 0.7216lm14 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width+kangaSet$crest.width,data=kangaSet)
summary(lm14)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$crest.width,
## data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.73119 -0.33283 -0.08059 0.34260 0.95536
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.900375 0.782810 -1.150 0.25296
## kangaSet$occipitonasal.length 0.006371 0.001267 5.030 2.32e-06 ***
## kangaSet$nasal.length -0.009333 0.001710 -5.458 3.83e-07 ***
## kangaSet$nasal.width 0.009536 0.003554 2.684 0.00859 **
## kangaSet$lacrymal.width -0.007481 0.003008 -2.487 0.01463 *
## kangaSet$crest.width -0.002721 0.001596 -1.705 0.09146 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4154 on 95 degrees of freedom
## Multiple R-squared: 0.3397, Adjusted R-squared: 0.3049
## F-statistic: 9.774 on 5 and 95 DF, p-value: 1.476e-07drop1(lm14,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$crest.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 16.397 -171.62
## kangaSet$occipitonasal.length 1 4.3664 20.763 -149.78 25.2985 2.315e-06 ***
## kangaSet$nasal.length 1 5.1413 21.538 -146.07 29.7878 3.832e-07 ***
## kangaSet$nasal.width 1 1.2429 17.640 -166.24 7.2013 0.008595 **
## kangaSet$lacrymal.width 1 1.0674 17.464 -167.25 6.1844 0.014633 *
## kangaSet$crest.width 1 0.5017 16.898 -170.58 2.9070 0.091464 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm14)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$crest.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 95 16.397 -13 -2.1662 0.9602 0.4969lm15 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$nasal.length+kangaSet$nasal.width+kangaSet$lacrymal.width,data=kangaSet)
summary(lm15)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6725 -0.3315 -0.1239 0.2905 1.0247
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.818560 0.573752 -3.170 0.00205 **
## kangaSet$occipitonasal.length 0.006745 0.001260 5.353 5.88e-07 ***
## kangaSet$nasal.length -0.008667 0.001681 -5.155 1.36e-06 ***
## kangaSet$nasal.width 0.009424 0.003588 2.626 0.01004 *
## kangaSet$lacrymal.width -0.008413 0.002987 -2.816 0.00590 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4196 on 96 degrees of freedom
## Multiple R-squared: 0.3195, Adjusted R-squared: 0.2911
## F-statistic: 11.27 on 4 and 96 DF, p-value: 1.547e-07drop1(lm15,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 16.898 -170.58
## kangaSet$occipitonasal.length 1 5.0447 21.943 -146.19 28.6587 5.881e-07 ***
## kangaSet$nasal.length 1 4.6778 21.576 -147.90 26.5745 1.357e-06 ***
## kangaSet$nasal.width 1 1.2143 18.113 -165.57 6.8983 0.010043 *
## kangaSet$lacrymal.width 1 1.3961 18.295 -164.56 7.9314 0.005897 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm15)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 96 16.898 -14 -2.6679 1.0981 0.372lm16 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$nasal.length+kangaSet$lacrymal.width,data=kangaSet)
summary(lm16)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$lacrymal.width, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7273 -0.3494 -0.1372 0.3427 0.9878
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.815176 0.590938 -3.072 0.00276 **
## kangaSet$occipitonasal.length 0.005975 0.001262 4.734 7.50e-06 ***
## kangaSet$nasal.length -0.006323 0.001467 -4.309 3.94e-05 ***
## kangaSet$lacrymal.width -0.004250 0.002608 -1.630 0.10643
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4321 on 97 degrees of freedom
## Multiple R-squared: 0.2706, Adjusted R-squared: 0.248
## F-statistic: 11.99 on 3 and 97 DF, p-value: 9.564e-07drop1(lm16,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$lacrymal.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 18.113 -165.57
## kangaSet$occipitonasal.length 1 4.1851 22.298 -146.57 22.4129 7.497e-06 ***
## kangaSet$nasal.length 1 3.4665 21.579 -149.88 18.5642 3.940e-05 ***
## kangaSet$lacrymal.width 1 0.4959 18.609 -164.84 2.6556 0.1064
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm16)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$lacrymal.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 97 18.113 -15 -3.8822 1.4914 0.1278lm17 <- lm(Type_kanga~kangaSet$occipitonasal.length+kangaSet$nasal.length,data=kangaSet)
summary(lm17)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length,
## data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7722 -0.3403 -0.1879 0.3473 0.9876
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.8846011 0.5943578 -3.171 0.002029 **
## kangaSet$occipitonasal.length 0.0044443 0.0008502 5.228 9.71e-07 ***
## kangaSet$nasal.length -0.0054523 0.0013783 -3.956 0.000144 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4358 on 98 degrees of freedom
## Multiple R-squared: 0.2506, Adjusted R-squared: 0.2353
## F-statistic: 16.39 on 2 and 98 DF, p-value: 7.257e-07drop1(lm17,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 18.609 -164.84
## kangaSet$occipitonasal.length 1 5.1891 23.798 -142.00 27.328 9.712e-07 ***
## kangaSet$nasal.length 1 2.9714 21.580 -151.88 15.649 0.0001443 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm17)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 98 18.609 -16 -4.3781 1.5767 0.09398 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lm18 <- lm(Type_kanga~kangaSet$occipitonasal.length,data=kangaSet)
summary(lm18)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6896 -0.4087 -0.1811 0.4155 0.8589
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.6494718 0.5418665 -1.199 0.233551
## kangaSet$occipitonasal.length 0.0013313 0.0003447 3.862 0.000201 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4669 on 99 degrees of freedom
## Multiple R-squared: 0.1309, Adjusted R-squared: 0.1222
## F-statistic: 14.92 on 1 and 99 DF, p-value: 0.0002006drop1(lm18,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ kangaSet$occipitonasal.length
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 21.580 -151.88
## kangaSet$occipitonasal.length 1 3.2516 24.832 -139.70 14.917 0.0002006 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm1,lm18)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ kangaSet$occipitonasal.length
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 99 21.580 -17 -7.3495 2.4912 0.003259 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lm19 <- lm(Type_kanga~1,data=kangaSet)
summary(lm19)##
## Call:
## lm(formula = Type_kanga ~ 1, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4356 -0.4356 -0.4356 0.5644 0.5644
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.43564 0.04958 28.95 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4983 on 100 degrees of freedomdrop1(lm19,test="F")## Single term deletions
##
## Model:
## Type_kanga ~ 1
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 24.832 -139.7anova(lm1,lm19)## Analysis of Variance Table
##
## Model 1: Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
## Model 2: Type_kanga ~ 1
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 82 14.231
## 2 100 24.832 -18 -10.601 3.3937 8.044e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##Score AIC for each model:
data.frame(model=paste("lm",1:18,sep=""),
rbind(extractAIC(lm1),
extractAIC(lm2),
extractAIC(lm3),
extractAIC(lm4),
extractAIC(lm5),
extractAIC(lm6),
extractAIC(lm7),
extractAIC(lm8),
extractAIC(lm9),
extractAIC(lm10),
extractAIC(lm11),
extractAIC(lm12),
extractAIC(lm13),
extractAIC(lm14),
extractAIC(lm15),
extractAIC(lm16),
extractAIC(lm17),
extractAIC(lm18)))## model X1 X2
## 1 lm1 19 -159.9326
## 2 lm2 18 -161.9309
## 3 lm3 17 -163.8193
## 4 lm4 16 -165.5199
## 5 lm5 15 -167.3157
## 6 lm6 14 -169.0313
## 7 lm7 13 -170.6310
## 8 lm8 12 -172.2478
## 9 lm9 11 -173.0403
## 10 lm10 10 -173.8045
## 11 lm11 9 -173.3554
## 12 lm12 8 -173.1655
## 13 lm13 7 -173.7271
## 14 lm14 6 -171.6218
## 15 lm15 5 -170.5775
## 16 lm16 4 -165.5688
## 17 lm17 3 -164.8409
## 18 lm18 2 -151.8783##Compare to bayes factor:
library(BayesFactor)## Warning: package 'BayesFactor' was built under R version 3.6.2## Loading required package: coda## Warning: package 'coda' was built under R version 3.6.2## Loading required package: Matrix## ************
## Welcome to BayesFactor 0.9.12-4.2. If you have questions, please contact Richard Morey (richarddmorey@gmail.com).
##
## Type BFManual() to open the manual.
## ************#bmodel <- regressionBF(Type_kanga~basilar.length+occipitonasal.length+palate.length+palate.width+nasal.length+nasal.width+squamosal.depth+lacrymal.width+zygomatic.width+orbital.width+occipital.depth+crest.width+foramina.length+mandible.length+mandible.width+mandible.depth+ramus.height+.rostral.width,data=kangaSet)
#plot(head(bmodel))
#head(bmodel)
##Use stepwise model search. Here, we use both directions every time.
