This suite of functions provides the basic quantities which are used in forming a wide variety of diagnostics for checking the quality of regression fits.
Usage
# S3 method for class 'cmp'
influence(model, ...)
# S3 method for class 'cmp'
hatvalues(model, ...)
# S3 method for class 'cmp'
rstandard(
model,
infl = influence.cmp(model),
type = c("deviance", "pearson"),
...
)
# S3 method for class 'cmp'
cooks.distance(
model,
infl = influence(model),
res = infl$pear_res,
hat = infl$hat,
...
)Arguments
- model
an object class 'cmp', obtained from a call to
glm.cmp.- ...
other arguments passed to or from other methods (currently unused).
- infl
influence structure as returned by
influence, only forrstudentandcooks.distance.- type
type of residuals for
rstandard. The alternatives are: 'deviance' (default), and 'pearson'.- res
residuals, with proper default.
- hat
hat values \(H[i,i]\), see default.
Value
influence.cmp returns a list with components hat (the
leverage values), dev_res (the deviance residuals) and
pear_res (the Pearson residuals).
hatvalues.cmp returns a numeric vector of leverage values.
rstandard.cmp returns a numeric vector of standardized residuals.
cooks.distance.cmp returns a numeric vector of Cook's distances.
Examples
data(attendance)
M.attendance <- glm.cmp(daysabs ~ gender + math + prog, data = attendance)
influence(M.attendance)
#> $hat
#> 1 2 3 4 5 6
#> 0.011522827 0.010632763 0.012781978 0.014026784 0.020060946 0.013743373
#> 7 8 9 10 11 12
#> 0.011673460 0.018385257 0.009677630 0.012421447 0.016174725 0.011662760
#> 13 14 15 16 17 18
#> 0.014363242 0.033768524 0.023438692 0.020310790 0.010023059 0.009918405
#> 19 20 21 22 23 24
#> 0.034193688 0.017916760 0.012503108 0.011113570 0.009296421 0.011522827
#> 25 26 27 28 29 30
#> 0.013073726 0.029299981 0.017018891 0.012503108 0.013265512 0.034898026
#> 31 32 33 34 35 36
#> 0.019361683 0.010728631 0.009318287 0.009351266 0.012718943 0.012781978
#> 37 38 39 40 41 42
#> 0.015378079 0.018141277 0.042465745 0.009918405 0.010268665 0.010023059
#> 43 44 45 46 47 48
#> 0.009574397 0.010303698 0.012158816 0.011096970 0.014473168 0.009395409
#> 49 50 51 52 53 54
#> 0.011904733 0.017240084 0.013297415 0.010744457 0.009450190 0.010278484
#> 55 56 57 58 59 60
#> 0.019035244 0.010415895 0.040116864 0.041261488 0.011983752 0.009918405
#> 61 62 63 64 65 66
#> 0.009785413 0.011096970 0.014281254 0.009351980 0.010563029 0.009897636
#> 67 68 69 70 71 72
#> 0.031516121 0.014727603 0.016174725 0.009632306 0.013850382 0.016193259
#> 73 74 75 76 77 78
#> 0.021160080 0.011214951 0.012184511 0.036508084 0.009684666 0.012460161
#> 79 80 81 82 83 84
#> 0.019361683 0.012503108 0.010139795 0.015830799 0.036497013 0.010744457
#> 85 86 87 88 89 90
#> 0.014798646 0.032715111 0.009691062 0.015097830 0.014151026 0.010632763
#> 91 92 93 94 95 96
#> 0.011096970 0.013448620 0.023707877 0.031582967 0.016288485 0.013940826
#> 97 98 99 100 101 102
#> 0.012158816 0.014999820 0.009285619 0.018866880 0.032109019 0.009450769
#> 103 104 105 106 107 108
#> 0.014281254 0.018385257 0.032060744 0.011096970 0.043390956 0.011260414
#> 109 110 111 112 113 114
#> 0.009296990 0.009595345 0.015830799 0.019541135 0.011904733 0.010814960
#> 115 116 117 118 119 120
#> 0.009296990 0.009584872 0.009918405 0.039102177 0.019803600 0.018385257
#> 121 122 123 124 125 126
#> 0.017018891 0.039032828 0.014281254 0.018141277 0.020770702 0.013743373
#> 127 128 129 130 131 132
#> 0.035577291 0.009541068 0.011673460 0.010023059 0.009524193 0.010728631
#> 133 134 135 136 137 138
#> 0.019541135 0.009595345 0.030218327 0.011662760 0.017240084 0.014363242
#> 139 140 141 142 143 144
#> 0.012987414 0.031233627 0.015097830 0.015368184 0.039667426 0.010744457
#> 145 146 147 148 149 150
#> 0.010728631 0.010562513 0.009511052 0.010038289 0.011983752 0.030710982
#> 151 152 153 154 155 156
#> 0.009318287 0.009515373 0.029043898 0.030408634 0.033143131 0.038510492
#> 157 158 159 160 161 162
#> 0.009450769 0.009882075 0.016174725 0.011939315 0.011939315 0.011904622
#> 163 164 165 166 167 168
#> 0.016769717 0.009541068 0.012383792 0.012055711 0.012383792 0.012434894
#> 169 170 171 172 173 174
#> 0.013045220 0.013448620 0.014999321 0.011904622 0.011999583 0.010906595
