library(heteroTests)
# Fit a simple linear model on real data
model <- lm(stations ~ mag + depth, data = quakes)
# A second dataset demonstrates collinearity and mild nonlinearity
data(diagnostic_data)
diag_model <- lm(y ~ x1 + x2, data = diagnostic_data)
# Run White's test and get an htest object
performWhiteTest(model, quakes)
# [INFO] Running White test
# [INFO] White test completed: statistic = 125.558 df = 5 p = 0
#
# White's test for heteroscedasticity
#
# data: model
# X-squared = 125.56, df = 5, p-value < 2.2e-16
# alternative hypothesis: heteroscedasticity present
performWhiteTest(diag_model, diagnostic_data)
# [INFO] Running White test
# [INFO] White test completed: statistic = 1.5791 df = 5 p = 0.9038
#
# White's test for heteroscedasticity
#
# data: diag_model
# X-squared = 1.5791, df = 5, p-value = 0.9038
# alternative hypothesis: heteroscedasticity present
Other available tests
Many additional diagnostics follow the same interface and also return
an htest object.
# Breusch-Pagan and its robust Koenker version. The data argument must be
# the data the model was fitted on.
performBPTest(model, quakes)
# [INFO] Running Breusch-Pagan test
#
# Breusch-Pagan test for heteroscedasticity
#
# data: stations ~ mag + depth
# X-squared = 191.93, df = 2, p-value < 2.2e-16
performKoenkerTest(model, quakes)
# [INFO] Running Koenker test
#
# Koenker studentized Breusch-Pagan test
#
# data: stations ~ mag + depth
# X-squared = 111.31, df = 2, p-value < 2.2e-16
# Group-based tests need a grouping factor in that same data
quakes_grouped <- quakes
quakes_grouped$depth_band <- cut(quakes_grouped$depth, 3,
labels = c("shallow", "mid", "deep"))
performLeveneTest(model, quakes_grouped, "depth_band")
#
# Levene's test for equality of variances
#
# data: stations ~ mag + depth
# F = 11.207, df1 = 2, df2 = 997, p-value = 1.537e-05
# ARCH effects in time series
performArchLMTest(model, lags = 2)
# [INFO] Running ARCH LM test
#
# Engle's ARCH LM test
#
# data: stations ~ mag + depth
# X-squared = 2.1647, df = 2, p-value = 0.3388
Several diagnostics can also be run together.
# Alternatively run multiple tests at once
runHeteroTests(model, quakes)
# $white
#
# White's test for heteroscedasticity
#
# data: model
# X-squared = 125.56, df = 5, p-value < 2.2e-16
# alternative hypothesis: heteroscedasticity present
#
#
# $breusch_pagan
#
# Breusch-Pagan test for heteroscedasticity
#
# data: stations ~ mag + depth
# X-squared = 191.93, df = 2, p-value < 2.2e-16
#
#
# attr(,"class")
# [1] "hetero_test_suite" "list"
# attr(,"tests")
# [1] "white" "breusch_pagan"
# attr(,"model")
#
# Call:
# lm(formula = stations ~ mag + depth, data = quakes)
#
# Coefficients:
# (Intercept) mag depth
# -192.04290 47.90872 0.01318
#
# attr(,"data_source")
# [1] "data.frame"
# Choose a subset of diagnostics
runHeteroTests(model, quakes, tests = c("white", "koenker", "ncv"))
# [INFO] Running Koenker test
# [INFO] Running NCV score test
# $white
#
# White's test for heteroscedasticity
#
# data: model
# X-squared = 125.56, df = 5, p-value < 2.2e-16
# alternative hypothesis: heteroscedasticity present
#
#
# $koenker
#
# Koenker studentized Breusch-Pagan test
#
# data: stations ~ mag + depth
# X-squared = 111.31, df = 2, p-value < 2.2e-16
#
#
# $ncv
#
# Cook-Weisberg score test for non-constant variance
#
# data: stations ~ mag + depth; variance model: fitted values
# X-squared = 187.98, df = 1, p-value < 2.2e-16
# alternative hypothesis: error variance depends on the variance model
#
#
# attr(,"class")
# [1] "hetero_test_suite" "list"
# attr(,"tests")
# [1] "white" "koenker" "ncv"
# attr(,"model")
#
# Call:
# lm(formula = stations ~ mag + depth, data = quakes)
#
# Coefficients:
# (Intercept) mag depth
# -192.04290 47.90872 0.01318
#
# attr(,"data_source")
# [1] "data.frame"
runDiagnostics(model, quakes)
# $white
#
# White's test for heteroscedasticity
#
# data: model
# X-squared = 125.56, df = 5, p-value < 2.2e-16
# alternative hypothesis: heteroscedasticity present
#
#
# $breusch_pagan
#
# Breusch-Pagan test for heteroscedasticity
#
# data: stations ~ mag + depth
# X-squared = 191.93, df = 2, p-value < 2.2e-16
#
#
# $vif
# mag depth
# 1.056182 1.056182
#
# $reset
#
# RESET test for nonlinearity
#
# data: stations ~ mag + depth
# F = 130.76, df1 = 2, df2 = 995, p-value < 2.2e-16
#
#
# $influence
# $influence$cooks_distance
# 1 2 3 4 5 6
# 1.454504e-04 8.010212e-05 8.607284e-03 4.476282e-04 1.083646e-04 1.101297e-03
# 7 8 9 10 11 12
# 9.346367e-05 1.896963e-04 2.711637e-06 8.889251e-05 1.290241e-03 7.175734e-04
# 13 14 15 16 17 18
# 3.149500e-04 2.130391e-03 2.575807e-03 2.204550e-04 6.057777e-03 7.650046e-04
# 19 20 21 22 23 24
# 1.190645e-03 5.675233e-04 1.346824e-03 1.460858e-08 2.996695e-04 7.652187e-04
# 25 26 27 28 29 30
# 3.698536e-03 7.253494e-04 6.479370e-04 2.918215e-03 2.676040e-04 1.288935e-04
# 31 32 33 34 35 36
# 1.322797e-03 9.548130e-05 1.742009e-07 3.095089e-04 1.540495e-03 6.444379e-04
# 37 38 39 40 41 42
# 3.260122e-04 2.439560e-03 2.378747e-04 4.890376e-04 1.933416e-05 3.213154e-05
# 43 44 45 46 47 48
# 3.286688e-05 9.828450e-04 6.219085e-05 6.215958e-04 4.397684e-05 2.226081e-05
# 49 50 51 52 53 54
# 1.627580e-06 2.684053e-03 9.471056e-05 1.672773e-03 6.134508e-05 6.147939e-04
# 55 56 57 58 59 60
# 9.598194e-07 1.531032e-04 5.821807e-04 1.577887e-04 4.602208e-05 5.081784e-04
# 61 62 63 64 65 66
# 2.555869e-04 1.404548e-04 3.687735e-04 3.866285e-05 1.120433e-03 3.959218e-04
# 67 68 69 70 71 72
# 7.711234e-06 1.525450e-03 6.805645e-05 6.242748e-03 1.107397e-03 5.611105e-05
# 73 74 75 76 77 78
# 1.265586e-05 1.599208e-03 5.009306e-04 2.932025e-04 1.477644e-04 5.132385e-05
# 79 80 81 82 83 84
# 1.406470e-05 3.708912e-04 4.770958e-04 5.773726e-06 2.887050e-05 3.410668e-05
# 85 86 87 88 89 90
# 2.795555e-04 9.271635e-06 3.468520e-05 1.217204e-04 2.481608e-04 6.814963e-03
# 91 92 93 94 95 96
# 3.669910e-04 6.172743e-04 1.669868e-06 9.655687e-06 5.355154e-04 1.648327e-03
# 97 98 99 100 101 102
# 1.628626e-04 4.319054e-04 5.695834e-04 2.039865e-04 4.447047e-04 8.648204e-04
# 103 104 105 106 107 108
# 1.060195e-03 8.762672e-04 5.391740e-04 2.282779e-05 2.876198e-04 3.213382e-04
# 109 110 111 112 113 114
# 7.318723e-04 1.233571e-03 1.777470e-06 4.652695e-07 9.803300e-04 4.875947e-04
# 115 116 117 118 119 120
# 2.593973e-04 5.672999e-04 2.534789e-04 2.487786e-03 5.464304e-04 2.000237e-06
# 121 122 123 124 125 126
# 7.066360e-04 1.439374e-04 1.686707e-03 4.291146e-04 8.996980e-05 8.922963e-04
# 127 128 129 130 131 132
# 1.774334e-04 2.216767e-03 2.182832e-03 4.403744e-06 6.631434e-05 4.506828e-04
# 133 134 135 136 137 138
# 8.167050e-05 1.288742e-04 6.006885e-04 3.127797e-03 2.116238e-03 1.004081e-03
# 139 140 141 142 143 