gsmall <- step(lm1,direction="both", k=log(nrow(kangaSet)))## Start: AIC=-110.25
## Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$squamosal.depth + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
##
## Df Sum of Sq RSS AIC
## - kangaSet$squamosal.depth 1 0.00023 14.231 -114.859
## - kangaSet$palate.width 1 0.01583 14.246 -114.748
## - kangaSet$basilar.length 1 0.02939 14.260 -114.652
## - kangaSet$mandible.depth 1 0.05075 14.281 -114.501
## - kangaSet$.rostral.width 1 0.05364 14.284 -114.480
## - kangaSet$foramina.length 1 0.06128 14.292 -114.426
## - kangaSet$occipital.depth 1 0.07100 14.302 -114.358
## - kangaSet$palate.length 1 0.11349 14.344 -114.058
## - kangaSet$zygomatic.width 1 0.17190 14.402 -113.648
## - kangaSet$ramus.height 1 0.25279 14.483 -113.082
## - kangaSet$mandible.width 1 0.27931 14.510 -112.897
## - kangaSet$mandible.length 1 0.30620 14.537 -112.710
## - kangaSet$lacrymal.width 1 0.38596 14.617 -112.158
## - kangaSet$orbital.width 1 0.44698 14.678 -111.737
## - kangaSet$nasal.width 1 0.57120 14.802 -110.886
## <none> 14.231 -110.245
## - kangaSet$crest.width 1 0.97100 15.202 -108.194
## - kangaSet$occipitonasal.length 1 1.02263 15.253 -107.851
## - kangaSet$nasal.length 1 2.69254 16.923 -97.358
##
## Step: AIC=-114.86
## Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$palate.width + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$zygomatic.width +
## kangaSet$orbital.width + kangaSet$occipital.depth + kangaSet$crest.width +
## kangaSet$foramina.length + kangaSet$mandible.length + kangaSet$mandible.width +
## kangaSet$mandible.depth + kangaSet$ramus.height + kangaSet$.rostral.width
##
## Df Sum of Sq RSS AIC
## - kangaSet$palate.width 1 0.01574 14.246 -119.36
## - kangaSet$basilar.length 1 0.02945 14.260 -119.27
## - kangaSet$mandible.depth 1 0.05235 14.283 -119.10
## - kangaSet$.rostral.width 1 0.05382 14.285 -119.09
## - kangaSet$foramina.length 1 0.06123 14.292 -119.04
## - kangaSet$occipital.depth 1 0.07388 14.305 -118.95
## - kangaSet$palate.length 1 0.11431 14.345 -118.67
## - kangaSet$zygomatic.width 1 0.18755 14.418 -118.15
## - kangaSet$ramus.height 1 0.25312 14.484 -117.69
## - kangaSet$mandible.length 1 0.30599 14.537 -117.33
## - kangaSet$mandible.width 1 0.31586 14.547 -117.26
## - kangaSet$lacrymal.width 1 0.38606 14.617 -116.77
## - kangaSet$orbital.width 1 0.45965 14.690 -116.26
## - kangaSet$nasal.width 1 0.57167 14.803 -115.50
## <none> 14.231 -114.86
## - kangaSet$crest.width 1 0.97352 15.204 -112.79
## - kangaSet$occipitonasal.length 1 1.02284 15.254 -112.46
## + kangaSet$squamosal.depth 1 0.00023 14.231 -110.25
## - kangaSet$nasal.length 1 2.71850 16.949 -101.82
##
## Step: AIC=-119.36
## Type_kanga ~ kangaSet$basilar.length + kangaSet$occipitonasal.length +
## kangaSet$palate.length + kangaSet$nasal.length + kangaSet$nasal.width +
## kangaSet$lacrymal.width + kangaSet$zygomatic.width + kangaSet$orbital.width +
## kangaSet$occipital.depth + kangaSet$crest.width + kangaSet$foramina.length +
## kangaSet$mandible.length + kangaSet$mandible.width + kangaSet$mandible.depth +
## kangaSet$ramus.height + kangaSet$.rostral.width
##
## Df Sum of Sq RSS AIC
## - kangaSet$basilar.length 1 0.04229 14.289 -123.68
## - kangaSet$mandible.depth 1 0.04685 14.293 -123.65
## - kangaSet$.rostral.width 1 0.05532 14.302 -123.59
## - kangaSet$foramina.length 1 0.06317 14.310 -123.53
## - kangaSet$occipital.depth 1 0.06828 14.315 -123.49
## - kangaSet$palate.length 1 0.10764 14.354 -123.22
## - kangaSet$zygomatic.width 1 0.17190 14.418 -122.77
## - kangaSet$ramus.height 1 0.24924 14.496 -122.23
## - kangaSet$mandible.width 1 0.32417 14.571 -121.70
## - kangaSet$mandible.length 1 0.35195 14.598 -121.51
## - kangaSet$lacrymal.width 1 0.37288 14.619 -121.37
## - kangaSet$orbital.width 1 0.46503 14.712 -120.73
## - kangaSet$nasal.width 1 0.56456 14.811 -120.05
## <none> 14.246 -119.36
## - kangaSet$crest.width 1 0.96554 15.212 -117.35
## - kangaSet$occipitonasal.length 1 1.01727 15.264 -117.01
## + kangaSet$palate.width 1 0.01574 14.231 -114.86
## + kangaSet$squamosal.depth 1 0.00015 14.246 -114.75
## - kangaSet$nasal.length 1 2.70323 16.950 -106.43
##
## Step: AIC=-123.68
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$mandible.depth + kangaSet$ramus.height +
## kangaSet$.rostral.width
##
## Df Sum of Sq RSS AIC
## - kangaSet$mandible.depth 1 0.02892 14.318 -128.09
## - kangaSet$.rostral.width 1 0.03728 14.326 -128.03
## - kangaSet$occipital.depth 1 0.05262 14.341 -127.92
## - kangaSet$foramina.length 1 0.07876 14.368 -127.74
## - kangaSet$zygomatic.width 1 0.14949 14.438 -127.24
## - kangaSet$ramus.height 1 0.23101 14.520 -126.67
## - kangaSet$palate.length 1 0.26041 14.549 -126.47
## - kangaSet$mandible.length 1 0.30965 14.598 -126.13
## - kangaSet$mandible.width 1 0.34415 14.633 -125.89
## - kangaSet$lacrymal.width 1 0.37682 14.666 -125.66
## - kangaSet$orbital.width 1 0.50927 14.798 -124.76
## - kangaSet$nasal.width 1 0.53260 14.821 -124.60
## <none> 14.289 -123.68
## - kangaSet$crest.width 1 0.93102 15.220 -121.92
## + kangaSet$basilar.length 1 0.04229 14.246 -119.36
## + kangaSet$palate.width 1 0.02859 14.260 -119.27
## + kangaSet$squamosal.depth 1 0.00017 14.289 -119.06
## - kangaSet$occipitonasal.length 1 1.74679 16.036 -116.64
## - kangaSet$nasal.length 1 3.15458 17.443 -108.14
##
## Step: AIC=-128.09
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height + kangaSet$.rostral.width
##
## Df Sum of Sq RSS AIC
## - kangaSet$.rostral.width 1 0.04037 14.358 -132.42
## - kangaSet$occipital.depth 1 0.05625 14.374 -132.31
## - kangaSet$foramina.length 1 0.06743 14.385 -132.23
## - kangaSet$zygomatic.width 1 0.17426 14.492 -131.48
## - kangaSet$palate.length 1 0.25761 14.575 -130.90
## - kangaSet$mandible.width 1 0.32220 14.640 -130.46
## - kangaSet$ramus.height 1 0.32942 14.647 -130.41
## - kangaSet$mandible.length 1 0.34635 14.664 -130.29
## - kangaSet$lacrymal.width 1 0.37035 14.688 -130.12
## - kangaSet$orbital.width 1 0.48856 14.806 -129.31
## - kangaSet$nasal.width 1 0.50407 14.822 -129.21
## <none> 14.318 -128.09
## - kangaSet$crest.width 1 1.01590 15.334 -125.78
## + kangaSet$mandible.depth 1 0.02892 14.289 -123.68
## + kangaSet$basilar.length 1 0.02437 14.293 -123.65
## + kangaSet$palate.width 1 0.01912 14.299 -123.61
## + kangaSet$squamosal.depth 1 0.00099 14.317 -123.48
## - kangaSet$occipitonasal.length 1 1.74817 16.066 -121.07
## - kangaSet$nasal.length 1 3.12657 17.444 -112.75
##
## Step: AIC=-132.42
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$occipital.depth +
## kangaSet$crest.width + kangaSet$foramina.length + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height
##
## Df Sum of Sq RSS AIC
## - kangaSet$occipital.depth 1 0.05702 14.415 -136.63
## - kangaSet$foramina.length 1 0.06371 14.422 -136.59
## - kangaSet$zygomatic.width 1 0.14658 14.505 -136.01
## - kangaSet$palate.length 1 0.25746 14.616 -135.24
## - kangaSet$ramus.height 1 0.33889 14.697 -134.68
## - kangaSet$mandible.length 1 0.37801 14.736 -134.41
## - kangaSet$mandible.width 1 0.38030 14.738 -134.39
## - kangaSet$lacrymal.width 1 0.47202 14.830 -133.77
## - kangaSet$nasal.width 1 0.51118 14.869 -133.50
## - kangaSet$orbital.width 1 0.51176 14.870 -133.50
## <none> 14.358 -132.42
## - kangaSet$crest.width 1 0.97837 15.336 -130.38
## + kangaSet$.rostral.width 1 0.04037 14.318 -128.09
## + kangaSet$mandible.depth 1 0.03200 14.326 -128.03
## + kangaSet$palate.width 1 0.01715 14.341 -127.92
## + kangaSet$basilar.length 1 0.01100 14.347 -127.88
## + kangaSet$squamosal.depth 1 0.00090 14.357 -127.81
## - kangaSet$occipitonasal.length 1 1.77733 16.135 -125.25
## - kangaSet$nasal.length 1 3.15151 17.510 -116.99
##
## Step: AIC=-136.63
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$crest.width +