#> 175 176 177 178 179 180
#> 0.013045220 0.011999583 0.012718209 0.025288351 0.012101869 0.013211355
#> 181 182 183 184 185 186
#> 0.010562513 0.028461203 0.018443158 0.014151026 0.012718209 0.013634188
#> 187 188 189 190 191 192
#> 0.028588754 0.012948487 0.011971824 0.028537886 0.013010583 0.013506390
#> 193 194 195 196 197 198
#> 0.019976532 0.014026784 0.025926910 0.031861247 0.012747764 0.010562513
#> 199 200 201 202 203 204
#> 0.012625687 0.014999321 0.012434894 0.019576775 0.016174725 0.011935193
#> 205 206 207 208 209 210
#> 0.009511052 0.014883818 0.033768524 0.016699591 0.028731543 0.012227377
#> 211 212 213 214 215 216
#> 0.012045613 0.013799395 0.029959091 0.011935193 0.013211355 0.012747764
#> 217 218 219 220 221 222
#> 0.024426372 0.011260414 0.013743373 0.012131868 0.009541068 0.013297415
#> 223 224 225 226 227 228
#> 0.019187983 0.010415895 0.009842343 0.014473168 0.013473769 0.014730566
#> 229 230 231 232 233 234
#> 0.012096107 0.025926910 0.011673460 0.012131868 0.012520978 0.013045220
#> 235 236 237 238 239 240
#> 0.030817136 0.016462081 0.019976532 0.036839194 0.010462361 0.019976532
#> 241 242 243 244 245 246
#> 0.017078742 0.015023254 0.012071143 0.013829159 0.009897636 0.013612900
#> 247 248 249 250 251 252
#> 0.012184511 0.010268665 0.009684666 0.012227377 0.013819928 0.013473769
#> 253 254 255 256 257 258
#> 0.010728631 0.013155728 0.015722998 0.012304053 0.013310028 0.012248540
#> 259 260 261 262 263 264
#> 0.012096107 0.012421447 0.009745111 0.011999583 0.028967602 0.009632306
#> 265 266 267 268 269 270
#> 0.044087556 0.015360645 0.014730566 0.012794687 0.010562513 0.011903398
#> 271 272 273 274 275 276
#> 0.032910957 0.012434894 0.018127941 0.012574067 0.012043855 0.010415895
#> 277 278 279 280 281 282
#> 0.013045220 0.012110839 0.012574067 0.014151026 0.017733749 0.013211355
#> 283 284 285 286 287 288
#> 0.013010583 0.013506390 0.029125642 0.013470124 0.012747764 0.009918405
#> 289 290 291 292 293 294
#> 0.012071143 0.012948487 0.014381798 0.009296421 0.015892955 0.014634234
#> 295 296 297 298 299 300
#> 0.011903398 0.025926910 0.031307980 0.015110001 0.012434894 0.014999321
#> 301 302 303 304 305 306
#> 0.012300177 0.010415895 0.013010583 0.017741648 0.011935193 0.017149520
#> 307 308 309 310 311 312
#> 0.011935193 0.012055711 0.013019187 0.010814960 0.013506390 0.010889963
#> 313 314
#> 0.015684207 0.013211355
#>
#> $dev_res
#> 1 2 3 4 5 6
#> -0.264431012 -0.464137177 -1.137050858 -0.907077078 -0.975541893 0.836872639
#> 7 8 9 10 11 12
#> 0.561358082 -0.108788372 0.605119059 1.468062912 0.114354834 -0.304941513
#> 13 14 15 16 17 18
#> -0.205905445 -0.413390019 -0.834216769 -1.884087266 -1.420603965 -2.150003744
#> 19 20 21 22 23 24
#> -0.375219202 1.468969284 -1.132530084 -1.968586213 -1.254485960 -1.962546694
#> 25 26 27 28 29 30
#> -0.090579641 -0.343694861 -0.090124123 -2.192511846 -0.747483552 -0.759671179
#> 31 32 33 34 35 36
#> -2.150129851 -1.440686754 -0.616246146 -2.035063837 -1.947450419 1.559609126
#> 37 38 39 40 41 42
#> 0.069638238 0.063669866 -0.794306116 1.640264602 -0.441466783 0.990429449
#> 43 44 45 46 47 48
#> 1.120302460 0.324432972 0.262711559 -0.646728391 -0.728359958 -0.626501161
#> 49 50 51 52 53 54
#> 0.269537221 1.565492698 -0.175745577 -1.974626408 2.108171868 0.610269640
#> 55 56 57 58 59 60
#> 1.745950017 -1.188726166 1.116959999 -0.395382557 -0.872605764 -1.068970109
#> 61 62 63 64 65 66
#> -1.287173952 -0.170327623 -0.540058225 0.308774414 -0.294815927 1.086435428
#> 67 68 69 70 71 72
#> -0.702750468 -0.715281202 -0.146944863 -0.350633458 -1.935376059 0.679889712
#> 73 74 75 76 77 78
#> -1.712453459 0.161463314 -1.694337746 0.007218208 -0.425820818 -0.761790008
#> 79 80 81 82 83 84
#> 2.117266900 1.246871512 0.546128509 0.210352798 -0.903468584 0.089284059
#> 85 86 87 88 89 90
#> -1.926321678 0.039332889 0.459385767 0.205096654 0.657176570 -0.109085485
#> 91 92 93 94 95 96
#> 1.300390076 -0.223460455 0.137758085 1.456204375 -0.273958794 -1.364325963
#> 97 98 99 100 101 102
#> 0.262711559 0.430279366 1.350221783 0.469534272 -0.522836660 -2.041111396
#> 103 104 105 106 107 108
#> -0.540058225 0.263758194 1.092100817 -1.448709214 -0.234861993 -0.682397705
#> 109 110 111 112 113 114