144
# 9.299250e-04 1.804579e-04 3.572856e-04 5.178035e-04 1.004533e-04 7.195587e-04
# 145 146 147 148 149 150
# 3.116365e-04 1.990741e-05 2.728980e-05 1.294776e-05 3.390635e-04 1.573656e-03
# 151 152 153 154 155 156
# 1.360986e-02 1.896685e-03 2.604840e-04 8.298848e-04 1.575989e-03 3.239846e-05
# 157 158 159 160 161 162
# 1.678554e-04 4.248443e-06 1.011350e-03 5.040741e-07 4.476282e-04 6.733230e-04
# 163 164 165 166 167 168
# 3.444458e-06 6.973463e-05 8.824090e-05 9.927529e-04 6.812188e-03 6.498815e-04
# 169 170 171 172 173 174
# 2.270698e-06 3.125087e-07 2.438938e-05 1.719060e-04 2.999155e-05 8.219002e-04
# 175 176 177 178 179 180
# 9.285053e-07 8.359222e-04 2.152513e-04 6.901722e-05 6.377049e-04 9.174977e-05
# 181 182 183 184 185 186
# 2.020731e-03 9.618092e-04 8.136624e-05 4.393195e-06 5.803189e-05 2.541396e-03
# 187 188 189 190 191 192
# 2.221635e-04 1.295871e-04 6.758772e-04 2.713664e-05 3.786639e-04 3.596338e-06
# 193 194 195 196 197 198
# 3.789532e-03 7.784533e-04 1.713832e-04 3.015250e-04 5.545890e-05 6.063209e-04
# 199 200 201 202 203 204
# 6.453820e-04 1.324058e-03 8.072757e-05 3.973659e-04 2.675495e-05 4.011410e-04
# 205 206 207 208 209 210
# 1.407020e-03 9.454527e-05 1.548665e-05 1.302680e-03 9.641889e-05 1.993678e-04
# 211 212 213 214 215 216
# 4.196361e-05 1.288936e-04 1.158573e-03 4.022601e-03 6.262349e-06 1.971215e-06
# 217 218 219 220 221 222
# 2.178179e-04 1.705779e-04 2.017235e-04 5.743189e-07 1.027551e-04 3.806313e-04
# 223 224 225 226 227 228
# 1.321782e-04 3.275625e-04 8.601217e-05 4.586044e-04 2.643659e-04 6.050473e-05
# 229 230 231 232 233 234
# 1.012548e-04 2.298672e-04 6.736951e-04 1.040411e-04 2.849544e-04 1.077104e-03
# 235 236 237 238 239 240
# 1.275991e-03 2.631424e-04 5.638491e-07 6.907381e-04 3.080151e-04 5.050617e-05
# 241 242 243 244 245 246
# 9.059249e-05 9.687826e-04 2.673171e-02 8.418424e-04 1.375358e-05 5.113758e-04
# 247 248 249 250 251 252
# 1.322236e-04 1.679069e-03 1.128422e-03 6.064643e-06 3.326078e-04 8.474387e-06
# 253 254 255 256 257 258
# 2.276769e-03 2.148537e-04 2.253596e-05 1.761104e-04 7.382196e-06 6.357909e-06
# 259 260 261 262 263 264
# 3.457661e-04 3.432381e-04 1.699472e-03 4.533231e-04 6.434685e-04 4.594787e-06
# 265 266 267 268 269 270
# 4.831830e-05 2.899479e-04 9.381715e-04 2.560821e-04 2.355808e-05 5.659708e-04
# 271 272 273 274 275 276
# 1.802743e-04 2.397531e-03 8.998723e-06 1.582943e-04 7.625471e-03 5.861506e-04
# 277 278 279 280 281 282
# 1.924824e-04 1.107913e-04 8.970116e-04 1.167657e-03 1.846352e-05 1.730819e-04
# 283 284 285 286 287 288
# 7.920044e-04 2.609575e-04 5.391706e-06 6.975056e-04 4.653230e-05 7.404759e-06
# 289 290 291 292 293 294
# 1.710657e-04 1.873463e-04 6.666394e-04 2.698283e-03 1.229054e-04 1.750572e-09
# 295 296 297 298 299 300
# 3.170299e-04 3.544604e-05 3.660165e-04 8.561011e-04 2.362550e-03 2.197877e-04
# 301 302 303 304 305 306
# 2.770440e-04 4.111539e-06 1.070166e-04 2.662680e-03 1.738459e-05 5.963423e-04
# 307 308 309 310 311 312
# 5.132561e-04 8.988712e-03 5.424953e-06 1.050619e-03 3.464273e-03 2.215072e-04
# 313 314 315 316 317 318
# 1.448382e-03 3.059074e-04 3.246473e-04 5.743752e-04 3.454396e-05 1.431169e-03
# 319 320 321 322 323 324
# 1.163457e-04 1.813361e-03 6.527792e-04 6.963019e-04 7.674768e-05 2.572294e-04
# 325 326 327 328 329 330
# 8.315699e-04 6.089535e-04 1.991033e-04 5.185259e-04 1.115880e-03 7.399841e-04
# 331 332 333 334 335 336
# 5.165306e-03 2.132156e-03 6.131062e-04 2.603176e-03 2.506294e-05 7.819124e-04
# 337 338 339 340 341 342
# 1.698762e-05 2.571719e-06 5.144821e-04 1.916724e-03 1.747126e-04 3.974441e-03
# 343 344 345 346 347 348
# 9.515094e-04 7.608203e-05 7.073745e-06 1.522752e-04 2.172272e-03 1.081543e-03
# 349 350 351 352 353 354
# 2.891747e-03 2.466954e-03 1.346290e-03 1.870995e-03 2.457227e-04 2.980428e-04
# 355 356 357 358 359 360
# 1.046704e-03 4.461092e-04 1.981092e-04 4.960450e-04 4.381174e-04 1.149823e-03
# 361 362 363 364 365 366
# 7.627428e-05 5.547037e-03 1.147347e-03 4.532987e-07 1.390313e-04 3.430484e-04
# 367 368 369 370 371 372
# 1.230063e-03 7.095661e-04 2.278052e-04 1.848886e-03 1.168403e-03 1.610536e-02
# 373 374 375 376 377 378
# 3.100138e-05 6.661052e-04 4.271869e-06 3.983228e-02 9.135738e-04 8.049329e-05
# 379 380 381 382 383 384
# 1.783047e-06 7.596862e-03 1.181469e-03 7.748307e-05 3.657023e-03 7.482897e-06
# 385 386 387 388 389 390
# 1.799792e-03 3.984432e-04 6.173186e-05 3.370196e-04 1.594575e-03 3.862815e-04
# 391 392 393 394 395 396
# 2.650254e-04 9.117874e-04 1.647818e-04 2.591620e-06 3.034451e-04 1.155703e-04
# 397 398 399 400 401 402
# 6.754566e-03 2.593063e-03 1.732800e-02 1.080629e-02 6.488127e-04 2.036229e-04
# 403 404 405 406 407 408
# 6.494197e-05 1.556864e-03 6.067727e-04 2.664229e-04 3.644854e-05 2.155424e-04
# 409 410 411 412 413 414
# 4.480440e-06 8.012708e-04 5.701054e-04 1.714623e-03 2.003942e-05 1.523301e-04
# 415 416 417 418 419 420
# 1.848538e-04 1.094555e-04 7.906993e-05 1.526538e-03 1.696066e-04 2.598171e-03
# 421 422 423 424 425 426
# 2.421435e-04 8.371938e-05 3.606731e-03 4.834455e-05 6.600910e-04 2.714689e-05
# 427 428 429 430 431 432
# 7.181677e-05 2.352459e-03 1.858691e-04 3.368187e-04 8.712020e-06 1.960936e-03
# 433 434 435 436 437 438
# 1.094602e-03 1.003610e-03 5.697673e-05 9.225951e-06 5.285353e-06 1.684751e-03
# 439 440 441 442 443 444
# 5.976188e-06 1.232448e-04 2.250342e-05 1.562610e-04 2.091322e-04 2.430178e-03
# 445 446 447 448 449 450
# 1.771010e-03 1.294777e-03 1.948488e-04 1.058032e-02 1.466783e-02 9.123870e-05
# 451 452 453 454 455 456
# 1.767965e-04 1.952028e-08 7.831851e-04 4.303933e-06 9.991133e-05 4.739780e-04
# 457 458 459 460 461 462
# 5.532880e-04 5.808676e-04 3.387232e-03 4.607543e-05 6.113513e-04 2.642472e-02
# 463 464 465 466 467 468
# 7.763971e-04 1.280139e-03 1.119801e-04 5.261916e-04 1.304009e-06 9.110953e-04
# 469 470 471 472 473 474
# 1.206394e-04 5.181372e-05 9.163320e-05 4.070636e-04 8.691006e-05 5.259315e-04
# 475 476 477 478 479 480
# 2.079891e-04 5.040618e-05 9.032160e-05 2.495771e-04 1.199250e-03 3.439535e-04
# 481 482 483 484 485 486
# 1.515597e-03 2.303425e-05 1.431066e-03 1.351893e-04 6.491783e-06 4.093342e-03
# 487 488 489 490 491 492
# 1.781758e-03 1.855779e-06 5.769551e-04 2.559844e-03 3.830718e-04 4.104833e-04
# 493 494 495 496 497 498
# 6.293088e-05 4.330607e-04 5.075353e-04 2.312563e-05 2.142592e-06 2.325249e-03
# 499 500 501 502 503 504
# 3.507072e-04 8.735888e-05 4.160862e-05 6.759620e-04 2.326792e-04 7.488486e-05
# 505 506 507 508 509 510
# 3.311136e-04 3.724447e-05 2.229418e-04 8.787383e-03 5.077269e-03 8.041707e-06
# 511 512 513 514 515 516
# 2.750208e-11 6.618443e-03 9.950213e-05 7.020521e-05 3.082069e-05 2.229626e-04
# 517 518 519 520 521 522
# 4.093466e-04 5.848930e-04 