## kangaSet$foramina.length + kangaSet$mandible.length + kangaSet$mandible.width +
## kangaSet$ramus.height
##
## Df Sum of Sq RSS AIC
## - kangaSet$foramina.length 1 0.05481 14.470 -140.87
## - kangaSet$zygomatic.width 1 0.15362 14.569 -140.18
## - kangaSet$palate.length 1 0.24152 14.657 -139.57
## - kangaSet$ramus.height 1 0.29885 14.714 -139.18
## - kangaSet$mandible.length 1 0.34508 14.760 -138.86
## - kangaSet$lacrymal.width 1 0.43758 14.853 -138.23
## - kangaSet$mandible.width 1 0.45433 14.870 -138.12
## - kangaSet$orbital.width 1 0.49750 14.913 -137.82
## - kangaSet$nasal.width 1 0.56135 14.976 -137.39
## <none> 14.415 -136.63
## - kangaSet$crest.width 1 0.99753 15.413 -134.49
## + kangaSet$occipital.depth 1 0.05702 14.358 -132.42
## + kangaSet$.rostral.width 1 0.04114 14.374 -132.31
## + kangaSet$mandible.depth 1 0.03586 14.379 -132.27
## + kangaSet$palate.width 1 0.00944 14.406 -132.09
## + kangaSet$basilar.length 1 0.00380 14.411 -132.05
## + kangaSet$squamosal.depth 1 0.00001 14.415 -132.02
## - kangaSet$occipitonasal.length 1 1.88114 16.296 -128.86
## - kangaSet$nasal.length 1 3.12616 17.541 -121.42
##
## Step: AIC=-140.87
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$zygomatic.width + kangaSet$orbital.width + kangaSet$crest.width +
## kangaSet$mandible.length + kangaSet$mandible.width + kangaSet$ramus.height
##
## Df Sum of Sq RSS AIC
## - kangaSet$zygomatic.width 1 0.1740 14.644 -144.27
## - kangaSet$palate.length 1 0.2211 14.691 -143.95
## - kangaSet$ramus.height 1 0.2911 14.761 -143.47
## - kangaSet$mandible.length 1 0.3531 14.823 -143.05
## - kangaSet$orbital.width 1 0.4636 14.934 -142.30
## - kangaSet$mandible.width 1 0.4851 14.955 -142.15
## - kangaSet$lacrymal.width 1 0.5155 14.985 -141.95
## - kangaSet$nasal.width 1 0.5588 15.029 -141.65
## <none> 14.470 -140.87
## - kangaSet$crest.width 1 1.0013 15.471 -138.72
## + kangaSet$foramina.length 1 0.0548 14.415 -136.63
## + kangaSet$occipital.depth 1 0.0481 14.422 -136.59
## + kangaSet$.rostral.width 1 0.0376 14.432 -136.51
## + kangaSet$mandible.depth 1 0.0237 14.446 -136.42
## + kangaSet$palate.width 1 0.0141 14.456 -136.35
## + kangaSet$basilar.length 1 0.0104 14.460 -136.32
## + kangaSet$squamosal.depth 1 0.0003 14.470 -136.25
## - kangaSet$occipitonasal.length 1 2.1332 16.603 -131.59
## - kangaSet$nasal.length 1 3.4126 17.883 -124.09
##
## Step: AIC=-144.27
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$orbital.width + kangaSet$crest.width + kangaSet$mandible.length +
## kangaSet$mandible.width + kangaSet$ramus.height
##
## Df Sum of Sq RSS AIC
## - kangaSet$ramus.height 1 0.1803 14.824 -147.65
## - kangaSet$mandible.length 1 0.2353 14.879 -147.28
## - kangaSet$palate.length 1 0.2651 14.909 -147.08
## - kangaSet$orbital.width 1 0.3989 15.043 -146.18
## - kangaSet$lacrymal.width 1 0.4625 15.106 -145.75
## - kangaSet$mandible.width 1 0.5583 15.202 -145.11
## - kangaSet$nasal.width 1 0.6423 15.286 -144.55
## <none> 14.644 -144.27
## - kangaSet$crest.width 1 0.8273 15.471 -143.34
## + kangaSet$zygomatic.width 1 0.1740 14.470 -140.87
## + kangaSet$foramina.length 1 0.0752 14.569 -140.18
## + kangaSet$occipital.depth 1 0.0535 14.590 -140.03
## + kangaSet$mandible.depth 1 0.0433 14.601 -139.96
## + kangaSet$.rostral.width 1 0.0093 14.635 -139.72
## + kangaSet$squamosal.depth 1 0.0066 14.637 -139.70
## + kangaSet$basilar.length 1 0.0023 14.642 -139.67
## + kangaSet$palate.width 1 0.0013 14.643 -139.67
## - kangaSet$occipitonasal.length 1 2.1047 16.749 -135.33
## - kangaSet$nasal.length 1 3.8842 18.528 -125.13
##
## Step: AIC=-147.65
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$palate.length +
## kangaSet$nasal.length + kangaSet$nasal.width + kangaSet$lacrymal.width +
## kangaSet$orbital.width + kangaSet$crest.width + kangaSet$mandible.length +
## kangaSet$mandible.width
##
## Df Sum of Sq RSS AIC
## - kangaSet$palate.length 1 0.3639 15.188 -149.82
## - kangaSet$mandible.width 1 0.4173 15.242 -149.47
## - kangaSet$orbital.width 1 0.4202 15.244 -149.45
## <none> 14.824 -147.65
## - kangaSet$mandible.length 1 0.6936 15.518 -147.65
## - kangaSet$lacrymal.width 1 0.8275 15.652 -146.78
## - kangaSet$crest.width 1 0.8507 15.675 -146.63
## - kangaSet$nasal.width 1 1.1182 15.942 -144.92
## + kangaSet$ramus.height 1 0.1803 14.644 -144.27
## + kangaSet$mandible.depth 1 0.1109 14.713 -143.80
## + kangaSet$zygomatic.width 1 0.0632 14.761 -143.47
## + kangaSet$foramina.length 1 0.0599 14.764 -143.45
## + kangaSet$.rostral.width 1 0.0213 14.803 -143.18
## + kangaSet$occipital.depth 1 0.0190 14.805 -143.17
## + kangaSet$squamosal.depth 1 0.0016 14.823 -143.05
## + kangaSet$palate.width 1 0.0006 14.824 -143.04
## + kangaSet$basilar.length 1 0.0001 14.824 -143.04
## - kangaSet$occipitonasal.length 1 2.0400 16.864 -139.25
## - kangaSet$nasal.length 1 3.7997 18.624 -129.22
##
## Step: AIC=-149.82
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width + kangaSet$mandible.length + kangaSet$mandible.width
##
## Df Sum of Sq RSS AIC
## - kangaSet$mandible.length 1 0.3329 15.521 -152.25
## - kangaSet$orbital.width 1 0.4295 15.618 -151.62
## - kangaSet$mandible.width 1 0.4745 15.663 -151.33
## <none> 15.188 -149.82
## - kangaSet$lacrymal.width 1 0.7745 15.963 -149.41
## - kangaSet$nasal.width 1 1.0331 16.221 -147.79
## + kangaSet$palate.length 1 0.3639 14.824 -147.65
## - kangaSet$crest.width 1 1.1084 16.297 -147.32
## + kangaSet$ramus.height 1 0.2791 14.909 -147.08
## + kangaSet$mandible.depth 1 0.1392 15.049 -146.13
## + kangaSet$zygomatic.width 1 0.0740 15.114 -145.70
## + kangaSet$basilar.length 1 0.0738 15.114 -145.70
## + kangaSet$foramina.length 1 0.0324 15.156 -145.42
## + kangaSet$.rostral.width 1 0.0216 15.166 -145.35
## + kangaSet$occipital.depth 1 0.0059 15.182 -145.24
## + kangaSet$palate.width 1 0.0005 15.188 -145.21
## + kangaSet$squamosal.depth 1 0.0004 15.188 -145.21
## - kangaSet$occipitonasal.length 1 2.5914 17.779 -138.52
## - kangaSet$nasal.length 1 3.6249 18.813 -132.82
##
## Step: AIC=-152.24
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width + kangaSet$mandible.width
##
## Df Sum of Sq RSS AIC
## - kangaSet$mandible.width 1 0.2226 15.744 -155.42
## <none> 15.521 -152.25
## - kangaSet$orbital.width 1 0.7910 16.312 -151.84
## + kangaSet$ramus.height 1 0.5746 14.946 -151.44
## - kangaSet$crest.width 1 1.0459 16.567 -150.27
## + kangaSet$mandible.length 1 0.3329 15.188 -149.82
## + kangaSet$mandible.depth 1 0.3017 15.219 -149.61
## - kangaSet$nasal.width 1 1.1964 16.717 -149.36
## + kangaSet$.rostral.width 1 0.1227 15.398 -148.43
## - kangaSet$lacrymal.width 1 1.3591 16.880 -148.38
## + kangaSet$squamosal.depth 1 0.0813 15.440 -148.16
## + kangaSet$basilar.length 1 0.0485 15.473 -147.94
## + kangaSet$palate.width 1 0.0416 15.479 -147.90
## + kangaSet$foramina.length 1 0.0393 15.482 -147.89
## + kangaSet$zygomatic.width 1 0.0248 15.496 -147.79
## + kangaSet$occipital.depth 1 0.0115 15.509 -147.70
## + kangaSet$palate.length 1 0.0032 15.518 -147.65
## - kangaSet$occipitonasal.length 1 2.3714 17.892 -142.50
## - kangaSet$nasal.length 1 3.4529 18.974 -136.57
##
## Step: AIC=-155.42
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$orbital.width +
## kangaSet$crest.width
##
## Df Sum of Sq RSS AIC
## - kangaSet$orbital.width 1 0.6531 16.397 -155.93
## <none> 15.744 -155.42
## - kangaSet$crest.width 1 0.9308 16.674 -154.24
## - kangaSet$nasal.width 1 1.0204 16.764 -153.69
## - kangaSet$lacrymal.width 1 1.1376 16.881 -152.99
## + kangaSet$mandible.width 1 0.2226 15.521 -152.25
## + kangaSet$ramus.height 1 0.1682 15.575 -151.89
## + kangaSet$.rostral.width 1 0.1044 15.639 -151.48
## + kangaSet$mandible.depth 1 0.0985 15.645 -151.44
## + kangaSet$mandible.length 1 0.0811 15.663 -151.33
## + kangaSet$squamosal.depth 1 0.0717 15.672 -151.27
## + kangaSet$foramina.length 1 0.0631 15.681 -151.21
## + kangaSet$palate.length 1 0.0552 15.688 -151.16
## + kangaSet$palate.width 1 0.0129 15.731 -150.89
## + kangaSet$occipital.depth 1 0.0089 15.735 -150.86
## + kangaSet$zygomatic.width 1 0.0073 15.736 -150.85
## + kangaSet$basilar.length 1 0.0000 15.744 -150.81
## - kangaSet$occipitonasal.length 1 3.7454 19.489 -138.48
## - kangaSet$nasal.length 1 4.8274 20.571 -133.02
##
## Step: AIC=-155.93
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width + kangaSet$crest.width