#> -2.019948078 0.365951223 1.277017721 -0.316132979 -0.713006349 0.424810443
#> 115 116 117 118 119 120
#> 0.784627804 -0.193545952 2.117705421 0.121611969 -0.548959360 0.263758194
#> 121 122 123 124 125 126
#> -0.235700445 -0.709293864 -1.014259547 0.249111858 0.100598789 0.836872639
#> 127 128 129 130 131 132
#> -0.640162681 -0.390539047 -0.672232741 1.817248363 0.913757050 0.699075217
#> 133 134 135 136 137 138
#> 0.233655031 -1.279013570 -0.795133058 0.010430499 -1.229716231 0.518167288
#> 139 140 141 142 143 144
#> -0.465617735 1.118708377 -1.168627424 0.876233367 -0.942730520 -0.087759432
#> 145 146 147 148 149 150
#> -0.458350244 -0.485698591 -0.768160860 1.311929408 0.375666941 1.339704326
#> 151 152 153 154 155 156
#> -0.029313270 1.035007596 0.339418726 -0.109086199 0.140367332 0.290978301
#> 157 158 159 160 161 162
#> -2.041111396 -1.205215135 0.114354834 -1.586940927 -1.586940927 -0.148942645
#> 163 164 165 166 167 168
#> -0.898463787 -1.041569772 -1.545383985 -1.682353341 -1.545383985 1.009923018
#> 169 170 171 172 173 174
#> -0.054955887 0.373189124 0.934064138 0.496977926 -0.593956430 -0.164176365
#> 175 176 177 178 179 180
#> -1.527629573 -1.563172868 0.371421104 -0.607567428 -1.688344571 0.396413390
#> 181 182 183 184 185 186
#> -0.968001963 0.762113430 -0.919828531 -1.506963298 -0.708108700 2.799196939
#> 187 188 189 190 191 192
#> -0.191591771 2.382483209 -1.956507776 -0.040627461 -0.686403737 -0.221118065
#> 193 194 195 196 197 198
#> -0.207509039 -0.704779897 -0.771112884 -0.311721806 1.084637000 -2.083341944
#> 199 200 201 202 203 204
#> -1.287004495 -0.646701815 -1.649439662 1.509090051 -0.889902263 -1.569109946
#> 205 206 207 208 209 210
#> -1.380318704 -1.655543238 -0.737624877 -1.577897935 -0.923515010 -1.658409430
#> 211 212 213 214 215 216
#> -0.313230638 -1.512862681 -0.810463804 -1.569109946 0.396413390 0.129435743
#> 217 218 219 220 221 222
#> -0.842835445 -2.071235745 -1.270675656 0.321699117 -1.392421504 0.235490336
#> 223 224 225 226 227 228
#> -1.793459853 -0.298181310 0.115641994 1.134231842 -1.634626403 -1.498122674
#> 229 230 231 232 233 234
#> -1.557239513 -1.956382179 -0.940218373 0.562471880 -0.716849462 -1.527629573
#> 235 236 237 238 239 240
#> -0.986564713 -1.237924035 -0.518811736 -0.519898225 -0.270261300 -0.207509039
#> 241 242 243 244 245 246
#> -0.764958581 -0.610898704 0.763201394 1.215124984 1.507273921 -1.360281476
#> 247 248 249 250 251 252
#> 0.898860177 -0.441466783 -1.283094715 -0.734306600 -1.736340347 0.383646874
#> 253 254 255 256 257 258
#> -2.168211855 2.150848368 -0.874955325 -0.353811834 -0.399196432 -1.604801038
#> 259 260 261 262 263 264
#> -0.585109733 2.815366934 -1.059847693 1.930267052 -0.937998598 -0.350633458
#> 265 266 267 268 269 270
#> 0.807026150 -1.757370852 0.943779474 0.298195226 -0.968001963 -0.138549489
#> 271 272 273 274 275 276
#> 0.041945468 -1.649439662 0.239841692 -1.539461815 -0.589533989 0.520796394
#> 277 278 279 280 281 282
#> -0.540773571 -1.598844538 -1.539461815 -0.509640734 1.093265264 0.112424752
#> 283 284 285 286 287 288
#> -1.625671576 -0.681838341 -0.086190230 -0.838347762 -0.677635518 -0.120940762
#> 289 290 291 292 293 294
#> 0.763201394 -1.634502273 1.302245797 -2.029017066 -0.885618409 -2.116780814
#> 295 296 297 298 299 300
#> 0.509676348 1.464884344 0.126093021 -1.754365348 -1.649439662 -0.646701815
#> 301 302 303 304 305 306
#> 0.268845155 -1.188726166 -0.226477946 -0.489101521 -0.128143892 -0.575296118
#> 307 308 309 310 311 312
#> 0.227929365 0.928302045 -0.825410236 -1.315675470 0.123920620 -2.077288335
#> 313 314
#> -1.589792055 -0.231407020
#>
#> $pear_res
#> 1 2 3 4 5 6
#> -0.243678918 -0.402285522 -0.791080887 -0.683891320 -0.721028357 1.051034713
#> 7 8 9 10 11 12
#> 0.656271807 -0.105384509 0.717390282 2.203676900 0.118457256 -0.278091560
#> 13 14 15 16 17 18
#> -0.193462029 -0.365945477 -0.628111607 -0.947929237 -0.888703362 -1.015626727
#> 19 20 21 22 23 24
#> -0.335054654 2.119655162 -0.788975833 -0.969648871 -0.824624314 -0.968111759
#> 25 26 27 28 29 30
#> -0.088251576 -0.310479536 -0.087780858 -1.026576817 -0.586218819 -0.598532062
#> 31 32 33 34 35 36
#> -1.015659051 -0.896099069 -0.507388453 -0.986482018 -0.964261437 2.280621532
#> 37 38 39 40 41 42