1.916268e-06 9.987753e-05 9.496668e-04 9.703981e-04
# 523 524 525 526 527 528
# 9.950213e-05 4.467513e-04 1.397896e-03 1.435793e-03 8.655248e-04 1.463409e-03
# 529 530 531 532 533 534
# 6.054252e-05 9.539230e-06 8.271521e-06 7.213105e-04 1.501862e-03 1.734793e-04
# 535 536 537 538 539 540
# 1.395680e-04 2.389608e-05 3.541492e-04 6.581780e-04 5.663764e-03 1.314865e-05
# 541 542 543 544 545 546
# 3.391677e-03 2.006795e-04 4.608500e-05 8.994636e-05 2.264099e-03 6.989653e-04
# 547 548 549 550 551 552
# 2.041812e-03 3.282826e-05 2.607819e-03 1.127666e-04 6.635391e-05 1.396609e-06
# 553 554 555 556 557 558
# 7.882728e-04 2.062552e-05 8.759916e-04 4.060994e-04 3.169261e-04 2.172569e-02
# 559 560 561 562 563 564
# 4.727893e-04 8.468366e-07 1.720969e-05 1.934250e-03 2.335144e-03 1.647439e-03
# 565 566 567 568 569 570
# 2.502536e-04 6.653024e-04 2.663844e-04 8.400234e-05 6.262081e-05 6.106452e-05
# 571 572 573 574 575 576
# 6.271639e-03 8.441752e-05 2.287273e-08 3.125011e-03 4.863026e-06 2.928999e-04
# 577 578 579 580 581 582
# 2.540225e-04 2.979886e-04 1.333432e-03 5.272996e-06 8.759020e-05 1.293530e-04
# 583 584 585 586 587 588
# 7.342273e-06 3.509985e-03 2.019662e-03 8.410665e-04 2.498742e-04 3.103613e-08
# 589 590 591 592 593 594
# 4.820507e-04 1.452900e-03 3.470369e-05 1.002250e-04 1.143857e-04 4.096423e-04
# 595 596 597 598 599 600
# 1.189062e-03 3.913174e-05 4.652351e-04 1.322955e-03 5.610553e-05 2.936843e-05
# 601 602 603 604 605 606
# 1.015027e-02 8.058720e-04 4.205245e-05 8.513408e-03 3.572264e-03 3.343216e-04
# 607 608 609 610 611 612
# 1.768871e-05 2.085399e-04 4.677359e-08 5.287110e-05 1.743867e-05 9.013439e-05
# 613 614 615 616 617 618
# 2.064262e-04 8.242024e-06 6.489838e-06 8.013945e-04 9.719191e-05 1.400797e-04
# 619 620 621 622 623 624
# 3.140498e-04 8.144097e-04 5.364940e-06 4.608256e-04 4.792040e-03 1.531676e-03
# 625 626 627 628 629 630
# 2.163090e-04 2.809024e-04 2.806910e-04 3.576925e-04 8.135362e-05 7.327558e-04
# 631 632 633 634 635 636
# 1.098637e-05 2.063031e-03 2.530280e-06 2.611493e-04 1.184755e-07 4.906597e-02
# 637 638 639 640 641 642
# 1.584843e-03 1.347520e-03 3.252513e-03 9.801511e-05 2.770572e-03 1.769412e-05
# 643 644 645 646 647 648
# 2.036713e-03 3.565046e-04 2.398026e-07 4.103639e-04 8.210783e-04 6.047580e-05
# 649 650 651 652 653 654
# 1.438482e-03 9.673131e-05 4.016773e-03 1.377735e-04 5.285564e-03 8.632848e-06
# 655 656 657 658 659 660
# 1.568621e-03 2.698125e-05 4.515412e-03 2.973097e-04 6.681463e-05 3.082506e-04
# 661 662 663 664 665 666
# 5.529114e-06 1.077364e-07 1.714489e-02 1.795071e-03 1.271018e-04 2.302518e-04
# 667 668 669 670 671 672
# 1.088180e-03 1.908814e-04 1.181343e-04 3.085384e-04 2.328757e-06 3.428290e-07
# 673 674 675 676 677 678
# 1.108826e-03 5.411973e-06 2.278891e-02 3.514741e-07 5.192652e-04 3.645797e-04
# 679 680 681 682 683 684
# 3.886925e-03 5.209815e-08 2.747551e-04 1.347936e-04 6.909379e-07 2.246006e-04
# 685 686 687 688 689 690
# 6.526249e-05 1.543942e-03 1.163792e-05 7.226645e-06 8.701434e-04 2.318997e-05
# 691 692 693 694 695 696
# 6.784884e-05 2.243106e-04 2.548919e-04 1.556602e-04 7.314943e-05 7.577799e-04
# 697 698 699 700 701 702
# 1.106356e-03 6.782817e-04 8.864887e-04 2.058625e-04 5.444202e-04 1.002087e-02
# 703 704 705 706 707 708
# 1.600480e-04 1.803078e-03 2.460335e-05 2.069061e-04 3.165046e-03 2.358445e-03
# 709 710 711 712 713 714
# 7.031996e-04 1.059012e-04 4.403328e-05 1.726870e-02 4.600677e-05 7.334050e-03
# 715 716 717 718 719 720
# 3.839671e-03 6.552220e-04 1.148730e-04 3.271510e-04 1.531447e-03 1.768982e-05
# 721 722 723 724 725 726
# 8.951990e-06 1.100596e-03 6.252350e-04 3.780479e-04 4.012709e-04 7.788258e-07
# 727 728 729 730 731 732
# 7.799883e-04 1.027596e-05 1.981505e-03 1.292803e-04 3.795289e-05 1.038615e-04
# 733 734 735 736 737 738
# 1.147388e-03 2.027998e-05 2.694623e-04 5.660228e-04 3.577965e-04 1.004580e-04
# 739 740 741 742 743 744
# 4.354559e-03 1.688785e-04 2.976606e-04 5.688377e-04 3.401688e-04 2.157617e-06
# 745 746 747 748 749 750
# 9.418815e-04 8.055503e-04 9.429964e-06 8.097102e-04 1.282625e-03 4.039396e-04
# 751 752 753 754 755 756
# 7.221887e-05 4.944557e-04 1.811121e-02 2.174841e-05 7.114780e-05 2.591806e-04
# 757 758 759 760 761 762
# 5.901567e-04 6.151635e-03 3.190628e-04 2.729119e-03 2.485600e-06 1.534935e-03
# 763 764 765 766 767 768
# 6.175267e-05 1.730799e-03 9.005416e-04 1.745883e-04 6.251554e-04 1.148522e-04
# 769 770 771 772 773 774
# 4.808785e-04 1.308032e-03 4.701841e-04 1.150277e-03 1.128134e-04 4.666687e-06
# 775 776 777 778 779 780
# 2.488478e-03 6.896079e-05 9.256739e-05 1.269279e-03 2.105541e-06 2.498533e-04
# 781 782 783 784 785 786
# 8.468366e-07 3.504641e-05 1.323630e-06 4.530716e-04 1.293002e-05 4.223379e-07
# 787 788 789 790 791 792
# 4.773331e-04 6.832607e-04 1.798748e-04 4.348118e-03 1.458296e-04 7.183720e-03
# 793 794 795 796 797 798
# 1.564156e-04 2.144356e-03 1.704494e-06 2.024022e-04 4.799621e-04 2.244956e-04
# 799 800 801 802 803 804
# 1.545022e-04 1.539064e-03 1.178145e-03 2.258859e-04 8.577806e-04 6.252462e-05
# 805 806 807 808 809 810
# 8.684960e-05 1.954506e-03 6.867399e-03 1.447474e-03 7.233463e-06 2.838495e-05
# 811 812 813 814 815 816
# 3.450252e-04 8.049103e-04 2.048382e-04 1.574569e-04 1.611919e-03 5.668589e-04
# 817 818 819 820 821 822
# 5.175394e-04 4.537397e-04 2.873279e-04 1.831688e-05 2.888562e-06 1.624922e-04
# 823 824 825 826 827 828
# 1.175545e-03 6.731792e-06 6.584022e-05 5.571627e-04 2.312258e-03 1.808312e-04
# 829 830 831 832 833 834
# 1.661190e-03 3.361467e-04 1.178129e-03 1.216249e-03 2.413154e-04 4.678317e-04
# 835 836 837 838 839 840
# 2.927428e-04 1.357345e-03 1.565820e-04 2.538871e-06 7.224042e-04 4.787038e-04
# 841 842 843 844 845 846
# 4.584536e-04 2.761186e-03 1.103406e-03 2.896864e-05 1.007796e-04 1.539240e-04
# 847 848 849 850 851 852
# 1.295321e-03 3.550946e-05 1.504903e-05 5.147707e-03 1.425211e-03 2.978816e-04
# 853 854 855 856 857 858
# 9.658880e-06 5.237535e-04 2.112962e-05 6.986277e-04 5.488686e-04 3.094403e-04
# 859 860 861 862 863 864
# 4.015529e-07 1.856976e-06 4.660315e-04 8.403742e-04 2.163241e-03 1.008769e-04
# 865 866 867 868 869 870
# 5.638730e-05 3.525929e-04 2.006359e-06 2.337344e-03 2.978989e-04 3.970738e-02
# 871 872 873 874 875 876
# 1.079820e-04 2.335804e-04 3.854268e-04 1.365224e-04 7.325721e-04 1.462793e-05
# 877 878 879 880 881 882
# 3.534996e-04 3.498689e-06 1.858280e-03 1.544534e-05 2.396300e-04 1.656366e-04
# 883 884 885 886 887 888
# 2.156032e-03 1.388267e-04 1.975113e-04 5.737835e-06 5.405373e-05 5.326550e-03
# 889 890 891 892 893 894
# 1.176008e-04 1.242068e-04 5.745081e-04 1.386001e-04 6.947351e-05 4.630405e-04
# 895 896 897 898 899 900
# 1.670376e-04 7.488923e-05 6.111467e-03 1.357382e-03 3.857840e-04 