##
## Df Sum of Sq RSS AIC
## - kangaSet$crest.width 1 0.5017 16.898 -157.50
## <none> 16.397 -155.93
## + kangaSet$orbital.width 1 0.6531 15.744 -155.42
## - kangaSet$lacrymal.width 1 1.0674 17.464 -154.18
## + kangaSet$ramus.height 1 0.3947 16.002 -153.78
## + kangaSet$mandible.length 1 0.3246 16.072 -153.34
## - kangaSet$nasal.width 1 1.2429 17.640 -153.17
## + kangaSet$squamosal.depth 1 0.2683 16.128 -152.98
## + kangaSet$.rostral.width 1 0.2604 16.136 -152.93
## + kangaSet$mandible.depth 1 0.1613 16.235 -152.31
## + kangaSet$palate.width 1 0.1080 16.289 -151.98
## + kangaSet$mandible.width 1 0.0847 16.312 -151.84
## + kangaSet$zygomatic.width 1 0.0484 16.348 -151.61
## + kangaSet$basilar.length 1 0.0349 16.362 -151.53
## + kangaSet$foramina.length 1 0.0125 16.384 -151.39
## + kangaSet$occipital.depth 1 0.0082 16.389 -151.37
## + kangaSet$palate.length 1 0.0000 16.397 -151.32
## - kangaSet$occipitonasal.length 1 4.3664 20.763 -136.70
## - kangaSet$nasal.length 1 5.1413 21.538 -133.00
##
## Step: AIC=-157.5
## Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width
##
## Df Sum of Sq RSS AIC
## <none> 16.898 -157.50
## + kangaSet$crest.width 1 0.5017 16.397 -155.93
## + kangaSet$ramus.height 1 0.3738 16.525 -155.15
## - kangaSet$nasal.width 1 1.2143 18.113 -155.11
## + kangaSet$squamosal.depth 1 0.2971 16.601 -154.68
## + kangaSet$mandible.depth 1 0.2371 16.661 -154.31
## + kangaSet$orbital.width 1 0.2241 16.674 -154.24
## + kangaSet$mandible.length 1 0.2187 16.680 -154.20
## - kangaSet$lacrymal.width 1 1.3961 18.295 -154.10
## + kangaSet$.rostral.width 1 0.1478 16.751 -153.77
## + kangaSet$zygomatic.width 1 0.1184 16.780 -153.60
## + kangaSet$mandible.width 1 0.0593 16.839 -153.24
## + kangaSet$palate.width 1 0.0283 16.870 -153.06
## + kangaSet$palate.length 1 0.0249 16.874 -153.04
## + kangaSet$basilar.length 1 0.0171 16.881 -152.99
## + kangaSet$foramina.length 1 0.0107 16.888 -152.95
## + kangaSet$occipital.depth 1 0.0030 16.895 -152.91
## - kangaSet$nasal.length 1 4.6778 21.576 -137.44
## - kangaSet$occipitonasal.length 1 5.0447 21.943 -135.73summary(gsmall)##
## Call:
## lm(formula = Type_kanga ~ kangaSet$occipitonasal.length + kangaSet$nasal.length +
## kangaSet$nasal.width + kangaSet$lacrymal.width, data = kangaSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6725 -0.3315 -0.1239 0.2905 1.0247
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.818560 0.573752 -3.170 0.00205 **
## kangaSet$occipitonasal.length 0.006745 0.001260 5.353 5.88e-07 ***
## kangaSet$nasal.length -0.008667 0.001681 -5.155 1.36e-06 ***
## kangaSet$nasal.width 0.009424 0.003588 2.626 0.01004 *
## kangaSet$lacrymal.width -0.008413 0.002987 -2.816 0.00590 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4196 on 96 degrees of freedom
## Multiple R-squared: 0.3195, Adjusted R-squared: 0.2911
## F-statistic: 11.27 on 4 and 96 DF, p-value: 1.547e-07Problem 3:
library(faraway)
data("kanga")
KANGA<-faraway::kanga
KANGA## species sex basilar.length occipitonasal.length palate.length
## 1 giganteus Male 1312 1445 882
## 2 giganteus Male 1439 1503 985
## 3 giganteus Male 1378 1464 934
## 4 giganteus Male 1315 1367 895
## 5 giganteus Male 1413 1500 969
## 6 giganteus Male 1090 1195 740
## 7 giganteus Male 1294 1421 872
## 8 giganteus Male 1377 1504 954
## 9 giganteus Male 1296 1439 878
## 10 giganteus Male 1470 1563 987
## 11 giganteus Male 1612 1699 1119
## 12 giganteus Male 1388 1500 936
## 13 giganteus Male 1575 1655 1100
## 14 giganteus Male 1717 1821 1184
## 15 giganteus Male 1587 1711 1115
## 16 giganteus Male 1604 1770 1132
## 17 giganteus Male 1630 1703 1122
## 18 giganteus Male 1490 1599 1007
## 19 giganteus Male 1552 1540 1031
## 20 giganteus Male 1595 1709 1092
## 21 giganteus Male 1840 1907 1279
## 22 giganteus Male 1740 1817 1225
## 23 giganteus Male 1846 1893 1300
## 24 giganteus Male 1702 1860 1270
## 25 giganteus Male 1768 1890 1173
## 26 giganteus Female 1112 1225 755
## 27 giganteus Female 1262 1367 855
## 28 giganteus Female 1423 1490 971
## 29 giganteus Female 1373 1494 952
## 30 giganteus Female 1414 1517 971
## 31 giganteus Female 1415 1523 973
## 32 giganteus Female 1374 1463 927
## 33 giganteus Female 1427 1487 978
## 34 giganteus Female 1382 1494 942
## 35 giganteus Female 1440 1557 985
## 36 giganteus Female 1575 1667 1105
## 37 giganteus Female 1462 1516 1016
## 38 giganteus Female 1559 1650 1087
## 39 giganteus Female 1507 1590 1043
## 40 giganteus Female 1546 1621 1072
## 41 giganteus Female 1512 1567 1052
## 42 giganteus Female 1400 1501 1041
## 43 giganteus Female 1464 1573 1037
## 44 giganteus Female 1491 1578 1028
## 45 giganteus Female 1530 1576 1037
## 46 giganteus Female 1570 1618 1064
## 47 giganteus Female 1607 1647 1118
## 48 giganteus Female 1558 1646 1087
## 49 giganteus Female 1589 1750 1128
## 50 giganteus Female 1548 1663 1079
## 51 melanops Male NA 1493 980
## 52 melanops Male 1299 1345 895
## 53 melanops Male 1337 1395 910
## 54 melanops Male 1372 1456 920
## 55 melanops Male 1336 1441 903
## 56 melanops Male 1301 1387 888
## 57 melanops Male 1360 1467 915
## 58 melanops Male 1276 1351 824
## 59 melanops Male 1351 NA 921
## 60 melanops Male 1613 1726 1136
## 61 melanops Male 1542 1628 1020
## 62 melanops Male 1440 1580 972
## 63 melanops Male 1474 1555 989
## 64 melanops Male 1503 1603 1031
## 65 melanops Male 1597 1653 1060
## 66 melanops Male 1671 1689 1130
## 67 melanops Male 1673 1720 1140
## 68 melanops Male 1458 1588 969
## 69 melanops Male 1568 1689 1086
## 70 melanops Male 1650 1707 1173
## 71 melanops Male 1774 1838 1210
## 72 melanops Male 1893 1945 1315
## 73 melanops Male 1765 1781 1240
## 74 melanops Female 1030 1121 665
## 75 melanops Female 1389 1486 931
## 76 melanops Female 1263 1372 857
## 77 melanops Female 1067 1167 702
## 78 melanops Female 1379 1500 947
## 79 melanops Female 1335 1407 900
## 80 melanops Female 1282 NA 835
## 81 melanops Female 1413 1490 962
## 82 melanops Female 1470 1583 1000
## 83 melanops Female 1377 1479 923
## 84 melanops Female 1464 1539 971
## 85 melanops Female 1452 1592 973
## 86 melanops Female 1444 1552 972
## 87 melanops Female 1487 1586 1002
## 88 melanops Female 1515 1617 1036
## 89 melanops Female 1536 1620 1070
## 90 melanops Female 1499 1606 1028
## 91 melanops Female 1505 1569 1042
## 92 melanops Female 1519 1594 1066
## 93 melanops Female 1566 1606 1046
## 94 melanops Female 1509 1601 1023
## 95 melanops Female 1553 1607 1059
## 96 melanops Female 1660 1701 1171
## 97 melanops Female 1719 1757 1190
## 98 melanops Female 1688 1720 1188
## 99 fuliginosus Male 1382 1493 928
## 100 fuliginosus Male 1438 1481 976
## 101 fuliginosus Male 1304 1408 959
## 102 fuliginosus Male 1391 1430 950
## 103 fuliginosus Male 1716 1688 1158
## 104 fuliginosus Male 1530 1578 1046
## 105 fuliginosus Male 1625 1630 1132
## 106 fuliginosus Male 1559 1567 1069
## 107 fuliginosus Male 1578 1566 1094
## 108 fuliginosus Male 1562 1580 1076
## 109 fuliginosus Male 1656 1640 1146
## 110 fuliginosus Male 1477 1486 1001
## 111 fuliginosus Male 1568 1601 1095
## 112 fuliginosus Male 1656 1646 1142
## 113 fuliginosus Male 1619 1678 1106
## 114 fuliginosus Male 1687 1692 1153
## 115 fuliginosus Male 1748 1731 1212
## 116 fuliginosus Male 1783 1788 1243
## 117 