#> 0.071051280 0.064909307 -0.628345916 2.451497595 -0.386516983 1.282200480
#> 43 44 45 46 47 48
#> 1.496837262 0.355862700 0.283132445 -0.530552994 -0.574722140 -0.514194817
#> 49 50 51 52 53 54
#> 0.291054837 2.335522665 -0.166805584 -0.971184292 3.520651751 0.721916936
#> 55 56 57 58 59 60
#> 2.635343579 -0.797522458 1.464433651 -0.353448072 -0.664618465 -0.758802703
#> 61 62 63 64 65 66
#> -0.837696798 -0.162070225 -0.457433449 0.337572694 -0.270163558 1.448461443
#> 67 68 69 70 71 72
#> -0.573326465 -0.575038047 -0.140272077 -0.315410035 -0.961172209 0.824721355
#> 73 74 75 76 77 78
#> -0.901354359 0.169168704 -0.896163917 0.007231926 -0.373415591 -0.594719742
#> 79 80 81 82 83 84
#> 3.477722983 1.705834503 0.633720120 0.223933385 -0.681892418 0.091688601
#> 85 86 87 88 89 90
#> -0.958849674 0.039762170 0.522030473 0.217101701 0.802217669 -0.105603484
#> 91 92 93 94 95 96
#> 1.803171212 -0.208846385 0.143621221 2.071880392 -0.252983301 -0.867613110
#> 97 98 99 100 101 102
#> 0.283132445 0.485002824 1.917809215 0.534292408 -0.448511739 -0.988009276
#> 103 104 105 106 107 108
#> -0.457433449 0.284068046 1.448580031 -0.899035764 -0.220546730 -0.550491925
#> 109 110 111 112 113 114
#> -0.982663570 0.406180910 1.797872744 -0.288416230 -0.569810225 0.478778086
#> 115 116 117 118 119 120
#> 0.973583652 -0.182735164 3.478793691 0.125514493 -0.461557308 0.284068046
#> 121 122 123 124 125 126
#> -0.219781383 -0.567487497 -0.731909395 0.268260353 0.103709237 1.051034713
#> 127 128 129 130 131 132
#> -0.533617400 -0.347144380 -0.543990325 2.814603191 1.164140476 0.842705973
#> 133 134 135 136 137 138
#> 0.249106771 -0.834456851 -0.624576436 0.010462393 -0.814546406 0.599526181
#> 139 140 141 142 143 144
#> -0.401850805 1.461940859 -0.805641283 1.112213153 -0.716537232 -0.085456881
#> 145 146 147 148 149 150
#> -0.399297629 -0.418221101 -0.603665107 1.836745334 0.416531833 1.834142394
#> 151 152 153 154 155 156
#> -0.029058569 1.367593811 0.371049235 -0.105773678 0.145649569 0.314299367
#> 157 158 159 160 161 162
#> -0.988009276 -0.804424109 0.118457256 -0.863999218 -0.863999218 -0.141894068
#> 163 164 165 166 167 168
#> -0.662175038 -0.745445389 -0.850842044 -0.892695194 -0.850842044 1.350020959
#> 169 170 171 172 173 174
#> -0.053983064 0.415069379 1.226499675 0.578353972 -0.484913877 -0.156496608
#> 175 176 177 178 179 180
#> -0.845088652 -0.856526344 0.416175020 -0.498417434 -0.894432772 0.447552077
#> 181 182 183 184 185 186
#> -0.708449857 0.924596464 -0.673141703 -0.838287753 -0.556214944 5.619984170
#> 187 188 189 190 191 192
#> -0.181525849 4.362837919 -0.966572948 -0.040176059 -0.543129326 -0.205749700
#> 193 194 195 196 197 198
#> -0.194320475 -0.568344535 -0.600213806 -0.284751366 1.480014518 -0.998678614
#> 199 200 201 202 203 204
#> -0.837629509 -0.518627358 -0.883019742 2.261028390 -0.657730742 -0.858405575
#> 205 206 207 208 209 210
#> -0.873664312 -0.884830928 -0.589139139 -0.861172343 -0.699577809 -0.885678713
#> 211 212 213 214 215 216
#> -0.282819533 -0.840240446 -0.633822530 -0.858405575 0.447552077 0.134817414
#> 217 218 219 220 221 222
#> -0.632777790 -0.995617753 -0.831130338 0.355062571 -0.878212392 0.251831033
#> 223 224 225 226 227 228
#> -0.923862560 -0.271935497 0.119566707 1.542240640 -0.878590715 -0.835343935
#> 229 230 231 232 233 234
#> -0.854639280 -0.966541053 -0.694023091 0.665688900 -0.561424028 -0.845088652
#> 235 236 237 238 239 240
#> -0.726872538 -0.817902909 -0.438044824 -0.443049891 -0.249048408 -0.194320475
#> 241 242 243 244 245 246
#> -0.589481943 -0.503820989 0.954781812 1.712086193 2.211051886 -0.866075161
#> 247 248 249 250 251 252
#> 1.165049137 -0.386516983 -0.836079130 -0.571724559 -0.908106607 0.431468357
#> 253 254 255 256 257 258
#> -1.020299429 3.757260943 -0.659082753 -0.315251968 -0.350456157 -0.869525657
#> 259 260 261 262 263 264
#> -0.479126687 5.620376789 -0.754379906 3.231210793 -0.700846443 -0.315410035
#> 265 266 267 268 269 270
#> 0.999468717 -0.913968457 1.247218569 0.327401937 -0.708449857 -0.132440919
#> 271 272 273 274 275 276
#> 0.042455860 -0.883019742 0.258592361 -0.848932078 -0.482025665 0.604042771
#> 277 278 279 280 281 282
#> -0.449535858 -0.867690957 -0.848932078 -0.428161397 1.474194506 0.116475456