7.251249e-03
# 901 902 903 904 905 906
# 2.409060e-06 5.256316e-04 9.719191e-05 6.205035e-08 4.527863e-08 3.255239e-03
# 907 908 909 910 911 912
# 2.201119e-03 7.471355e-03 5.891925e-05 8.942198e-04 1.233727e-03 1.294729e-03
# 913 914 915 916 917 918
# 1.230718e-03 2.170011e-04 2.653200e-03 1.499562e-03 1.882859e-03 1.027551e-04
# 919 920 921 922 923 924
# 2.097703e-03 2.762033e-02 2.888581e-03 6.460248e-03 2.159218e-04 1.710444e-05
# 925 926 927 928 929 930
# 1.105967e-03 1.489553e-04 2.621228e-03 5.913036e-04 6.063600e-05 5.970866e-04
# 931 932 933 934 935 936
# 8.895451e-06 3.343695e-04 1.172793e-03 7.047283e-06 3.605056e-02 2.675004e-02
# 937 938 939 940 941 942
# 1.850290e-03 1.581126e-03 1.776866e-04 2.001583e-03 4.560962e-04 6.846274e-04
# 943 944 945 946 947 948
# 1.796572e-04 5.243167e-03 8.985467e-04 3.359145e-04 2.936231e-04 5.159867e-04
# 949 950 951 952 953 954
# 2.033926e-03 7.428518e-06 7.076266e-06 3.545068e-04 2.886557e-04 7.967128e-04
# 955 956 957 958 959 960
# 2.784865e-03 7.501866e-04 3.034125e-04 2.429106e-04 2.072199e-06 1.080548e-03
# 961 962 963 964 965 966
# 3.442114e-05 8.862949e-05 1.285736e-04 2.116088e-03 6.813540e-04 1.924525e-03
# 967 968 969 970 971 972
# 1.361347e-04 7.131638e-05 1.208481e-03 7.242327e-03 2.554560e-04 2.729120e-03
# 973 974 975 976 977 978
# 7.439769e-04 4.683381e-04 1.700287e-03 3.237171e-03 2.456969e-03 4.734591e-05
# 979 980 981 982 983 984
# 8.290908e-04 3.969786e-03 1.567362e-03 1.111097e-03 1.818735e-04 4.633508e-04
# 985 986 987 988 989 990
# 3.908670e-04 5.306012e-05 5.421865e-04 8.648190e-04 2.279865e-04 1.221198e-05
# 991 992 993 994 995 996
# 9.360577e-05 2.680374e-04 1.473071e-03 1.046325e-03 6.445468e-07 3.948441e-05
# 997 998 999 1000
# 5.766960e-06 1.744932e-04 8.057529e-04 1.604166e-02
#
# $influence$influential
# 3 17 70 90 151 167 214 243 275 308 331 362 372 376 380 397
# 3 17 70 90 151 167 214 243 275 308 331 362 372 376 380 397
# 399 400 448 449 462 486 508 509 512 539 558 571 601 604 623 636
# 399 400 448 449 462 486 508 509 512 539 558 571 601 604 623 636
# 651 653 657 663 675 702 712 714 739 753 758 790 792 807 850 870
# 651 653 657 663 675 702 712 714 739 753 758 790 792 807 850 870
# 888 897 900 908 920 922 935 936 944 970 1000
# 888 897 900 908 920 922 935 936 944 970 1000
#
# $influence$cutoff
# [1] 0.004012036
Remediation helpers operate on the fitted model directly.
fitWLS(model)
#
# Call:
# lm(formula = stations ~ mag + depth, data = quakes)
#
# Coefficients:
# (Intercept) mag depth
# -1.540e+02 3.980e+01 9.189e-03
fitRobust(model)
# Call:
# rlm(formula = form, data = data)
# Converged in 7 iterations
#
# Coefficients:
# (Intercept) mag depth
# -180.64561558 45.40282582 0.01238906
#
# Degrees of freedom: 1000 total; 997 residual
# Scale estimate: 9.68
autoTransform(model)
# [INFO] Running Breusch-Pagan test
# [INFO] Running Breusch-Pagan test
# [INFO] Running Breusch-Pagan test
# [INFO] Running Breusch-Pagan test
# $model
#
# Call:
# lm(formula = formula_trans, data = df)
#
# Coefficients:
# (Intercept) mag depth
# -2.5048466 1.2426849 0.0003033
#
#
# $method
# [1] "log"
#
# $lambda
# [1] NA
See the package README for a complete list of implemented tests.
Earthquake station-count example
R’s built-in quakes dataset records 1,000 seismic events
near Fiji. We can run the diagnostics and attempt a remedial fit on this
real-world data.
quakes_model <- lm(stations ~ mag + depth, data = quakes)
runDiagnostics(quakes_model, quakes)
# $white
#
# White's test for heteroscedasticity
#
# data: model
# X-squared = 125.56, df = 5, p-value < 2.2e-16
# alternative hypothesis: heteroscedasticity present
#
#
# $breusch_pagan
#
# Breusch-Pagan test for heteroscedasticity
#
# data: stations ~ mag + depth
# X-squared = 191.93, df = 2, p-value < 2.2e-16
#
#
# $vif
# mag depth
# 1.056182 1.056182
#
# $reset
#
# RESET test for nonlinearity
#
# data: stations ~ mag + depth
# F = 130.76, df1 = 2, df2 = 995, p-value < 2.2e-16
#
#
# $influence
# $influence$cooks_distance
# 1 2 3 4 5 6
# 1.454504e-04 8.010212e-05 8.607284e-03 4.476282e-04 1.083646e-04 1.101297e-03
# 7 8 9 10 11 12
# 9.346367e-05 1.896963e-04 2.711637e-06 8.889251e-05 1.290241e-03 7.175734e-04
# 13 14 15 16 17 18
# 3.149500e-04 2.130391e-03 2.575807e-03 2.204550e-04 6.057777e-03 7.650046e-04
# 19 20 21 22 23 24
# 1.190645e-03 5.675233e-04 1.346824e-03 1.460858e-08 2.996695e-04 7.652187e-04
# 25 26 27 28 29 30
# 3.698536e-03 7.253494e-04 6.479370e-04 2.918215e-03 2.676040e-04 1.288935e-04
# 31 32 33 34 35 36
# 1.322797e-03 9.548130e-05 1.742009e-07 3.095089e-04 1.540495e-03 6.444379e-04
# 37 38 39 40 41 42
# 3.260122e-04 2.439560e-03 2.378747e-04 4.890376e-04 1.933416e-05 3.213154e-05
# 43 44 45 46 47 48
# 3.286688e-05 9.828450e-04 6.219085e-05 6.215958e-04 4.397684e-05 2.226081e-05
# 49 50 51 52 53 54
# 1.627580e-06 2.684053e-03 9.471056e-05 1.672773e-03 6.134508e-05 6.147939e-04
# 55 56 57 58 59 60
# 9.598194e-07 1.531032e-04 5.821807e-04 1.577887e-04 4.602208e-05 5.081784e-04
# 61 62 63 64 65 66
# 2.555869e-04 1.404548e-04 3.687735e-04 3.866285e-05 1.120433e-03 3.959218e-04
# 67 68 69 70 71 72
# 7.711234e-06 1.525450e-03 6.805645e-05 6.242748e-03 1.107397e-03 5.611105e-05
# 73 74 75 76 77 78
# 1.265586e-05 1.599208e-03 5.009306e-04 2.932025e-04 1.477644e-04 5.132385e-05
# 79 80 81 82 83 84
# 1.406470e-05 3.708912e-04 4.770958e-04 5.773726e-06 2.887050e-05 3.410668e-05
# 85 86 87 88 89 90
# 2.795555e-04 9.271635e-06 3.468520e-05 1.217204e-04 2.481608e-04 6.814963e-03
# 91 92 93 94 95 96
# 3.669910e-04 6.172743e-04 1.669868e-06 9.655687e-06 5.355154e-04 1.648327e-03
# 97 98 99 100 101 102
# 1.628626e-04 4.319054e-04 5.695834e-04 2.039865e-04 4.447047e-04 8.648204e-04
# 103 104 105 106 107 108
# 1.060195e-03 8.762672e-04 5.391740e-04 2.282779e-05 2.876198e-04 3.213382e-04
# 109 110 111 112 113 114
# 7.318723e-04 1.233571e-03 1.777470e-06 4.652695e-07 9.803300e-04 4.875947e-04
# 115 116 117 118 119 120
# 2.593973e-04 5.672999e-04 2.534789e-04 2.487786e-03 5.464304e-04 2.000237e-06
# 121 122 123 124 125 126
# 7.066360e-04 1.439374e-04 1.686707e-03 4.291146e-04 8.996980e-05 8.922963e-04
# 127 128 129 130 131 132
# 1.774334e-04 2.216767e-03 2.182832e-03 4.403744e-06 6.631434e-05 4.506828e-04
# 133 134 135 136 137 138
# 8.167050e-05 1.288742e-04 6.006885e-04 3.127797e-03 2.116238e-03 1.004081e-03
# 139 140 141 142 143 144
# 9.299250e-04 1.804579e-04 3.572856e-04 5.178035e-04 1.004533e-04 7.195587e-04
# 145 146 147 148 149 150
# 3.116365e-04 1.990741e-05 2.728980e-05 1.294776e-05 3.390635e-04 1.573656e-03
# 151 152 153 154 155 156
# 1.360986e-02 1.896685e-03 2.604840e-04 8.298848e-04 1.575989e-03 3.239846e-05
# 157 158 159 160 161 162
# 1.678554e-04 4.248443e-06 