fuliginosus Male 1745 1738 1235
## 118 fuliginosus Male 1680 1668 1151
## 119 fuliginosus Male 1653 1701 1151
## 120 fuliginosus Male 1732 1702 1200
## 121 fuliginosus Male 1729 1694 1199
## 122 fuliginosus Male 1711 1695 1191
## 123 fuliginosus Male 1834 1823 1247
## 124 fuliginosus Female 1271 1334 859
## 125 fuliginosus Female 1329 1375 885
## 126 fuliginosus Female 1248 1286 827
## 127 fuliginosus Female 1271 1355 855
## 128 fuliginosus Female 1317 1311 891
## 129 fuliginosus Female 1356 1387 926
## 130 fuliginosus Female 1250 1327 859
## 131 fuliginosus Female 1048 1145 693
## 132 fuliginosus Female 1363 1430 926
## 133 fuliginosus Female 1389 1415 944
## 134 fuliginosus Female 1370 1424 934
## 135 fuliginosus Female 1405 1426 956
## 136 fuliginosus Female 1428 1430 977
## 137 fuliginosus Female 1456 1489 992
## 138 fuliginosus Female 1395 1426 942
## 139 fuliginosus Female 1385 1399 945
## 140 fuliginosus Female 1441 1449 984
## 141 fuliginosus Female 1464 1496 1008
## 142 fuliginosus Female 1486 1483 1019
## 143 fuliginosus Female 1499 1511 NA
## 144 fuliginosus Female 1485 1500 1016
## 145 fuliginosus Female 1468 1536 996
## 146 fuliginosus Female 1510 1546 1043
## 147 fuliginosus Female 1526 1512 1052
## 148 fuliginosus Female 1570 1583 987
## palate.width nasal.length nasal.width squamosal.depth lacrymal.width
## 1 NA 609 241 180 394
## 2 230 629 222 150 416
## 3 NA 620 233 135 403
## 4 230 564 207 158 394
## 5 NA 645 247 161 426
## 6 NA 493 189 122 350
## 7 239 606 226 155 396
## 8 248 660 240 159 417
## 9 208 630 215 NA 387
## 10 236 672 231 185 429
## 11 281 778 263 185 441
## 12 227 616 220 150 412
## 13 295 727 271 178 461
## 14 307 810 284 185 490
## 15 293 778 279 184 461
## 16 268 823 272 173 474
## 17 294 755 268 190 467
## 18 289 710 278 179 483
## 19 234 701 238 192 447
## 20 267 803 255 204 455
## 21 297 855 308 225 536
## 22 291 838 281 185 493
## 23 NA 830 288 213 527
## 24 332 864 306 221 513
## 25 NA 837 285 252 512
## 26 NA 525 175 141 354
## 27 211 575 200 145 386
## 28 229 626 226 159 441
## 29 247 664 238 171 428
## 30 256 659 229 197 433
## 31 257 671 247 181 443
## 32 241 629 205 169 393
## 33 221 646 210 173 402
## 34 229 674 221 170 407
## 35 233 687 225 175 413
## 36 285 756 249 185 467
## 37 255 687 223 190 432
## 38 282 734 245 182 462
## 39 NA 700 255 175 446
## 40 275 729 238 180 445
## 41 287 695 251 183 439
## 42 267 731 242 167 440
## 43 286 717 258 182 450
## 44 259 682 253 177 455
## 45 276 704 241 191 449
## 46 294 725 261 160 455
## 47 276 741 261 184 475
## 48 NA 740 232 177 478
## 49 311 811 289 187 479
## 50 265 784 251 206 457
## 51 NA 635 236 161 394
## 52 219 565 204 163 385
## 53 234 562 216 145 404
## 54 NA 580 225 156 420
## 55 185 596 220 151 414
## 56 225 579 219 157 411
## 57 NA 636 201 158 406
## 58 NA 559 213 134 408
## 59 NA 615 228 180 424
## 60 269 740 234 180 496
## 61 213 677 237 187 455
## 62 248 675 217 158 399
## 63 239 629 211 170 433
## 64 259 692 238 152 454
## 65 NA 710 221 178 470
## 66 248 730 281 191 495
## 67 NA 763 292 299 497
## 68 NA 686 251 183 435
## 69 290 717 231 183 450
## 70 319 737 275 200 523
## 71 281 816 275 198 547
## 72 267 893 260 213 499
## 73 295 766 261 192 476
## 74 174 454 141 124 303
## 75 245 625 203 152 411
## 76 225 587 203 146 400
## 77 NA 474 151 121 320
## 78 NA 676 222 160 427
## 79 NA 586 189 136 397
## 80 172 NA 186 165 385
## 81 244 630 235 170 430
## 82 211 690 242 166 451
## 83 NA 630 239 162 452
## 84 246 663 196 165 411
## 85 236 694 236 176 461
## 86 217 667 261 156 467
## 87 242 681 240 171 439
## 88 NA 712 217 153 440
## 89 255 716 242 165 455
## 90 275 699 254 177 439
## 91 220 703 207 164 433
## 92 259 704 238 184 430
## 93 227 669 238 198 450
## 94 256 693 228 183 434
## 95 235 675 259 203 484
## 96 300 769 253 188 482
## 97 275 800 245 194 492
## 98 285 798 235 183 459
## 99 230 573 231 169 427
## 100 250 566 218 173 428
## 101 261 525 200 176 413
## 102 256 551 202 176 421
## 103 249 698 247 192 471
## 104 259 638 208 185 452
## 105 274 658 234 193 470
## 106 243 630 216 196 461
## 107 263 628 237 203 472
## 108 295 638 240 177 455
## 109 280 624 226 194 500
## 110 244 590 206 155 402
## 111 262 628 250 205 504
## 112 297 656 232 198 471
## 113 256 719 253 193 473
## 114 260 687 263 204 491
## 115 282 700 262 243 494
## 116 303 746 275 239 503
## 117 304 715 246 237 513
## 118 293 685 255 224 479
## 119 299 734 239 215 490
## 120 328 708 255 230 496
## 121 303 691 259 229 494
## 122 291 699 233 221 461
## 123 320 737 278 280 535
## 124 211 503 171 152 381
## 125 229 549 197 172 396
## 126 236 494 196 154 380
## 127 212 522 190 138 374
## 128 198 497 167 152 390
## 129 214 554 195 160 392
## 130 249 532 232 176 421
## 131 NA 434 167 131 337
## 132 227 578 217 167 408
## 133 230 574 212 172 405
## 134 248 571 205 171 408
## 135 212 571 199 182 407
## 136 252 570 214 162 437
## 137 245 602 219 188 427
## 138 240 571 222 182 430
## 139 215 553 191 156 386
## 140 NA 568 221 166 435
## 141 226 636 230 183 436
## 142 287 603 213 180 442
## 143 255 699 212 190 435
## 144 277 552 205 203 454
## 145 264 667 222 190 431
## 146 264 656 218 197 423
## 147 281 625 250 201 470
## 148 285 646 244 198 482
## zygomatic.width orbital.width .rostral.width occipital.depth crest.width
## 1 782 249 227 531 153
## 2 824 233 248 632 141
## 3 778 244 240 575 144
## 4 801 224 242 568 116
## 5 823 241 252 607 120
## 6 673 234 185 462 188
## 7 780 237 238 577 149
## 8 812 240 245 614 128
## 9 759 248 219 584 151
## 10 856 227 268 659 103
## 11 921 251 284 699 86
## 12 805 236 249 628 107
## 13 905 251 281 692 82
## 14 960 258 288 764 104
## 15 910 234 282 673 81
## 16 880 249 258 702 57
## 17 902 261 314 710 81
## 18 897 250 299 674 115
## 19 852 246 287 691 82
## 20 904 243 306 695 83
## 21 984 277 350 780 84
## 22 977 273 265 736 121
## 23 1013 252 330 784 21
## 24 947 239 315 765 39
## 25 968 233 347 798 41
## 26 702 221 201 497 203
## 27 760 226 220 569 164
## 28 839 256 234 613 148
## 29 828 249 228 605 147
## 30 853 233 264 664 131
## 31 859 240 288 665 125
## 32 833 235 247 615 129
## 33 823 238 242 589 125
## 34 803 210 222 599 101
## 35 832 229 265 646 121
## 36 903 233 301 722 104
## 37 873 222 286 663 135
## 38 920 248 258 699 103
## 39 NA 236 264 644 112
## 40 914 251 272 672 80
## 41 885 235 271 646 82
## 42 878 234 259 688 123
## 43 848 205 262 625 70
## 44 875 244 288 647 114
## 45 910 243 271 NA 193
## 46 894 212 302 684 74
## 47 911 222 306 699 95
## 48 908 205 320 704 28
## 49 911 238 326 716 122
## 50 907 244 282 687 100
## 51 798 242 269 589 135
## 52 764 235 215 542 153
## 53 794 272 236 577 154
## 54 814 230 250 589 124
## 55 788 245 240 574 156
## 56 787 231 229 582 113
## 57 813 226 261 570 138
## 58 766 212 235 533 129
## 59 833 231 275 640 136
## 60 883 246 302 NA 75
## 61 885 242 247 NA 94
## 62 815 227 234 647 129
## 63 888 251 253 662 134
## 64 825 220 268 638 83
## 65 908 243 294 NA 104
## 66 892 236 306 NA 62
## 67 946 270 318 709 107
## 68 836 239 243 624 115
## 69 900 252 318 694 18
## 70 943 268 NA 744 72
## 71 994 275 368 753 56
## 72 994 234 345 754 13
## 73 978 220 313 726 38
## 74 640 202 NA 435 216
## 75 801 245 242 587 125
## 76 782 232 237 554 170
## 77 683 215 193 475 209
## 78 801 236 248 607 129
## 79 899 233 NA 603 159
## 80 785 233 235 NA 157
## 81 834 240 271 626 88
## 82 855 249 271 634 129
## 83 874 283 256 NA 148
## 84 821 236 237 645 138
## 85 855 261 240 656 140
## 86 869 262 251 650 176
## 87 822 245 290 656 112
## 88 854 245 271 641 101
## 89 894 222 326 625 87
## 90 835 254 264 650 112
## 91 843 230 266 629 127
## 92 865 238 273 645 70
## 93 882 268 267 656 135
## 94 828 240 256 638 120
## 95 882 239 294 698 140
## 96 960 247 320 695 86
## 97 939 270 333 705 65
## 98 893 247 312 NA 73
## 99 861 