#> 283 284 285 286 287 288
#> -0.875890013 -0.540349087 -0.084080704 -0.630352302 -0.537781138 -0.116742643
#> 289 290 291 292 293 294
#> 0.954781812 -0.878553371 1.878016898 -0.984954654 -0.655495885 -1.007155089
#> 295 296 297 298 299 300
#> 0.595395869 2.147240547 0.130698558 -0.913135446 -0.883019742 -0.518627358
#> 301 302 303 304 305 306
#> 0.292494840 -0.797522458 -0.210368639 -0.416973598 -0.122910160 -0.484277417
#> 307 308 309 310 311 312
#> 0.244837547 1.213132532 -0.623311692 -0.848895241 0.128849686 -0.997147767
#> 313 314
#> -0.864886323 -0.214601165
#>
hatvalues(M.attendance)
#> 1 2 3 4 5 6
#> 0.011522827 0.010632763 0.012781978 0.014026784 0.020060946 0.013743373
#> 7 8 9 10 11 12
#> 0.011673460 0.018385257 0.009677630 0.012421447 0.016174725 0.011662760
#> 13 14 15 16 17 18
#> 0.014363242 0.033768524 0.023438692 0.020310790 0.010023059 0.009918405
#> 19 20 21 22 23 24
#> 0.034193688 0.017916760 0.012503108 0.011113570 0.009296421 0.011522827
#> 25 26 27 28 29 30
#> 0.013073726 0.029299981 0.017018891 0.012503108 0.013265512 0.034898026
#> 31 32 33 34 35 36
#> 0.019361683 0.010728631 0.009318287 0.009351266 0.012718943 0.012781978
#> 37 38 39 40 41 42
#> 0.015378079 0.018141277 0.042465745 0.009918405 0.010268665 0.010023059
#> 43 44 45 46 47 48
#> 0.009574397 0.010303698 0.012158816 0.011096970 0.014473168 0.009395409
#> 49 50 51 52 53 54
#> 0.011904733 0.017240084 0.013297415 0.010744457 0.009450190 0.010278484
#> 55 56 57 58 59 60
#> 0.019035244 0.010415895 0.040116864 0.041261488 0.011983752 0.009918405
#> 61 62 63 64 65 66
#> 0.009785413 0.011096970 0.014281254 0.009351980 0.010563029 0.009897636
#> 67 68 69 70 71 72
#> 0.031516121 0.014727603 0.016174725 0.009632306 0.013850382 0.016193259
#> 73 74 75 76 77 78
#> 0.021160080 0.011214951 0.012184511 0.036508084 0.009684666 0.012460161
#> 79 80 81 82 83 84
#> 0.019361683 0.012503108 0.010139795 0.015830799 0.036497013 0.010744457
#> 85 86 87 88 89 90
#> 0.014798646 0.032715111 0.009691062 0.015097830 0.014151026 0.010632763
#> 91 92 93 94 95 96
#> 0.011096970 0.013448620 0.023707877 0.031582967 0.016288485 0.013940826
#> 97 98 99 100 101 102
#> 0.012158816 0.014999820 0.009285619 0.018866880 0.032109019 0.009450769
#> 103 104 105 106 107 108
#> 0.014281254 0.018385257 0.032060744 0.011096970 0.043390956 0.011260414
#> 109 110 111 112 113 114
#> 0.009296990 0.009595345 0.015830799 0.019541135 0.011904733 0.010814960
#> 115 116 117 118 119 120
#> 0.009296990 0.009584872 0.009918405 0.039102177 0.019803600 0.018385257
#> 121 122 123 124 125 126
#> 0.017018891 0.039032828 0.014281254 0.018141277 0.020770702 0.013743373
#> 127 128 129 130 131 132
#> 0.035577291 0.009541068 0.011673460 0.010023059 0.009524193 0.010728631
#> 133 134 135 136 137 138
#> 0.019541135 0.009595345 0.030218327 0.011662760 0.017240084 0.014363242
#> 139 140 141 142 143 144
#> 0.012987414 0.031233627 0.015097830 0.015368184 0.039667426 0.010744457
#> 145 146 147 148 149 150
#> 0.010728631 0.010562513 0.009511052 0.010038289 0.011983752 0.030710982
#> 151 152 153 154 155 156
#> 0.009318287 0.009515373 0.029043898 0.030408634 0.033143131 0.038510492
#> 157 158 159 160 161 162
#> 0.009450769 0.009882075 0.016174725 0.011939315 0.011939315 0.011904622
#> 163 164 165 166 167 168
#> 0.016769717 0.009541068 0.012383792 0.012055711 0.012383792 0.012434894
#> 169 170 171 172 173 174
#> 0.013045220 0.013448620 0.014999321 0.011904622 0.011999583 0.010906595
#> 175 176 177 178 179 180
#> 0.013045220 0.011999583 0.012718209 0.025288351 0.012101869 0.013211355
#> 181 182 183 184 185 186
#> 0.010562513 0.028461203 0.018443158 0.014151026 0.012718209 0.013634188
#> 187 188 189 190 191 192
#> 0.028588754 0.012948487 0.011971824 0.028537886 0.013010583 0.013506390
#> 193 194 195 196 197 198
#> 0.019976532 0.014026784 0.025926910 0.031861247 0.012747764 0.010562513
#> 199 200 201 202 203 204
#> 0.012625687 0.014999321 0.012434894 0.019576775 0.016174725 0.011935193
#> 205 206 207 208 209 210
#> 0.009511052 0.014883818 0.033768524 0.016699591 0.028731543 0.012227377
#> 211 212 213 214 215 216
#> 0.012045613 0.013799395 0.029959091 0.011935193 0.013211355 0.012747764
#> 217 218 219 220 221 222