1.011350e-03 5.040741e-07 4.476282e-04 6.733230e-04
# 163 164 165 166 167 168
# 3.444458e-06 6.973463e-05 8.824090e-05 9.927529e-04 6.812188e-03 6.498815e-04
# 169 170 171 172 173 174
# 2.270698e-06 3.125087e-07 2.438938e-05 1.719060e-04 2.999155e-05 8.219002e-04
# 175 176 177 178 179 180
# 9.285053e-07 8.359222e-04 2.152513e-04 6.901722e-05 6.377049e-04 9.174977e-05
# 181 182 183 184 185 186
# 2.020731e-03 9.618092e-04 8.136624e-05 4.393195e-06 5.803189e-05 2.541396e-03
# 187 188 189 190 191 192
# 2.221635e-04 1.295871e-04 6.758772e-04 2.713664e-05 3.786639e-04 3.596338e-06
# 193 194 195 196 197 198
# 3.789532e-03 7.784533e-04 1.713832e-04 3.015250e-04 5.545890e-05 6.063209e-04
# 199 200 201 202 203 204
# 6.453820e-04 1.324058e-03 8.072757e-05 3.973659e-04 2.675495e-05 4.011410e-04
# 205 206 207 208 209 210
# 1.407020e-03 9.454527e-05 1.548665e-05 1.302680e-03 9.641889e-05 1.993678e-04
# 211 212 213 214 215 216
# 4.196361e-05 1.288936e-04 1.158573e-03 4.022601e-03 6.262349e-06 1.971215e-06
# 217 218 219 220 221 222
# 2.178179e-04 1.705779e-04 2.017235e-04 5.743189e-07 1.027551e-04 3.806313e-04
# 223 224 225 226 227 228
# 1.321782e-04 3.275625e-04 8.601217e-05 4.586044e-04 2.643659e-04 6.050473e-05
# 229 230 231 232 233 234
# 1.012548e-04 2.298672e-04 6.736951e-04 1.040411e-04 2.849544e-04 1.077104e-03
# 235 236 237 238 239 240
# 1.275991e-03 2.631424e-04 5.638491e-07 6.907381e-04 3.080151e-04 5.050617e-05
# 241 242 243 244 245 246
# 9.059249e-05 9.687826e-04 2.673171e-02 8.418424e-04 1.375358e-05 5.113758e-04
# 247 248 249 250 251 252
# 1.322236e-04 1.679069e-03 1.128422e-03 6.064643e-06 3.326078e-04 8.474387e-06
# 253 254 255 256 257 258
# 2.276769e-03 2.148537e-04 2.253596e-05 1.761104e-04 7.382196e-06 6.357909e-06
# 259 260 261 262 263 264
# 3.457661e-04 3.432381e-04 1.699472e-03 4.533231e-04 6.434685e-04 4.594787e-06
# 265 266 267 268 269 270
# 4.831830e-05 2.899479e-04 9.381715e-04 2.560821e-04 2.355808e-05 5.659708e-04
# 271 272 273 274 275 276
# 1.802743e-04 2.397531e-03 8.998723e-06 1.582943e-04 7.625471e-03 5.861506e-04
# 277 278 279 280 281 282
# 1.924824e-04 1.107913e-04 8.970116e-04 1.167657e-03 1.846352e-05 1.730819e-04
# 283 284 285 286 287 288
# 7.920044e-04 2.609575e-04 5.391706e-06 6.975056e-04 4.653230e-05 7.404759e-06
# 289 290 291 292 293 294
# 1.710657e-04 1.873463e-04 6.666394e-04 2.698283e-03 1.229054e-04 1.750572e-09
# 295 296 297 298 299 300
# 3.170299e-04 3.544604e-05 3.660165e-04 8.561011e-04 2.362550e-03 2.197877e-04
# 301 302 303 304 305 306
# 2.770440e-04 4.111539e-06 1.070166e-04 2.662680e-03 1.738459e-05 5.963423e-04
# 307 308 309 310 311 312
# 5.132561e-04 8.988712e-03 5.424953e-06 1.050619e-03 3.464273e-03 2.215072e-04
# 313 314 315 316 317 318
# 1.448382e-03 3.059074e-04 3.246473e-04 5.743752e-04 3.454396e-05 1.431169e-03
# 319 320 321 322 323 324
# 1.163457e-04 1.813361e-03 6.527792e-04 6.963019e-04 7.674768e-05 2.572294e-04
# 325 326 327 328 329 330
# 8.315699e-04 6.089535e-04 1.991033e-04 5.185259e-04 1.115880e-03 7.399841e-04
# 331 332 333 334 335 336
# 5.165306e-03 2.132156e-03 6.131062e-04 2.603176e-03 2.506294e-05 7.819124e-04
# 337 338 339 340 341 342
# 1.698762e-05 2.571719e-06 5.144821e-04 1.916724e-03 1.747126e-04 3.974441e-03
# 343 344 345 346 347 348
# 9.515094e-04 7.608203e-05 7.073745e-06 1.522752e-04 2.172272e-03 1.081543e-03
# 349 350 351 352 353 354
# 2.891747e-03 2.466954e-03 1.346290e-03 1.870995e-03 2.457227e-04 2.980428e-04
# 355 356 357 358 359 360
# 1.046704e-03 4.461092e-04 1.981092e-04 4.960450e-04 4.381174e-04 1.149823e-03
# 361 362 363 364 365 366
# 7.627428e-05 5.547037e-03 1.147347e-03 4.532987e-07 1.390313e-04 3.430484e-04
# 367 368 369 370 371 372
# 1.230063e-03 7.095661e-04 2.278052e-04 1.848886e-03 1.168403e-03 1.610536e-02
# 373 374 375 376 377 378
# 3.100138e-05 6.661052e-04 4.271869e-06 3.983228e-02 9.135738e-04 8.049329e-05
# 379 380 381 382 383 384
# 1.783047e-06 7.596862e-03 1.181469e-03 7.748307e-05 3.657023e-03 7.482897e-06
# 385 386 387 388 389 390
# 1.799792e-03 3.984432e-04 6.173186e-05 3.370196e-04 1.594575e-03 3.862815e-04
# 391 392 393 394 395 396
# 2.650254e-04 9.117874e-04 1.647818e-04 2.591620e-06 3.034451e-04 1.155703e-04
# 397 398 399 400 401 402
# 6.754566e-03 2.593063e-03 1.732800e-02 1.080629e-02 6.488127e-04 2.036229e-04
# 403 404 405 406 407 408
# 6.494197e-05 1.556864e-03 6.067727e-04 2.664229e-04 3.644854e-05 2.155424e-04
# 409 410 411 412 413 414
# 4.480440e-06 8.012708e-04 5.701054e-04 1.714623e-03 2.003942e-05 1.523301e-04
# 415 416 417 418 419 420
# 1.848538e-04 1.094555e-04 7.906993e-05 1.526538e-03 1.696066e-04 2.598171e-03
# 421 422 423 424 425 426
# 2.421435e-04 8.371938e-05 3.606731e-03 4.834455e-05 6.600910e-04 2.714689e-05
# 427 428 429 430 431 432
# 7.181677e-05 2.352459e-03 1.858691e-04 3.368187e-04 8.712020e-06 1.960936e-03
# 433 434 435 436 437 438
# 1.094602e-03 1.003610e-03 5.697673e-05 9.225951e-06 5.285353e-06 1.684751e-03
# 439 440 441 442 443 444
# 5.976188e-06 1.232448e-04 2.250342e-05 1.562610e-04 2.091322e-04 2.430178e-03
# 445 446 447 448 449 450
# 1.771010e-03 1.294777e-03 1.948488e-04 1.058032e-02 1.466783e-02 9.123870e-05
# 451 452 453 454 455 456
# 1.767965e-04 1.952028e-08 7.831851e-04 4.303933e-06 9.991133e-05 4.739780e-04
# 457 458 459 460 461 462
# 5.532880e-04 5.808676e-04 3.387232e-03 4.607543e-05 6.113513e-04 2.642472e-02
# 463 464 465 466 467 468
# 7.763971e-04 1.280139e-03 1.119801e-04 5.261916e-04 1.304009e-06 9.110953e-04
# 469 470 471 472 473 474
# 1.206394e-04 5.181372e-05 9.163320e-05 4.070636e-04 8.691006e-05 5.259315e-04
# 475 476 477 478 479 480
# 2.079891e-04 5.040618e-05 9.032160e-05 2.495771e-04 1.199250e-03 3.439535e-04
# 481 482 483 484 485 486
# 1.515597e-03 2.303425e-05 1.431066e-03 1.351893e-04 6.491783e-06 4.093342e-03
# 487 488 489 490 491 492
# 1.781758e-03 1.855779e-06 5.769551e-04 2.559844e-03 3.830718e-04 4.104833e-04
# 493 494 495 496 497 498
# 6.293088e-05 4.330607e-04 5.075353e-04 2.312563e-05 2.142592e-06 2.325249e-03
# 499 500 501 502 503 504
# 3.507072e-04 8.735888e-05 4.160862e-05 6.759620e-04 2.326792e-04 7.488486e-05
# 505 506 507 508 509 510
# 3.311136e-04 3.724447e-05 2.229418e-04 8.787383e-03 5.077269e-03 8.041707e-06
# 511 512 513 514 515 516
# 2.750208e-11 6.618443e-03 9.950213e-05 7.020521e-05 3.082069e-05 2.229626e-04
# 517 518 519 520 521 522
# 4.093466e-04 5.848930e-04 1.916268e-06 9.987753e-05 9.496668e-04 9.703981e-04
# 523 524 525 526 527 528
# 9.950213e-05 4.467513e-04 1.397896e-03 1.435793e-03 8.655248e-04 1.463409e-03
# 529 530 531 532 533 534
# 6.054252e-05 9.539230e-06 8.271521e-06 7.213105e-04 1.501862e-03 1.734793e-04
# 535 536 537 538 539 540
# 1.395680e-04 2.389608e-05 3.541492e-04 6.581780e-04 5.663764e-03 