261 250 618 151
## 100 912 249 261 619 172
## 101 889 253 250 NA 138
## 102 886 260 252 646 140
## 103 972 290 300 687 189
## 104 929 243 265 667 134
## 105 939 240 283 685 144
## 106 955 230 280 678 110
## 107 953 254 294 687 172
## 108 925 243 272 675 118
## 109 969 235 314 738 114
## 110 867 242 268 639 160
## 111 932 265 290 719 115
## 112 947 217 309 721 104
## 113 946 242 276 689 119
## 114 986 240 288 735 111
## 115 1000 236 340 735 129
## 116 972 207 330 764 80
## 117 1070 258 328 744 149
## 118 1032 213 337 728 78
## 119 1004 239 319 742 126
## 120 990 233 312 703 106
## 121 1015 222 322 737 125
## 122 989 210 308 751 60
## 123 1090 262 371 770 151
## 124 824 240 216 563 199
## 125 838 214 239 587 153
## 126 804 230 227 574 169
## 127 799 247 215 585 167
## 128 807 226 237 609 155
## 129 837 220 245 611 181
## 130 830 274 266 NA 214
## 131 725 217 173 481 198
## 132 844 234 249 603 153
## 133 822 241 241 612 170
## 134 859 246 235 623 154
## 135 868 235 250 NA 167
## 136 880 248 263 620 170
## 137 878 235 253 657 118
## 138 853 228 259 650 138
## 139 827 217 247 585 137
## 140 879 231 257 635 160
## 141 897 234 264 646 172
## 142 927 230 274 649 139
## 143 936 256 278 642 200
## 144 919 225 278 676 122
## 145 951 217 305 650 178
## 146 891 190 270 651 78
## 147 934 236 289 680 145
## 148 984 253 291 699 188
## foramina.length mandible.length mandible.width mandible.depth ramus.height
## 1 88 1086 131 179 591
## 2 100 1158 148 181 643
## 3 107 1131 116 169 610
## 4 79 1090 132 189 594
## 5 99 1175 131 197 654
## 6 90 901 101 138 476
## 7 101 1084 124 168 578
## 8 91 1149 129 175 628
## 9 117 1069 121 159 578
## 10 94 1240 132 196 683
## 11 79 1345 148 232 772
## 12 85 1179 132 180 652
## 13 125 1309 145 210 712
## 14 81 1443 157 222 731
## 15 75 1339 135 207 692
## 16 109 1361 140 208 713
## 17 104 1377 137 206 754
## 18 107 1253 142 194 688
## 19 89 1293 137 213 722
## 20 130 NA 138 183 701
## 21 116 1539 163 238 795
## 22 83 NA 159 227 770
## 23 89 1530 152 232 829
## 24 137 1526 138 218 776
## 25 100 1547 140 243 842
## 26 82 933 106 154 533
## 27 72 1059 113 164 578
## 28 106 1197 129 173 651
## 29 99 1131 126 167 621
## 30 94 1215 139 200 660
## 31 104 1202 147 192 676
## 32 100 1176 128 171 638
## 33 99 1198 128 169 649
## 34 106 1151 122 176 629
## 35 88 1214 130 195 668
## 36 117 1324 147 198 731
## 37 105 1258 131 205 688
## 38 70 1355 149 193 724
## 39 91 1257 139 215 681
## 40 93 1344 137 204 735
## 41 67 1297 135 203 709
## 42 130 1265 137 175 684
## 43 118 1235 124 180 659
## 44 111 1290 148 194 706
## 45 101 1321 143 218 741
## 46 103 1355 141 206 706
## 47 97 1370 139 218 733
## 48 93 1394 131 182 733
## 49 90 1366 129 174 715
## 50 119 1314 126 198 706
## 51 85 1160 125 170 659
## 52 93 1054 118 156 556
## 53 102 1094 122 158 625
## 54 88 1110 136 179 636
## 55 95 1083 133 178 623
## 56 78 1115 123 164 616
## 57 76 1102 123 171 603
## 58 91 NA 112 159 608
## 59 100 1117 135 194 654
## 60 103 1365 148 184 745
## 61 100 1249 148 190 709
## 62 84 1213 131 186 634
## 63 91 1225 144 205 716
## 64 95 1264 141 203 712
## 65 107 NA 146 194 761
## 66 78 1357 138 208 770
## 67 120 1361 153 196 755
## 68 105 1181 128 192 676
## 69 98 1337 140 194 759
## 70 90 1395 146 184 768
## 71 80 1482 146 227 794
## 72 92 1568 163 216 824
## 73 95 1503 159 211 775
## 74 96 856 101 132 473
## 75 114 1164 123 166 645
## 76 113 1055 120 166 580
## 77 76 894 103 134 511
## 78 107 1125 130 171 631
## 79 72 1132 129 197 619
## 80 60 1070 132 182 612
## 81 96 1198 132 191 665
## 82 80 1209 138 210 708
## 83 95 1136 129 190 679
## 84 83 1219 143 188 702
## 85 87 1210 143 194 695
## 86 105 1194 138 197 704
## 87 108 1237 127 187 679
## 88 90 1245 132 196 729
## 89 85 1287 135 196 692
## 90 91 1243 125 200 668
## 91 88 1228 136 194 709
## 92 121 1275 131 192 689
## 93 114 1296 142 219 699
## 94 107 1248 129 198 692
## 95 117 1314 135 212 722
## 96 126 1430 154 205 770
## 97 97 1450 154 240 813
## 98 95 1415 138 220 760
## 99 98 1162 133 186 640
## 100 86 1220 147 193 655
## 101 96 1187 151 196 700
## 102 106 1187 146 202 688
## 103 88 1450 160 236 799
## 104 104 1315 144 201 750
## 105 102 NA 151 200 734
## 106 95 NA 156 212 760
## 107 93 NA 146 207 772
## 108 80 1320 154 217 753
## 109 92 1422 166 227 805
## 110 88 1245 147 185 672
## 111 96 1367 159 223 777
## 112 75 NA 149 207 778
## 113 94 1369 159 215 765
## 114 104 1412 157 227 823
## 115 98 NA 166 239 859
## 116 105 NA 159 226 841
## 117 96 1502 167 239 853
## 118 76 1466 158 214 835
## 119 94 1408 169 209 836
## 120 87 1474 158 239 822
## 121 117 NA 161 222 799
## 122 73 1452 154 215 815
## 123 100 1555 156 271 880
## 124 70 1078 130 181 634
## 125 79 1103 133 182 666
## 126 72 1046 131 170 616
## 127 90 1058 132 179 629
## 128 93 1073 130 178 648
## 129 85 1140 135 188 657
## 130 80 1067 127 176 639
## 131 61 880 108 152 511
## 132 73 1163 129 194 654
## 133 73 1163 139 191 641
## 134 98 1152 143 194 689
## 135 107 1176 134 194 683
## 136 83 1179 140 189 650
## 137 78 NA 141 193 717
## 138 79 1199 148 202 700
## 139 98 1156 134 190 642
## 140 82 1233 142 185 700
## 141 78 1263 150 216 715
## 142 97 1291 157 217 737
## 143 118 1291 150 200 740
## 144 74 1260 148 194 751
## 145 82 1287 141 199 736
## 146 87 1337 158 210 747
## 147 106 1334 153 211 739
## 148 103 1354 153 223 807####################################
lmpw1 <-lm(KANGA$palate.width~KANGA$basilar.length+KANGA$occipitonasal.length+KANGA$palate.length+KANGA$nasal.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$lacrymal.width+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth+KANGA$crest.width+KANGA$foramina.length+KANGA$mandible.length+KANGA$mandible.width+KANGA$mandible.depth+KANGA$ramus.height+KANGA$.rostral.width,data=KANGA)
drop1(lmpw1,test="F")## Single term deletions
##
## Model:
## KANGA$palate.width ~ KANGA$basilar.length + KANGA$occipitonasal.length +
## KANGA$palate.length + KANGA$nasal.length + KANGA$nasal.width +
## KANGA$squamosal.depth + KANGA$lacrymal.width + KANGA$zygomatic.width +
## KANGA$orbital.width + KANGA$occipital.depth + KANGA$crest.width +
## KANGA$foramina.length + KANGA$mandible.length + KANGA$mandible.width +
## KANGA$mandible.depth + KANGA$ramus.height + KANGA$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 20817 574.17
## KANGA$basilar.length 1 1145.34 21963 577.58 4.5665 0.035546 *
## KANGA$occipitonasal.length 1 13.28 20831 572.24 0.0530 0.818546
## KANGA$palate.length 1 166.14 20984 572.97 0.6624 0.418040
## KANGA$nasal.length 1 156.89 20974 572.93 0.6255 0.431257
## KANGA$nasal.width 1 1816.55 22634 580.62 7.2427 0.008607 **
## KANGA$squamosal.depth 1 13.84 20831 572.24 0.0552 0.814876
## KANGA$lacrymal.width 1 316.39 21134 573.69 1.2615 0.264610
## KANGA$zygomatic.width 1 1956.76 22774 581.24 7.8017 0.006479 **
## KANGA$orbital.width 1 11.79 20829 572.23 0.0470 0.828855
## KANGA$occipital.depth 1 161.49 20979 572.95 0.6439 0.424601
## KANGA$crest.width 1 1014.98 21832 576.98 4.0468 0.047501 *
## KANGA$foramina.length 1 15.06 20833 572.24 0.0600 0.807040
## KANGA$mandible.length 1 974.11 21792 576.79 3.8838 0.052086 .
## KANGA$mandible.width 1 32.08 20850 572.33 0.1279 0.721529
## KANGA$mandible.depth 1 263.36 21081 573.44 1.0500 0.308479
## KANGA$ramus.height 1 25.35 20843 572.29 0.1011 0.751332
## KANGA$.rostral.width 1 13.60 20831 572.24 0.0542 0.816467
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lmpw2 <-lm(KANGA$palate.width~KANGA$basilar.length+KANGA$occipitonasal.length+KANGA$palate.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$lacrymal.width+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth+KANGA$crest.width+KANGA$foramina.length+KANGA$mandible.length+KANGA$mandible.width+KANGA$mandible.depth+KANGA$ramus.height+KANGA$.rostral.width,data=KANGA)