#> 0.024426372 0.011260414 0.013743373 0.012131868 0.009541068 0.013297415
#> 223 224 225 226 227 228
#> 0.019187983 0.010415895 0.009842343 0.014473168 0.013473769 0.014730566
#> 229 230 231 232 233 234
#> 0.012096107 0.025926910 0.011673460 0.012131868 0.012520978 0.013045220
#> 235 236 237 238 239 240
#> 0.030817136 0.016462081 0.019976532 0.036839194 0.010462361 0.019976532
#> 241 242 243 244 245 246
#> 0.017078742 0.015023254 0.012071143 0.013829159 0.009897636 0.013612900
#> 247 248 249 250 251 252
#> 0.012184511 0.010268665 0.009684666 0.012227377 0.013819928 0.013473769
#> 253 254 255 256 257 258
#> 0.010728631 0.013155728 0.015722998 0.012304053 0.013310028 0.012248540
#> 259 260 261 262 263 264
#> 0.012096107 0.012421447 0.009745111 0.011999583 0.028967602 0.009632306
#> 265 266 267 268 269 270
#> 0.044087556 0.015360645 0.014730566 0.012794687 0.010562513 0.011903398
#> 271 272 273 274 275 276
#> 0.032910957 0.012434894 0.018127941 0.012574067 0.012043855 0.010415895
#> 277 278 279 280 281 282
#> 0.013045220 0.012110839 0.012574067 0.014151026 0.017733749 0.013211355
#> 283 284 285 286 287 288
#> 0.013010583 0.013506390 0.029125642 0.013470124 0.012747764 0.009918405
#> 289 290 291 292 293 294
#> 0.012071143 0.012948487 0.014381798 0.009296421 0.015892955 0.014634234
#> 295 296 297 298 299 300
#> 0.011903398 0.025926910 0.031307980 0.015110001 0.012434894 0.014999321
#> 301 302 303 304 305 306
#> 0.012300177 0.010415895 0.013010583 0.017741648 0.011935193 0.017149520
#> 307 308 309 310 311 312
#> 0.011935193 0.012055711 0.013019187 0.010814960 0.013506390 0.010889963
#> 313 314
#> 0.015684207 0.013211355
rstandard(M.attendance, type = "pearson")
#> 1 2 3 4 5 6
#> -0.245095104 -0.404441433 -0.796185666 -0.688738774 -0.728371278 1.058332401
#> 7 8 9 10 11 12
#> 0.660136155 -0.106366836 0.720887001 2.217492166 0.119427043 -0.279727542
#> 13 14 15 16 17 18
#> -0.194866549 -0.372285219 -0.635604644 -0.957705003 -0.893190887 -1.020701205
#> 19 20 21 22 23 24
#> -0.340934252 2.138902871 -0.793954897 -0.975082333 -0.828484275 -0.973738122
#> 25 26 27 28 29 30
#> -0.088834184 -0.315130517 -0.088537496 -1.033055333 -0.590146182 -0.609257407
#> 31 32 33 34 35 36
#> -1.025636608 -0.900945056 -0.509769100 -0.991127049 -0.970452753 2.295338191
#> 37 38 39 40 41 42
#> 0.071603979 0.065506209 -0.642128043 2.463746259 -0.388516906 1.288674977
#> 43 44 45 46 47 48
#> 1.504054788 0.357710341 0.284869580 -0.533521489 -0.578926862 -0.516627508
#> 49 50 51 52 53 54
#> 0.292802926 2.355919078 -0.167925810 -0.976444140 3.537406008 0.725655890
#> 55 56 57 58 59 60
#> 2.660789644 -0.801708644 1.494722318 -0.360973675 -0.668636930 -0.762593985
#> 61 62 63 64 65 66
#> -0.841825730 -0.162977023 -0.460735218 0.339162340 -0.271601835 1.455683269
#> 67 68 69 70 71 72
#> -0.582580296 -0.579319867 -0.141420458 -0.316940161 -0.967898462 0.831481025
#> 73 74 75 76 77 78
#> -0.911044786 0.170125367 -0.901673981 0.007367666 -0.375237034 -0.598459883
#> 79 80 81 82 83 84
#> 3.511887183 1.716599674 0.636957658 0.225727234 -0.694687251 0.092185178
#> 85 86 87 88 89 90
#> -0.966024242 0.040428989 0.524578523 0.218759378 0.807954732 -0.106169430
#> 91 92 93 94 95 96
#> 1.813260126 -0.210265058 0.145354580 2.105394434 -0.255069175 -0.873724706
#> 97 98 99 100 101 102
#> 0.284869580 0.488681741 1.926775731 0.539405083 -0.455890553 -0.992711355
#> 103 104 105 106 107 108
#> -0.460735218 0.286715946 1.472375026 -0.904065954 -0.225493165 -0.553617732
#> 109 110 111 112 113 114
#> -0.987263576 0.408143770 1.812274850 -0.291276204 -0.573232532 0.481388260
#> 115 116 117 118 119 120
#> 0.978141154 -0.183617256 3.496175138 0.128042832 -0.466196577 0.286715946
#> 121 122 123 124 125 126
#> -0.221675816 -0.578897964 -0.737192340 0.270727262 0.104803368 1.058332401
#> 127 128 129 130 131 132
#> -0.543370765 -0.348812390 -0.547193521 2.828815587 1.169724142 0.847263216
#> 133 134 135 136 137 138
#> 0.251576947 -0.838489344 -0.634232670 0.010523942 -0.821659942 0.603878695
#> 139 140 141 142 143 144
#> -0.404486003 1.485320847 -0.811792745 1.120859287 -0.731186109 -0.085919708
#> 145 146 147 148 149 150
#> -0.401456978 -0.420447487 -0.606556493 1.846034216 0.419050298 1.862972324
#> 151 152 153 154 155 156