1.314865e-05
# 541 542 543 544 545 546
# 3.391677e-03 2.006795e-04 4.608500e-05 8.994636e-05 2.264099e-03 6.989653e-04
# 547 548 549 550 551 552
# 2.041812e-03 3.282826e-05 2.607819e-03 1.127666e-04 6.635391e-05 1.396609e-06
# 553 554 555 556 557 558
# 7.882728e-04 2.062552e-05 8.759916e-04 4.060994e-04 3.169261e-04 2.172569e-02
# 559 560 561 562 563 564
# 4.727893e-04 8.468366e-07 1.720969e-05 1.934250e-03 2.335144e-03 1.647439e-03
# 565 566 567 568 569 570
# 2.502536e-04 6.653024e-04 2.663844e-04 8.400234e-05 6.262081e-05 6.106452e-05
# 571 572 573 574 575 576
# 6.271639e-03 8.441752e-05 2.287273e-08 3.125011e-03 4.863026e-06 2.928999e-04
# 577 578 579 580 581 582
# 2.540225e-04 2.979886e-04 1.333432e-03 5.272996e-06 8.759020e-05 1.293530e-04
# 583 584 585 586 587 588
# 7.342273e-06 3.509985e-03 2.019662e-03 8.410665e-04 2.498742e-04 3.103613e-08
# 589 590 591 592 593 594
# 4.820507e-04 1.452900e-03 3.470369e-05 1.002250e-04 1.143857e-04 4.096423e-04
# 595 596 597 598 599 600
# 1.189062e-03 3.913174e-05 4.652351e-04 1.322955e-03 5.610553e-05 2.936843e-05
# 601 602 603 604 605 606
# 1.015027e-02 8.058720e-04 4.205245e-05 8.513408e-03 3.572264e-03 3.343216e-04
# 607 608 609 610 611 612
# 1.768871e-05 2.085399e-04 4.677359e-08 5.287110e-05 1.743867e-05 9.013439e-05
# 613 614 615 616 617 618
# 2.064262e-04 8.242024e-06 6.489838e-06 8.013945e-04 9.719191e-05 1.400797e-04
# 619 620 621 622 623 624
# 3.140498e-04 8.144097e-04 5.364940e-06 4.608256e-04 4.792040e-03 1.531676e-03
# 625 626 627 628 629 630
# 2.163090e-04 2.809024e-04 2.806910e-04 3.576925e-04 8.135362e-05 7.327558e-04
# 631 632 633 634 635 636
# 1.098637e-05 2.063031e-03 2.530280e-06 2.611493e-04 1.184755e-07 4.906597e-02
# 637 638 639 640 641 642
# 1.584843e-03 1.347520e-03 3.252513e-03 9.801511e-05 2.770572e-03 1.769412e-05
# 643 644 645 646 647 648
# 2.036713e-03 3.565046e-04 2.398026e-07 4.103639e-04 8.210783e-04 6.047580e-05
# 649 650 651 652 653 654
# 1.438482e-03 9.673131e-05 4.016773e-03 1.377735e-04 5.285564e-03 8.632848e-06
# 655 656 657 658 659 660
# 1.568621e-03 2.698125e-05 4.515412e-03 2.973097e-04 6.681463e-05 3.082506e-04
# 661 662 663 664 665 666
# 5.529114e-06 1.077364e-07 1.714489e-02 1.795071e-03 1.271018e-04 2.302518e-04
# 667 668 669 670 671 672
# 1.088180e-03 1.908814e-04 1.181343e-04 3.085384e-04 2.328757e-06 3.428290e-07
# 673 674 675 676 677 678
# 1.108826e-03 5.411973e-06 2.278891e-02 3.514741e-07 5.192652e-04 3.645797e-04
# 679 680 681 682 683 684
# 3.886925e-03 5.209815e-08 2.747551e-04 1.347936e-04 6.909379e-07 2.246006e-04
# 685 686 687 688 689 690
# 6.526249e-05 1.543942e-03 1.163792e-05 7.226645e-06 8.701434e-04 2.318997e-05
# 691 692 693 694 695 696
# 6.784884e-05 2.243106e-04 2.548919e-04 1.556602e-04 7.314943e-05 7.577799e-04
# 697 698 699 700 701 702
# 1.106356e-03 6.782817e-04 8.864887e-04 2.058625e-04 5.444202e-04 1.002087e-02
# 703 704 705 706 707 708
# 1.600480e-04 1.803078e-03 2.460335e-05 2.069061e-04 3.165046e-03 2.358445e-03
# 709 710 711 712 713 714
# 7.031996e-04 1.059012e-04 4.403328e-05 1.726870e-02 4.600677e-05 7.334050e-03
# 715 716 717 718 719 720
# 3.839671e-03 6.552220e-04 1.148730e-04 3.271510e-04 1.531447e-03 1.768982e-05
# 721 722 723 724 725 726
# 8.951990e-06 1.100596e-03 6.252350e-04 3.780479e-04 4.012709e-04 7.788258e-07
# 727 728 729 730 731 732
# 7.799883e-04 1.027596e-05 1.981505e-03 1.292803e-04 3.795289e-05 1.038615e-04
# 733 734 735 736 737 738
# 1.147388e-03 2.027998e-05 2.694623e-04 5.660228e-04 3.577965e-04 1.004580e-04
# 739 740 741 742 743 744
# 4.354559e-03 1.688785e-04 2.976606e-04 5.688377e-04 3.401688e-04 2.157617e-06
# 745 746 747 748 749 750
# 9.418815e-04 8.055503e-04 9.429964e-06 8.097102e-04 1.282625e-03 4.039396e-04
# 751 752 753 754 755 756
# 7.221887e-05 4.944557e-04 1.811121e-02 2.174841e-05 7.114780e-05 2.591806e-04
# 757 758 759 760 761 762
# 5.901567e-04 6.151635e-03 3.190628e-04 2.729119e-03 2.485600e-06 1.534935e-03
# 763 764 765 766 767 768
# 6.175267e-05 1.730799e-03 9.005416e-04 1.745883e-04 6.251554e-04 1.148522e-04
# 769 770 771 772 773 774
# 4.808785e-04 1.308032e-03 4.701841e-04 1.150277e-03 1.128134e-04 4.666687e-06
# 775 776 777 778 779 780
# 2.488478e-03 6.896079e-05 9.256739e-05 1.269279e-03 2.105541e-06 2.498533e-04
# 781 782 783 784 785 786
# 8.468366e-07 3.504641e-05 1.323630e-06 4.530716e-04 1.293002e-05 4.223379e-07
# 787 788 789 790 791 792
# 4.773331e-04 6.832607e-04 1.798748e-04 4.348118e-03 1.458296e-04 7.183720e-03
# 793 794 795 796 797 798
# 1.564156e-04 2.144356e-03 1.704494e-06 2.024022e-04 4.799621e-04 2.244956e-04
# 799 800 801 802 803 804
# 1.545022e-04 1.539064e-03 1.178145e-03 2.258859e-04 8.577806e-04 6.252462e-05
# 805 806 807 808 809 810
# 8.684960e-05 1.954506e-03 6.867399e-03 1.447474e-03 7.233463e-06 2.838495e-05
# 811 812 813 814 815 816
# 3.450252e-04 8.049103e-04 2.048382e-04 1.574569e-04 1.611919e-03 5.668589e-04
# 817 818 819 820 821 822
# 5.175394e-04 4.537397e-04 2.873279e-04 1.831688e-05 2.888562e-06 1.624922e-04
# 823 824 825 826 827 828
# 1.175545e-03 6.731792e-06 6.584022e-05 5.571627e-04 2.312258e-03 1.808312e-04
# 829 830 831 832 833 834
# 1.661190e-03 3.361467e-04 1.178129e-03 1.216249e-03 2.413154e-04 4.678317e-04
# 835 836 837 838 839 840
# 2.927428e-04 1.357345e-03 1.565820e-04 2.538871e-06 7.224042e-04 4.787038e-04
# 841 842 843 844 845 846
# 4.584536e-04 2.761186e-03 1.103406e-03 2.896864e-05 1.007796e-04 1.539240e-04
# 847 848 849 850 851 852
# 1.295321e-03 3.550946e-05 1.504903e-05 5.147707e-03 1.425211e-03 2.978816e-04
# 853 854 855 856 857 858
# 9.658880e-06 5.237535e-04 2.112962e-05 6.986277e-04 5.488686e-04 3.094403e-04
# 859 860 861 862 863 864
# 4.015529e-07 1.856976e-06 4.660315e-04 8.403742e-04 2.163241e-03 1.008769e-04
# 865 866 867 868 869 870
# 5.638730e-05 3.525929e-04 2.006359e-06 2.337344e-03 2.978989e-04 3.970738e-02
# 871 872 873 874 875 876
# 1.079820e-04 2.335804e-04 3.854268e-04 1.365224e-04 7.325721e-04 1.462793e-05
# 877 878 879 880 881 882
# 3.534996e-04 3.498689e-06 1.858280e-03 1.544534e-05 2.396300e-04 1.656366e-04
# 883 884 885 886 887 888
# 2.156032e-03 1.388267e-04 1.975113e-04 5.737835e-06 5.405373e-05 5.326550e-03
# 889 890 891 892 893 894
# 1.176008e-04 1.242068e-04 5.745081e-04 1.386001e-04 6.947351e-05 4.630405e-04
# 895 896 897 898 899 900
# 1.670376e-04 7.488923e-05 6.111467e-03 1.357382e-03 3.857840e-04 7.251249e-03
# 901 902 903 904 905 906
# 2.409060e-06 5.256316e-04 9.719191e-05 6.205035e-08 4.527863e-08 3.255239e-03
# 907 908 909 910 911 912
# 2.201119e-03 7.471355e-03 5.891925e-05 8.942198e-04 1.233727e-03 1.294729e-03
# 913 914 915 916 917 918
# 1.230718e-03 2.170011e-04 2.653200e-03 1.499562e-03 1.882859e-03 1.027551e-04
# 919 920 921 