drop1(lmpw2,test="F")## Single term deletions
##
## Model:
## KANGA$palate.width ~ KANGA$basilar.length + KANGA$occipitonasal.length +
## KANGA$palate.length + KANGA$nasal.width + KANGA$squamosal.depth +
## KANGA$lacrymal.width + KANGA$zygomatic.width + KANGA$orbital.width +
## KANGA$occipital.depth + KANGA$crest.width + KANGA$foramina.length +
## KANGA$mandible.length + KANGA$mandible.width + KANGA$mandible.depth +
## KANGA$ramus.height + KANGA$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 20974 572.93
## KANGA$basilar.length 1 997.92 21972 575.62 3.9966 0.048826 *
## KANGA$occipitonasal.length 1 42.93 21017 571.14 0.1719 0.679464
## KANGA$palate.length 1 109.31 21084 571.45 0.4378 0.510013
## KANGA$nasal.width 1 1660.31 22635 578.62 6.6494 0.011662 *
## KANGA$squamosal.depth 1 23.88 20998 571.04 0.0956 0.757890
## KANGA$lacrymal.width 1 249.52 21224 572.12 0.9993 0.320350
## KANGA$zygomatic.width 1 2262.82 23237 581.28 9.0624 0.003445 **
## KANGA$orbital.width 1 1.99 20976 570.94 0.0080 0.929119
## KANGA$occipital.depth 1 163.71 21138 571.71 0.6556 0.420397
## KANGA$crest.width 1 1066.60 22041 575.94 4.2716 0.041833 *
## KANGA$foramina.length 1 4.91 20979 570.95 0.0197 0.888760
## KANGA$mandible.length 1 908.05 21882 575.21 3.6366 0.059939 .
## KANGA$mandible.width 1 12.72 20987 570.99 0.0510 0.821953
## KANGA$mandible.depth 1 259.88 21234 572.17 1.0408 0.310569
## KANGA$ramus.height 1 36.99 21011 571.11 0.1482 0.701280
## KANGA$.rostral.width 1 6.21 20981 570.96 0.0249 0.875067
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lmpw3 <-lm(KANGA$palate.width~KANGA$basilar.length+KANGA$occipitonasal.length+KANGA$palate.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$lacrymal.width+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth+KANGA$crest.width+KANGA$foramina.length+KANGA$mandible.length+KANGA$mandible.width+KANGA$mandible.depth+KANGA$.rostral.width,data=KANGA)
drop1(lmpw3,test="F")## Single term deletions
##
## Model:
## KANGA$palate.width ~ KANGA$basilar.length + KANGA$occipitonasal.length +
## KANGA$palate.length + KANGA$nasal.width + KANGA$squamosal.depth +
## KANGA$lacrymal.width + KANGA$zygomatic.width + KANGA$orbital.width +
## KANGA$occipital.depth + KANGA$crest.width + KANGA$foramina.length +
## KANGA$mandible.length + KANGA$mandible.width + KANGA$mandible.depth +
## KANGA$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 21011 571.11
## KANGA$basilar.length 1 1036.99 22048 573.97 4.1951 0.043628 *
## KANGA$occipitonasal.length 1 46.32 21058 569.33 0.1874 0.666196
## KANGA$palate.length 1 141.01 21152 569.78 0.5704 0.452171
## KANGA$nasal.width 1 2316.84 23328 579.67 9.3726 0.002948 **
## KANGA$squamosal.depth 1 20.03 21031 569.20 0.0810 0.776620
## KANGA$lacrymal.width 1 319.49 21331 570.63 1.2925 0.258786
## KANGA$zygomatic.width 1 2296.19 23308 579.58 9.2891 0.003072 **
## KANGA$orbital.width 1 1.54 21013 569.11 0.0062 0.937365
## KANGA$occipital.depth 1 140.25 21152 569.78 0.5674 0.453380
## KANGA$crest.width 1 1030.57 22042 573.94 4.1691 0.044268 *
## KANGA$foramina.length 1 4.36 21016 569.13 0.0176 0.894713
## KANGA$mandible.length 1 871.06 21882 573.21 3.5238 0.063923 .
## KANGA$mandible.width 1 20.23 21032 569.20 0.0818 0.775513
## KANGA$mandible.depth 1 342.55 21354 570.74 1.3857 0.242410
## KANGA$.rostral.width 1 6.03 21017 569.14 0.0244 0.876277
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lmpw4 <-lm(KANGA$palate.width~KANGA$basilar.length+KANGA$occipitonasal.length+KANGA$palate.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$lacrymal.width+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth+KANGA$crest.width+KANGA$foramina.length+KANGA$mandible.length+KANGA$.rostral.width,data=KANGA)
drop1(lmpw4,test="F")## Single term deletions
##
## Model:
## KANGA$palate.width ~ KANGA$basilar.length + KANGA$occipitonasal.length +
## KANGA$palate.length + KANGA$nasal.width + KANGA$squamosal.depth +
## KANGA$lacrymal.width + KANGA$zygomatic.width + KANGA$orbital.width +
## KANGA$occipital.depth + KANGA$crest.width + KANGA$foramina.length +
## KANGA$mandible.length + KANGA$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 21448 569.18
## KANGA$basilar.length 1 1829.86 23278 575.45 7.4226 0.007785 **
## KANGA$occipitonasal.length 1 0.58 21448 567.19 0.0023 0.961454
## KANGA$palate.length 1 262.74 21710 568.41 1.0658 0.304766
## KANGA$nasal.width 1 2331.00 23779 577.60 9.4555 0.002813 **
## KANGA$squamosal.depth 1 4.97 21453 567.21 0.0201 0.887452
## KANGA$lacrymal.width 1 401.58 21849 569.06 1.6290 0.205242
## KANGA$zygomatic.width 1 2454.46 23902 578.13 9.9562 0.002202 **
## KANGA$orbital.width 1 9.94 21458 567.23 0.0403 0.841330
## KANGA$occipital.depth 1 82.52 21530 567.57 0.3347 0.564389
## KANGA$crest.width 1 1146.67 22594 572.44 4.6513 0.033788 *
## KANGA$foramina.length 1 27.50 21475 567.31 0.1116 0.739182
## KANGA$mandible.length 1 754.82 22202 570.68 3.0619 0.083676 .
## KANGA$.rostral.width 1 25.07 21473 567.30 0.1017 0.750551
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lmpw5 <-lm(KANGA$palate.width~KANGA$basilar.length+KANGA$palate.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$lacrymal.width+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth+KANGA$crest.width+KANGA$foramina.length+KANGA$mandible.length+KANGA$.rostral.width,data=KANGA)
drop1(lmpw5,test="F")## Single term deletions
##
## Model:
## KANGA$palate.width ~ KANGA$basilar.length + KANGA$palate.length +
## KANGA$nasal.width + KANGA$squamosal.depth + KANGA$lacrymal.width +
## KANGA$zygomatic.width + KANGA$orbital.width + KANGA$occipital.depth +
## KANGA$crest.width + KANGA$foramina.length + KANGA$mandible.length +
## KANGA$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 21448 567.19
## KANGA$basilar.length 1 2268.00 23716 575.34 9.3054 0.0030191 **
## KANGA$palate.length 1 263.78 21712 566.42 1.0823 0.3010418
## KANGA$nasal.width 1 2911.94 24360 578.04 11.9474 0.0008447 ***
## KANGA$squamosal.depth 1 5.40 21454 565.21 0.0221 0.8820656
## KANGA$lacrymal.width 1 401.01 21849 567.06 1.6453 0.2029687
## KANGA$zygomatic.width 1 2570.29 24019 576.62 10.5457 0.0016490 **
## KANGA$orbital.width 1 10.89 21459 565.24 0.0447 0.8330552
## KANGA$occipital.depth 1 83.07 21531 565.58 0.3408 0.5608452
## KANGA$crest.width 1 1183.09 22631 570.61 4.8541 0.0301922 *
## KANGA$foramina.length 1 27.43 21476 565.31 0.1125 0.7380871
## KANGA$mandible.length 1 755.84 22204 568.68 3.1011 0.0817111 .
## KANGA$.rostral.width 1 25.69 21474 565.31 0.1054 0.7461904
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lmpw6 <-lm(KANGA$palate.width~KANGA$basilar.length+KANGA$palate.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$lacrymal.width+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth+KANGA$crest.width+KANGA$foramina.length+KANGA$.rostral.width,data=KANGA)
drop1(lmpw6,test="F")## Single term deletions
##
## Model:
## KANGA$palate.width ~ KANGA$basilar.length + KANGA$palate.length +
## KANGA$nasal.width + KANGA$squamosal.depth + KANGA$lacrymal.width +
## KANGA$zygomatic.width + KANGA$orbital.width + KANGA$occipital.depth +
## KANGA$crest.width + KANGA$foramina.length + KANGA$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 23894 620.28
## KANGA$basilar.length 1 1588.9 25483 625.42 6.5834 0.011792 *
## KANGA$palate.length 1 810.9 24705 621.98 3.3597 0.069814 .
## KANGA$nasal.width 1 3378.4 27273 632.96 13.9978 0.000307 ***
## KANGA$squamosal.depth 1 0.5 23895 618.28 0.0019 0.965108
## KANGA$lacrymal.width 1 405.2 24299 620.14 1.6790 0.198069
## KANGA$zygomatic.width 1 4414.9 28309 637.10 18.2922 4.374e-05 ***
## KANGA$orbital.width 1 219.1 24113 619.29 0.9076 0.343068
## KANGA$occipital.depth 1 390.4 24285 620.08 1.6176 0.206405
## KANGA$crest.width 1 1190.2 25084 623.67 4.9312 0.028656 *
## KANGA$foramina.length 1 13.3 23908 618.34 0.0552 0.814737
## KANGA$.rostral.width 1 54.2 23948 618.53 0.2244 0.636734
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lmpw7 <-lm(KANGA$palate.width~KANGA$basilar.length+KANGA$palate.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$lacrymal.width+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth+KANGA$crest.width+KANGA$.rostral.width,data=KANGA)
drop1(lmpw7,test="F")## Single term deletions
##
## Model:
## KANGA$palate.width ~ KANGA$basilar.length + KANGA$palate.length +
## KANGA$nasal.width + KANGA$squamosal.depth + KANGA$lacrymal.width +
## KANGA$zygomatic.width + KANGA$orbital.width + KANGA$occipital.depth +
## KANGA$crest.width + KANGA$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 23908 618.34
## KANGA$basilar.length 1 1758.6 25666 624.22 7.3560 0.0078698 **
## KANGA$palate.length 1 905.0 24813 620.46 3.7855 0.0545073 .
## KANGA$nasal.width 1 3421.8 27329 631.19 14.3127 0.0002639 ***
## KANGA$squamosal.depth 1 0.0 23908 616.34 0.0000 0.9956531
## KANGA$lacrymal.width 1 393.9 24301 618.15 1.6476 0.2022516
## KANGA$zygomatic.width 1 4528.9 28436 635.59 18.9435 3.255e-05 ***
## KANGA$orbital.width 1 209.2 24117 617.31 0.8749 0.3518562
## KANGA$occipital.depth 1 392.7 24300 618.15 1.6425 0.2029435
## KANGA$crest.width 1 1187.7 25095 621.72 4.9680 0.0280592 *
## KANGA$.rostral.width 1 59.1 23967 616.61 0.2474 0.6200138
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lmpw8 <-lm(KANGA$palate.width~KANGA$basilar.length+KANGA$palate.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth+KANGA$crest.width+KANGA$.rostral.width,data=KANGA)