#> -0.029194911 1.374147200 0.376557883 -0.107419527 0.148124914 0.320531881
#> 157 158 159 160 161 162
#> -0.992711355 -0.808428502 0.119427043 -0.869203647 -0.869203647 -0.142746282
#> 163 164 165 166 167 168
#> -0.667798105 -0.749027213 -0.856159811 -0.898125380 -0.856159811 1.358493744
#> 169 170 171 172 173 174
#> -0.054338657 0.417888905 1.235802793 0.581827559 -0.487849707 -0.157357075
#> 175 176 177 178 179 180
#> -0.850655359 -0.861712040 0.418847035 -0.504841614 -0.899894550 0.450538081
#> 181 182 183 184 185 186
#> -0.712221266 0.938041719 -0.679436337 -0.844282771 -0.559786074 5.658692400
#> 187 188 189 190 191 192
#> -0.184177644 4.391361295 -0.972411243 -0.040761899 -0.546697396 -0.207153404
#> 193 194 195 196 197 198
#> -0.196290972 -0.572372987 -0.608149296 -0.289398992 1.489539117 -1.003995045
#> 199 200 201 202 203 204
#> -0.842967938 -0.522561197 -0.888561608 2.283490557 -0.663115460 -0.863574508
#> 205 206 207 208 209 210
#> -0.877848920 -0.891490189 -0.599345550 -0.868454288 -0.709849666 -0.891143645
#> 211 212 213 214 215 216
#> -0.284538445 -0.846098550 -0.643535705 -0.863574508 0.450538081 0.135685028
#> 217 218 219 220 221 222
#> -0.640650547 -1.001271077 -0.836901156 0.357236154 -0.882432154 0.253522269
#> 223 224 225 226 227 228
#> -0.932855719 -0.273362883 0.120159494 1.553523820 -0.884570171 -0.841565298
#> 229 230 231 232 233 234
#> -0.859855555 -0.979319794 -0.698109731 0.669764042 -0.564972171 -0.850655359
#> 235 236 237 238 239 240
#> -0.738338301 -0.824719378 -0.442486795 -0.451443322 -0.250361538 -0.196290972
#> 241 242 243 244 245 246
#> -0.594581158 -0.507648687 0.960597168 1.724048768 2.222075881 -0.872030934
#> 247 248 249 250 251 252
#> 1.172212442 -0.388516906 -0.840157350 -0.575252290 -0.914447389 0.434404817
#> 253 254 255 256 257 258
#> -1.025817075 3.782222254 -0.664326043 -0.317209489 -0.352811991 -0.874900291
#> 259 260 261 262 263 264
#> -0.482051028 5.655611991 -0.758082750 3.250773621 -0.711223361 -0.316940161
#> 265 266 267 268 269 270
#> 1.022257128 -0.921069948 1.256507436 0.329516756 -0.712221266 -0.133236275
#> 271 272 273 274 275 276
#> 0.043172223 -0.888561608 0.260968591 -0.854320209 -0.484954874 0.607213384
#> 277 278 279 280 281 282
#> -0.452497008 -0.872993401 -0.854320209 -0.431223395 1.487442469 0.117252564
#> 283 284 285 286 287 288
#> -0.881644142 -0.544035555 -0.085332570 -0.634641141 -0.541242016 -0.117325936
#> 289 290 291 292 293 294
#> 0.960597168 -0.884297180 1.891668962 -0.989565102 -0.660767691 -1.014606445
#> 295 296 297 298 299 300
#> 0.598971439 2.175629439 0.132793842 -0.920113362 -0.888561608 -0.522561197
#> 301 302 303 304 305 306
#> 0.294310476 -0.801708644 -0.211750649 -0.420722455 -0.123650270 -0.488484165
#> 307 308 309 310 311 312
#> 0.246311849 1.220511909 -0.627409251 -0.853523198 0.129728748 -1.002621969
#> 313 314
#> -0.871749693 -0.216032953
cooks.distance(M.attendance)
#> 1 2 3 4 5 6
#> 1.400528e-04 3.515846e-04 1.641511e-03 1.349684e-03 2.172141e-03 3.121602e-03
#> 7 8 9 10 11 12
#> 1.029428e-03 4.238099e-05 1.015680e-03 1.236957e-02 4.689800e-05 1.846701e-04
#> 13 14 15 16 17 18
#> 1.106726e-04 9.687517e-04 1.939269e-03 3.803050e-03 1.615451e-03 2.087364e-03
#> 19 20 21 22 23 24
#> 8.230518e-04 1.669257e-02 1.596261e-03 2.137075e-03 1.288162e-03 2.210583e-03
#> 25 26 27 28 29 30
#> 2.090763e-05 5.995056e-04 2.714380e-05 2.702461e-03 9.364248e-04 2.684475e-03
#> 31 32 33 34 35 36
#> 4.153854e-03 1.760579e-03 4.888538e-04 1.854554e-03 2.426549e-03 1.364295e-02
#> 37 38 39 40 41 42
#> 1.601537e-05 1.585674e-05 3.657276e-03 1.216166e-02 3.132178e-04 3.362730e-03
#> 43 44 45 46 47 48
#> 4.373679e-03 2.664306e-04 1.997682e-04 6.388289e-04 9.844021e-04 5.062912e-04
#> 49 50 51 52 53 54
#> 2.065864e-04 1.947344e-02 7.600565e-05 2.071099e-03 2.387614e-02 1.093723e-03
#> 55 56 57 58 59 60
#> 2.747617e-02 1.353029e-03 1.867496e-02 1.121568e-03 1.084525e-03 1.165165e-03
#> 61 62 63 64 65 66
#> 1.400633e-03 5.961197e-05 6.151006e-04 2.171848e-04 1.575055e-04 4.236578e-03
#> 67 68 69 70 71 72
#> 2.208930e-03 1.003327e-03 6.576176e-05 1.953972e-04 2.631531e-03 2.275931e-03
#> 73 74 75 76 77 78
#> 3.588518e-03 6.565437e-05 2.005679e-03 4.113683e-07 2.753928e-04 9.037933e-04