922 923 924
# 2.097703e-03 2.762033e-02 2.888581e-03 6.460248e-03 2.159218e-04 1.710444e-05
# 925 926 927 928 929 930
# 1.105967e-03 1.489553e-04 2.621228e-03 5.913036e-04 6.063600e-05 5.970866e-04
# 931 932 933 934 935 936
# 8.895451e-06 3.343695e-04 1.172793e-03 7.047283e-06 3.605056e-02 2.675004e-02
# 937 938 939 940 941 942
# 1.850290e-03 1.581126e-03 1.776866e-04 2.001583e-03 4.560962e-04 6.846274e-04
# 943 944 945 946 947 948
# 1.796572e-04 5.243167e-03 8.985467e-04 3.359145e-04 2.936231e-04 5.159867e-04
# 949 950 951 952 953 954
# 2.033926e-03 7.428518e-06 7.076266e-06 3.545068e-04 2.886557e-04 7.967128e-04
# 955 956 957 958 959 960
# 2.784865e-03 7.501866e-04 3.034125e-04 2.429106e-04 2.072199e-06 1.080548e-03
# 961 962 963 964 965 966
# 3.442114e-05 8.862949e-05 1.285736e-04 2.116088e-03 6.813540e-04 1.924525e-03
# 967 968 969 970 971 972
# 1.361347e-04 7.131638e-05 1.208481e-03 7.242327e-03 2.554560e-04 2.729120e-03
# 973 974 975 976 977 978
# 7.439769e-04 4.683381e-04 1.700287e-03 3.237171e-03 2.456969e-03 4.734591e-05
# 979 980 981 982 983 984
# 8.290908e-04 3.969786e-03 1.567362e-03 1.111097e-03 1.818735e-04 4.633508e-04
# 985 986 987 988 989 990
# 3.908670e-04 5.306012e-05 5.421865e-04 8.648190e-04 2.279865e-04 1.221198e-05
# 991 992 993 994 995 996
# 9.360577e-05 2.680374e-04 1.473071e-03 1.046325e-03 6.445468e-07 3.948441e-05
# 997 998 999 1000
# 5.766960e-06 1.744932e-04 8.057529e-04 1.604166e-02
#
# $influence$influential
# 3 17 70 90 151 167 214 243 275 308 331 362 372 376 380 397
# 3 17 70 90 151 167 214 243 275 308 331 362 372 376 380 397
# 399 400 448 449 462 486 508 509 512 539 558 571 601 604 623 636
# 399 400 448 449 462 486 508 509 512 539 558 571 601 604 623 636
# 651 653 657 663 675 702 712 714 739 753 758 790 792 807 850 870
# 651 653 657 663 675 702 712 714 739 753 758 790 792 807 850 870
# 888 897 900 908 920 922 935 936 944 970 1000
# 888 897 900 908 920 922 935 936 944 970 1000
#
# $influence$cutoff
# [1] 0.004012036
fitWLS(quakes_model)
#
# Call:
# lm(formula = stations ~ mag + depth, data = quakes)
#
# Coefficients:
# (Intercept) mag depth
# -1.540e+02 3.980e+01 9.189e-03
Theophylline dosing example
The Theoph dataset from base R contains blood
concentration measures after a single dose. Diagnostics reveal
heteroscedasticity and let us visualise the residual spread.
data(Theoph, package = "datasets")
dose_model <- lm(conc ~ Time, data = Theoph)
performWhiteTest(dose_model, Theoph)
# [INFO] Running White test
# [INFO] White test completed: statistic = 40.4104 df = 2 p = 0
#
# White's test for heteroscedasticity
#
# data: dose_model
# X-squared = 40.41, df = 2, p-value = 1.679e-09
# alternative hypothesis: heteroscedasticity present
plot(HeteroDiagnostic(dose_model, Theoph))
# $residuals_fitted
# `geom_smooth()` using formula = 'y ~ x'
#
# $spread_level
# `geom_smooth()` using formula = 'y ~ x'
#
# $density
#
# $qq
#
# $bubble_variance
Step-by-step workflow
This short example shows how to detect heteroscedasticity, choose a
remedy and re-test the model.
hd <- HeteroDiagnostic(stations ~ mag + depth, quakes)
test(hd)
# $white
#
# White's test for heteroscedasticity
#
# data: model
# X-squared = 125.56, df = 5, p-value < 2.2e-16
# alternative hypothesis: heteroscedasticity present
#
#
# $breusch_pagan
#
# Breusch-Pagan test for heteroscedasticity
#
# data: stations ~ mag + depth
# X-squared = 191.93, df = 2, p-value < 2.2e-16
#
#
# $vif
# mag depth
# 1.056182 1.056182
#
# $reset
#
# RESET test for nonlinearity
#
# data: stations ~ mag + depth
# F = 130.76, df1 = 2, df2 = 995, p-value < 2.2e-16
#
#
# $influence
# $influence$cooks_distance
# 1 2 3 4 5 6
# 1.454504e-04 8.010212e-05 8.607284e-03 4.476282e-04 1.083646e-04 1.101297e-03
# 7 8 9 10 11 12
# 9.346367e-05 1.896963e-04 2.711637e-06 8.889251e-05 1.290241e-03 7.175734e-04
# 13 14 15 16 17 18
# 3.149500e-04 2.130391e-03 2.575807e-03 2.204550e-04 6.057777e-03 7.650046e-04
# 19 20 21 22 23 24
# 1.190645e-03 5.675233e-04 1.346824e-03 1.460858e-08 2.996695e-04 7.652187e-04
# 25 26 27 28 29 30
# 3.698536e-03 7.253494e-04 6.479370e-04 2.918215e-03 2.676040e-04 1.288935e-04
# 31 32 33 34 35 36
# 1.322797e-03 9.548130e-05 1.742009e-07 3.095089e-04 1.540495e-03 6.444379e-04
# 37 38 39 40 41 42
# 3.260122e-04 2.439560e-03 2.378747e-04 4.890376e-04 1.933416e-05 3.213154e-05
# 43 44 45 46 47 48
# 3.286688e-05 9.828450e-04 6.219085e-05 6.215958e-04 4.397684e-05 2.226081e-05
# 49 50 51 52 53 54
# 1.627580e-06 2.684053e-03 9.471056e-05 1.672773e-03 6.134508e-05 6.147939e-04
# 55 56 57 58 59 60
# 9.598194e-07 1.531032e-04 5.821807e-04 1.577887e-04 4.602208e-05 5.081784e-04
# 61 62 63 64 65 66
# 2.555869e-04 1.404548e-04 3.687735e-04 3.866285e-05 1.120433e-03 3.959218e-04
# 67 68 69 70 71 72
# 7.711234e-06 1.525450e-03 6.805645e-05 6.242748e-03 1.107397e-03 5.611105e-05
# 73 74 75 76 77 78
# 1.265586e-05 1.599208e-03 5.009306e-04 2.932025e-04 1.477644e-04 5.132385e-05
# 79 80 81 82 83 84
# 1.406470e-05 3.708912e-04 4.770958e-04 5.773726e-06 2.887050e-05 3.410668e-05
# 85 86 87 88 89 90
# 2.795555e-04 9.271635e-06 3.468520e-05 1.217204e-04 2.481608e-04 6.814963e-03
# 91 92 93 94 95 96
# 3.669910e-04 6.172743e-04 1.669868e-06 9.655687e-06 5.355154e-04 1.648327e-03
# 97 98 99 100 101 102
# 1.628626e-04 4.319054e-04 5.695834e-04 2.039865e-04 4.447047e-04 8.648204e-04
# 103 104 105 106 107 108
# 1.060195e-03 8.762672e-04 5.391740e-04 2.282779e-05 2.876198e-04 3.213382e-04
# 109 110 111 112 113 114
# 7.318723e-04 1.233571e-03 1.777470e-06 4.652695e-07 9.803300e-04 4.875947e-04
# 115 116 117 118 119 120
# 2.593973e-04 5.672999e-04 2.534789e-04 2.487786e-03 5.464304e-04 2.000237e-06
# 121 122 123 124 125 126
# 7.066360e-04 1.439374e-04 1.686707e-03 4.291146e-04 8.996980e-05 8.922963e-04
# 127 128 129 130 131 132
# 1.774334e-04 2.216767e-03 2.182832e-03 4.403744e-06 6.631434e-05 4.506828e-04
# 133 134 135 136 137 138
# 8.167050e-05 1.288742e-04 6.006885e-04 3.127797e-03 2.116238e-03 1.004081e-03
# 139 140 141 142 143 144
# 9.299250e-04 1.804579e-04 3.572856e-04 5.178035e-04 1.004533e-04 7.195587e-04
# 145 146 147 148 149 150
# 3.116365e-04 1.990741e-05 2.728980e-05 1.294776e-05 3.390635e-04 1.573656e-03
# 151 152 153 154 155 156
# 1.360986e-02 1.896685e-03 2.604840e-04 8.298848e-04 1.575989e-03 3.239846e-05
# 157 158 159 160 161 162
# 1.678554e-04 4.248443e-06 1.011350e-03 5.040741e-07 4.476282e-04 6.733230e-04
# 163 164 165 166 167 168
# 3.444458e-06 6.973463e-05 8.824090e-05 9.927529e-04 6.812188e-03 6.498815e-04
# 169 170 171 172 173 174
# 2.270698e-06 3.125087e-07 2.438938e-05 1.719060e-04 2.999155e-05 8.219002e-04
# 175 176 177 178 179 180
# 9.285053e-07 8.359222e-04 2.152513e-04 6.901722e-05 6.377049e-04 9.174977e-05
# 181 