drop1(lmpw8,test="F")## Single term deletions
##
## Model:
## KANGA$palate.width ~ KANGA$basilar.length + KANGA$palate.length +
## KANGA$nasal.width + KANGA$squamosal.depth + KANGA$zygomatic.width +
## KANGA$orbital.width + KANGA$occipital.depth + KANGA$crest.width +
## KANGA$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 24301 618.15
## KANGA$basilar.length 1 1859.9 26161 624.34 7.7301 0.0064791 **
## KANGA$palate.length 1 891.7 25193 620.15 3.7061 0.0570280 .
## KANGA$nasal.width 1 3136.4 27438 629.63 13.0355 0.0004778 ***
## KANGA$squamosal.depth 1 1.5 24303 616.16 0.0062 0.9376234
## KANGA$zygomatic.width 1 4165.0 28466 633.71 17.3105 6.68e-05 ***
## KANGA$orbital.width 1 445.0 24746 618.17 1.8495 0.1768688
## KANGA$occipital.depth 1 246.9 24548 617.27 1.0261 0.3135019
## KANGA$crest.width 1 1292.4 25594 621.90 5.3713 0.0224878 *
## KANGA$.rostral.width 1 7.7 24309 616.19 0.0321 0.8581692
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lmpw9 <-lm(KANGA$palate.width~KANGA$basilar.length+KANGA$palate.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth+KANGA$.rostral.width,data=KANGA)
drop1(lmpw9,test="F")## Single term deletions
##
## Model:
## KANGA$palate.width ~ KANGA$basilar.length + KANGA$palate.length +
## KANGA$nasal.width + KANGA$squamosal.depth + KANGA$zygomatic.width +
## KANGA$orbital.width + KANGA$occipital.depth + KANGA$.rostral.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 25594 621.90
## KANGA$basilar.length 1 1862.4 27456 627.70 7.4222 0.0075816 **
## KANGA$palate.length 1 1715.5 27309 627.10 6.8368 0.0102827 *
## KANGA$nasal.width 1 3439.4 29033 633.90 13.7070 0.0003468 ***
## KANGA$squamosal.depth 1 39.8 25634 620.08 0.1588 0.6910921
## KANGA$zygomatic.width 1 2906.9 28501 631.84 11.5849 0.0009514 ***
## KANGA$orbital.width 1 1295.7 26890 625.39 5.1639 0.0251597 *
## KANGA$occipital.depth 1 433.0 26027 621.77 1.7255 0.1919385
## KANGA$.rostral.width 1 104.3 25698 620.36 0.4157 0.5205585
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lmpw10 <-lm(KANGA$palate.width~KANGA$basilar.length+KANGA$palate.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth,data=KANGA)
drop1(lmpw10,test="F")## Single term deletions
##
## Model:
## KANGA$palate.width ~ KANGA$basilar.length + KANGA$palate.length +
## KANGA$nasal.width + KANGA$squamosal.depth + KANGA$zygomatic.width +
## KANGA$orbital.width + KANGA$occipital.depth
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 26642 633.30
## KANGA$basilar.length 1 2085.1 28727 639.82 8.2177 0.0050134 **
## KANGA$palate.length 1 1984.7 28627 639.42 7.8218 0.0061407 **
## KANGA$nasal.width 1 3693.1 30335 645.97 14.5551 0.0002302 ***
## KANGA$squamosal.depth 1 6.2 26648 631.33 0.0244 0.8760727
## KANGA$zygomatic.width 1 2940.0 29582 643.13 11.5870 0.0009414 ***
## KANGA$orbital.width 1 1307.2 27949 636.72 5.1518 0.0252650 *
## KANGA$occipital.depth 1 487.2 27129 633.35 1.9203 0.1687638
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lmpw11 <-lm(KANGA$palate.width~KANGA$basilar.length+KANGA$palate.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$zygomatic.width+KANGA$orbital.width,data=KANGA)
drop1(lmpw11,test="F")## Single term deletions
##
## Model:
## KANGA$palate.width ~ KANGA$basilar.length + KANGA$palate.length +
## KANGA$nasal.width + KANGA$squamosal.depth + KANGA$zygomatic.width +
## KANGA$orbital.width
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 31304 690.79
## KANGA$basilar.length 1 4513.0 35817 705.22 16.5793 8.600e-05 ***
## KANGA$palate.length 1 5276.8 36581 707.80 19.3853 2.405e-05 ***
## KANGA$nasal.width 1 5184.4 36488 707.49 19.0456 2.801e-05 ***
## KANGA$squamosal.depth 1 21.1 31325 688.87 0.0774 0.78130
## KANGA$zygomatic.width 1 5059.2 36363 707.07 18.5857 3.446e-05 ***
## KANGA$orbital.width 1 988.9 32293 692.59 3.6329 0.05914 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lmpw1,lmpw2)## Analysis of Variance Table
##
## Model 1: KANGA$palate.width ~ KANGA$basilar.length + KANGA$occipitonasal.length +
## KANGA$palate.length + KANGA$nasal.length + KANGA$nasal.width +
## KANGA$squamosal.depth + KANGA$lacrymal.width + KANGA$zygomatic.width +
## KANGA$orbital.width + KANGA$occipital.depth + KANGA$crest.width +
## KANGA$foramina.length + KANGA$mandible.length + KANGA$mandible.width +
## KANGA$mandible.depth + KANGA$ramus.height + KANGA$.rostral.width
## Model 2: KANGA$palate.width ~ KANGA$basilar.length + KANGA$occipitonasal.length +
## KANGA$palate.length + KANGA$nasal.width + KANGA$squamosal.depth +
## KANGA$lacrymal.width + KANGA$zygomatic.width + KANGA$orbital.width +
## KANGA$occipital.depth + KANGA$crest.width + KANGA$foramina.length +
## KANGA$mandible.length + KANGA$mandible.width + KANGA$mandible.depth +
## KANGA$ramus.height + KANGA$.rostral.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 83 20817
## 2 84 20974 -1 -156.89 0.6255 0.4313anova(lmpw1,lmpw3)## Analysis of Variance Table
##
## Model 1: KANGA$palate.width ~ KANGA$basilar.length + KANGA$occipitonasal.length +
## KANGA$palate.length + KANGA$nasal.length + KANGA$nasal.width +
## KANGA$squamosal.depth + KANGA$lacrymal.width + KANGA$zygomatic.width +
## KANGA$orbital.width + KANGA$occipital.depth + KANGA$crest.width +
## KANGA$foramina.length + KANGA$mandible.length + KANGA$mandible.width +
## KANGA$mandible.depth + KANGA$ramus.height + KANGA$.rostral.width
## Model 2: KANGA$palate.width ~ KANGA$basilar.length + KANGA$occipitonasal.length +
## KANGA$palate.length + KANGA$nasal.width + KANGA$squamosal.depth +
## KANGA$lacrymal.width + KANGA$zygomatic.width + KANGA$orbital.width +
## KANGA$occipital.depth + KANGA$crest.width + KANGA$foramina.length +
## KANGA$mandible.length + KANGA$mandible.width + KANGA$mandible.depth +
## KANGA$.rostral.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 83 20817
## 2 85 21011 -2 -193.88 0.3865 0.6806anova(lmpw1,lmpw4)## Analysis of Variance Table
##
## Model 1: KANGA$palate.width ~ KANGA$basilar.length + KANGA$occipitonasal.length +
## KANGA$palate.length + KANGA$nasal.length + KANGA$nasal.width +
## KANGA$squamosal.depth + KANGA$lacrymal.width + KANGA$zygomatic.width +
## KANGA$orbital.width + KANGA$occipital.depth + KANGA$crest.width +
## KANGA$foramina.length + KANGA$mandible.length + KANGA$mandible.width +
## KANGA$mandible.depth + KANGA$ramus.height + KANGA$.rostral.width
## Model 2: KANGA$palate.width ~ KANGA$basilar.length + KANGA$occipitonasal.length +
## KANGA$palate.length + KANGA$nasal.width + KANGA$squamosal.depth +
## KANGA$lacrymal.width + KANGA$zygomatic.width + KANGA$orbital.width +
## KANGA$occipital.depth + KANGA$crest.width + KANGA$foramina.length +
## KANGA$mandible.length + KANGA$.rostral.width
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 83 20817
## 2 87 21448 -4 -630.18 0.6281 0.6438################################################
SumofAll_q3<-KANGA$basilar.length+KANGA$occipitonasal.length+KANGA$palate.length+KANGA$nasal.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$lacrymal.width+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth+KANGA$crest.width+KANGA$foramina.length+KANGA$mandible.length+KANGA$mandible.width+KANGA$mandible.depth+KANGA$ramus.height+KANGA$.rostral.width
model_palatewidth <- lm(KANGA$palate.width~SumofAll_q3,data=KANGA)
missing <- KANGA[is.na(KANGA$palate.width),]
newpred <- round(predict(model_palatewidth,missing))## Warning: 'newdata' had 24 rows but variables found have 148 rowsKANGA$palate.width[is.na(KANGA$palate.width)] <- newpred## Warning in KANGA$palate.width[is.na(KANGA$palate.width)] <- newpred: number of
## items to replace is not a multiple of replacement lengthKANGA$palate.width## [1] 225 230 241 230 231 221 239 248 208 236 281 227 295 307 293 268 294 289
## [19] 234 267 297 291 242 332 184 223 211 229 247 256 257 241 221 229 233 285
## [37] 255 282 238 275 287 267 286 259 276 294 276 NA 311 265 251 219 234 277
## [55] 185 225 236 270 293 269 213 248 239 259 272 248 277 279 290 319 281 267
## [73] 295 174 245 225 261 260 NA 172 244 211 315 246 236 217 242 NA 255 275
## [91] 220 259 227 256 235 300 275 285 230 250 261 256 249 259 274 243 263 295
## [109] 280 244 262 297 256 260 282 303 304 293 299 328 303 291 320 211 229 236
## [127] 212 198 214 249 311 227 230 248 212 252 245 240 215 303 226 287 255 277
## [145] 264 264 281 285SumofAll_q4<-KANGA$basilar.length+KANGA$occipitonasal.length+KANGA$palate.length+KANGA$nasal.length+KANGA$nasal.width+KANGA$squamosal.depth+KANGA$lacrymal.width+KANGA$zygomatic.width+KANGA$orbital.width+KANGA$occipital.depth+KANGA$crest.width+KANGA$foramina.length+KANGA$mandible.length+KANGA$mandible.width+KANGA$mandible.depth+KANGA$ramus.height+KANGA$.rostral.width+KANGA$palate.width
Type_kanga2<-as.numeric(KANGA$sex)
modelgender <- lm(Type_kanga2 ~ SumofAll_q4)
modelgender##
## Call:
## lm(formula = Type_kanga2 ~ SumofAll_q4)
##
## Coefficients:
## (Intercept) SumofAll_q4
## -0.1216026 0.0001532#plot (modelgender$fit~KANGA$sex, xlab="Gender",ylab =" Gender coefficient ")
#points (Type_kanga,modelgender$fit )
#abline (1.5 ,0 , lwd =3)
predictedgender_new <- modelgender$ fit > 1.5
#table (Type_kanga2 ,c("Female","Male")[( predictedgender_new +1) ])