#> 79 80 81 82 83 84
#> 4.870184e-02 7.461915e-03 8.312017e-04 1.639196e-04 3.656057e-03 1.845985e-05
#> 85 86 87 88 89 90
#> 2.803516e-03 1.105630e-05 5.385818e-04 1.467185e-04 1.874052e-03 2.422800e-05
#> 91 92 93 94 95 96
#> 7.379058e-03 1.205375e-04 1.026125e-04 2.891262e-02 2.154561e-04 2.158563e-03
#> 97 98 99 100 101 102
#> 1.997682e-04 7.273308e-04 6.959127e-03 1.119005e-03 1.378960e-03 1.880473e-03
#> 103 104 105 106 107 108
#> 6.151006e-04 3.079373e-04 1.436125e-02 1.834345e-03 4.612767e-04 6.981077e-04
#> 109 110 111 112 113 114
#> 1.829343e-03 3.227782e-04 1.056601e-02 3.381897e-04 7.917946e-04 5.067204e-04
#> 115 116 117 118 119 120
#> 1.795692e-03 6.525684e-05 2.448991e-02 1.334333e-04 8.782117e-04 3.079373e-04
#> 121 122 123 124 125 126
#> 1.701581e-04 2.722422e-03 1.574726e-03 2.708400e-04 4.659585e-05 3.121602e-03
#> 127 128 129 130 131 132
#> 2.178352e-03 2.344090e-04 7.073120e-04 1.620371e-02 2.631366e-03 1.557025e-03
#> 133 134 135 136 137 138
#> 2.522854e-04 1.362301e-03 2.506823e-03 2.613864e-07 2.368679e-03 1.062833e-03
#> 139 140 141 142 143 144
#> 4.305633e-04 1.422571e-02 2.020421e-03 3.921759e-03 4.416703e-03 1.603583e-05
#> 145 146 147 148 149 150
#> 3.495722e-04 3.774265e-04 7.065639e-04 6.911158e-03 4.259818e-04 2.199294e-02
#> 151 152 153 154 155 156
#> 1.603416e-06 3.628061e-03 8.482987e-04 7.237768e-05 1.504242e-04 8.230135e-04
#> 157 158 159 160 161 162
#> 1.880473e-03 1.304591e-03 4.689800e-05 1.825866e-03 1.825866e-03 4.909942e-05
#> 163 164 165 166 167 168
#> 1.521216e-03 1.080900e-03 1.838252e-03 1.968631e-03 1.838252e-03 4.647524e-03
#> 169 170 171 172 173 174
#> 7.805522e-06 4.761126e-04 4.651183e-03 8.157091e-04 5.781109e-04 5.460777e-05
#> 175 176 177 178 179 180
#> 1.912896e-03 1.803696e-03 4.519868e-04 1.322466e-03 1.984054e-03 5.435209e-04
#> 181 182 183 184 185 186
#> 1.083026e-03 5.155460e-03 1.734792e-03 2.046366e-03 8.073447e-04 8.852245e-02
#> 187 188 189 190 191 192
#> 1.996622e-04 5.059499e-02 2.291506e-03 9.761909e-06 7.879674e-04 1.175058e-04
#> 193 194 195 196 197 198
#> 1.570776e-04 9.321402e-04 1.968836e-03 5.512507e-04 5.729803e-03 2.152147e-03
#> 199 200 201 202 203 204
#> 1.817294e-03 8.316477e-04 1.988298e-03 2.082361e-02 1.445863e-03 1.801663e-03
#> 205 206 207 208 209 210
#> 1.479955e-03 2.401541e-03 2.510819e-03 2.561790e-03 2.981140e-03 1.966083e-03
#> 211 212 213 214 215 216
#> 1.974258e-04 2.003395e-03 2.558079e-03 1.801663e-03 5.435209e-04 4.754444e-05
#> 217 218 219 220 221 222
#> 2.055281e-03 2.283525e-03 1.952009e-03 3.134509e-04 1.500214e-03 1.732380e-04
#> 223 224 225 226 227 228
#> 3.404885e-03 1.573088e-04 2.870386e-05 7.088608e-03 2.137347e-03 2.117727e-03
#> 229 230 231 232 233 234
#> 1.810556e-03 5.105500e-03 1.151268e-03 1.101799e-03 8.094583e-04 1.912896e-03
#> 235 236 237 238 239 240
#> 3.466788e-03 2.276858e-03 7.982046e-04 1.559006e-03 1.325448e-04 1.570776e-04
#> 241 242 243 244 245 246
#> 1.228540e-03 7.861304e-04 2.254942e-03 8.336288e-03 9.871864e-03 2.098926e-03
#> 247 248 249 250 251 252
#> 3.389807e-03 3.132178e-04 1.380583e-03 8.192624e-04 2.343673e-03 5.154656e-04
#> 253 254 255 256 257 258
#> 2.282437e-03 3.814085e-02 1.409972e-03 2.506959e-04 3.358265e-04 1.898383e-03
#> 259 260 261 262 263 264
#> 5.690455e-04 8.046180e-02 1.131105e-03 2.566921e-02 3.018011e-03 1.953972e-04
#> 265 266 267 268 269 270
#> 9.639360e-03 2.646961e-03 4.720897e-03 2.814538e-04 1.083026e-03 4.277072e-05
#> 271 272 273 274 275 276
#> 1.268565e-05 1.988298e-03 2.514780e-04 1.858843e-03 5.734037e-04 7.761694e-04
#> 277 278 279 280 281 282
#> 5.412720e-04 1.868607e-03 1.858843e-03 5.338413e-04 7.988803e-03 3.681272e-05
#> 283 284 285 286 287 288
#> 2.049278e-03 8.104562e-04 4.368900e-05 1.099886e-03 7.565173e-04 2.757966e-05
#> 289 290 291 292 293 294
#> 2.254942e-03 2.051661e-03 1.044299e-02 1.837769e-03 1.410230e-03 3.057720e-03
#> 295 296 297 298 299 300
#> 8.643981e-04 2.519759e-02 1.139870e-04 2.597703e-03 1.988298e-03 8.316477e-04
#> 301 302 303 304 305 306
#> 2.157386e-04 1.353029e-03 1.182126e-04 6.394250e-04 3.693721e-05 8.327133e-04
#> 307 308 309 310 311 312
#> 1.465698e-04 3.635586e-03 1.038501e-03 1.592972e-03 4.608371e-05 2.213534e-03
#> 313 314
#> 2.421819e-03 1.249664e-04