182 183 184 185 186
# 2.020731e-03 9.618092e-04 8.136624e-05 4.393195e-06 5.803189e-05 2.541396e-03
# 187 188 189 190 191 192
# 2.221635e-04 1.295871e-04 6.758772e-04 2.713664e-05 3.786639e-04 3.596338e-06
# 193 194 195 196 197 198
# 3.789532e-03 7.784533e-04 1.713832e-04 3.015250e-04 5.545890e-05 6.063209e-04
# 199 200 201 202 203 204
# 6.453820e-04 1.324058e-03 8.072757e-05 3.973659e-04 2.675495e-05 4.011410e-04
# 205 206 207 208 209 210
# 1.407020e-03 9.454527e-05 1.548665e-05 1.302680e-03 9.641889e-05 1.993678e-04
# 211 212 213 214 215 216
# 4.196361e-05 1.288936e-04 1.158573e-03 4.022601e-03 6.262349e-06 1.971215e-06
# 217 218 219 220 221 222
# 2.178179e-04 1.705779e-04 2.017235e-04 5.743189e-07 1.027551e-04 3.806313e-04
# 223 224 225 226 227 228
# 1.321782e-04 3.275625e-04 8.601217e-05 4.586044e-04 2.643659e-04 6.050473e-05
# 229 230 231 232 233 234
# 1.012548e-04 2.298672e-04 6.736951e-04 1.040411e-04 2.849544e-04 1.077104e-03
# 235 236 237 238 239 240
# 1.275991e-03 2.631424e-04 5.638491e-07 6.907381e-04 3.080151e-04 5.050617e-05
# 241 242 243 244 245 246
# 9.059249e-05 9.687826e-04 2.673171e-02 8.418424e-04 1.375358e-05 5.113758e-04
# 247 248 249 250 251 252
# 1.322236e-04 1.679069e-03 1.128422e-03 6.064643e-06 3.326078e-04 8.474387e-06
# 253 254 255 256 257 258
# 2.276769e-03 2.148537e-04 2.253596e-05 1.761104e-04 7.382196e-06 6.357909e-06
# 259 260 261 262 263 264
# 3.457661e-04 3.432381e-04 1.699472e-03 4.533231e-04 6.434685e-04 4.594787e-06
# 265 266 267 268 269 270
# 4.831830e-05 2.899479e-04 9.381715e-04 2.560821e-04 2.355808e-05 5.659708e-04
# 271 272 273 274 275 276
# 1.802743e-04 2.397531e-03 8.998723e-06 1.582943e-04 7.625471e-03 5.861506e-04
# 277 278 279 280 281 282
# 1.924824e-04 1.107913e-04 8.970116e-04 1.167657e-03 1.846352e-05 1.730819e-04
# 283 284 285 286 287 288
# 7.920044e-04 2.609575e-04 5.391706e-06 6.975056e-04 4.653230e-05 7.404759e-06
# 289 290 291 292 293 294
# 1.710657e-04 1.873463e-04 6.666394e-04 2.698283e-03 1.229054e-04 1.750572e-09
# 295 296 297 298 299 300
# 3.170299e-04 3.544604e-05 3.660165e-04 8.561011e-04 2.362550e-03 2.197877e-04
# 301 302 303 304 305 306
# 2.770440e-04 4.111539e-06 1.070166e-04 2.662680e-03 1.738459e-05 5.963423e-04
# 307 308 309 310 311 312
# 5.132561e-04 8.988712e-03 5.424953e-06 1.050619e-03 3.464273e-03 2.215072e-04
# 313 314 315 316 317 318
# 1.448382e-03 3.059074e-04 3.246473e-04 5.743752e-04 3.454396e-05 1.431169e-03
# 319 320 321 322 323 324
# 1.163457e-04 1.813361e-03 6.527792e-04 6.963019e-04 7.674768e-05 2.572294e-04
# 325 326 327 328 329 330
# 8.315699e-04 6.089535e-04 1.991033e-04 5.185259e-04 1.115880e-03 7.399841e-04
# 331 332 333 334 335 336
# 5.165306e-03 2.132156e-03 6.131062e-04 2.603176e-03 2.506294e-05 7.819124e-04
# 337 338 339 340 341 342
# 1.698762e-05 2.571719e-06 5.144821e-04 1.916724e-03 1.747126e-04 3.974441e-03
# 343 344 345 346 347 348
# 9.515094e-04 7.608203e-05 7.073745e-06 1.522752e-04 2.172272e-03 1.081543e-03
# 349 350 351 352 353 354
# 2.891747e-03 2.466954e-03 1.346290e-03 1.870995e-03 2.457227e-04 2.980428e-04
# 355 356 357 358 359 360
# 1.046704e-03 4.461092e-04 1.981092e-04 4.960450e-04 4.381174e-04 1.149823e-03
# 361 362 363 364 365 366
# 7.627428e-05 5.547037e-03 1.147347e-03 4.532987e-07 1.390313e-04 3.430484e-04
# 367 368 369 370 371 372
# 1.230063e-03 7.095661e-04 2.278052e-04 1.848886e-03 1.168403e-03 1.610536e-02
# 373 374 375 376 377 378
# 3.100138e-05 6.661052e-04 4.271869e-06 3.983228e-02 9.135738e-04 8.049329e-05
# 379 380 381 382 383 384
# 1.783047e-06 7.596862e-03 1.181469e-03 7.748307e-05 3.657023e-03 7.482897e-06
# 385 386 387 388 389 390
# 1.799792e-03 3.984432e-04 6.173186e-05 3.370196e-04 1.594575e-03 3.862815e-04
# 391 392 393 394 395 396
# 2.650254e-04 9.117874e-04 1.647818e-04 2.591620e-06 3.034451e-04 1.155703e-04
# 397 398 399 400 401 402
# 6.754566e-03 2.593063e-03 1.732800e-02 1.080629e-02 6.488127e-04 2.036229e-04
# 403 404 405 406 407 408
# 6.494197e-05 1.556864e-03 6.067727e-04 2.664229e-04 3.644854e-05 2.155424e-04
# 409 410 411 412 413 414
# 4.480440e-06 8.012708e-04 5.701054e-04 1.714623e-03 2.003942e-05 1.523301e-04
# 415 416 417 418 419 420
# 1.848538e-04 1.094555e-04 7.906993e-05 1.526538e-03 1.696066e-04 2.598171e-03
# 421 422 423 424 425 426
# 2.421435e-04 8.371938e-05 3.606731e-03 4.834455e-05 6.600910e-04 2.714689e-05
# 427 428 429 430 431 432
# 7.181677e-05 2.352459e-03 1.858691e-04 3.368187e-04 8.712020e-06 1.960936e-03
# 433 434 435 436 437 438
# 1.094602e-03 1.003610e-03 5.697673e-05 9.225951e-06 5.285353e-06 1.684751e-03
# 439 440 441 442 443 444
# 5.976188e-06 1.232448e-04 2.250342e-05 1.562610e-04 2.091322e-04 2.430178e-03
# 445 446 447 448 449 450
# 1.771010e-03 1.294777e-03 1.948488e-04 1.058032e-02 1.466783e-02 9.123870e-05
# 451 452 453 454 455 456
# 1.767965e-04 1.952028e-08 7.831851e-04 4.303933e-06 9.991133e-05 4.739780e-04
# 457 458 459 460 461 462
# 5.532880e-04 5.808676e-04 3.387232e-03 4.607543e-05 6.113513e-04 2.642472e-02
# 463 464 465 466 467 468
# 7.763971e-04 1.280139e-03 1.119801e-04 5.261916e-04 1.304009e-06 9.110953e-04
# 469 470 471 472 473 474
# 1.206394e-04 5.181372e-05 9.163320e-05 4.070636e-04 8.691006e-05 5.259315e-04
# 475 476 477 478 479 480
# 2.079891e-04 5.040618e-05 9.032160e-05 2.495771e-04 1.199250e-03 3.439535e-04
# 481 482 483 484 485 486
# 1.515597e-03 2.303425e-05 1.431066e-03 1.351893e-04 6.491783e-06 4.093342e-03
# 487 488 489 490 491 492
# 1.781758e-03 1.855779e-06 5.769551e-04 2.559844e-03 3.830718e-04 4.104833e-04
# 493 494 495 496 497 498
# 6.293088e-05 4.330607e-04 5.075353e-04 2.312563e-05 2.142592e-06 2.325249e-03
# 499 500 501 502 503 504
# 3.507072e-04 8.735888e-05 4.160862e-05 6.759620e-04 2.326792e-04 7.488486e-05
# 505 506 507 508 509 510
# 3.311136e-04 3.724447e-05 2.229418e-04 8.787383e-03 5.077269e-03 8.041707e-06
# 511 512 513 514 515 516
# 2.750208e-11 6.618443e-03 9.950213e-05 7.020521e-05 3.082069e-05 2.229626e-04
# 517 518 519 520 521 522
# 4.093466e-04 5.848930e-04 1.916268e-06 9.987753e-05 9.496668e-04 9.703981e-04
# 523 524 525 526 527 528
# 9.950213e-05 4.467513e-04 1.397896e-03 1.435793e-03 8.655248e-04 1.463409e-03
# 529 530 531 532 533 534
# 6.054252e-05 9.539230e-06 8.271521e-06 7.213105e-04 1.501862e-03 1.734793e-04
# 535 536 537 538 539 540
# 1.395680e-04 2.389608e-05 3.541492e-04 6.581780e-04 5.663764e-03 1.314865e-05
# 541 542 543 544 545 546
# 3.391677e-03 2.006795e-04 4.608500e-05 8.994636e-05 2.264099e-03 6.989653e-04
# 547 548 549 550 551 552
# 2.041812e-03 3.282826e-05 2.607819e-03 1.127666e-04 6.635391e-05 1.396609e-06
# 553 554 555 556 557 558
# 7.882728e-04 2.062552e-05 8.759916e-04 4.060994e-04 3.169261e-04 2.172569e-02
# 559 560 561 562 563 564
# 4.727893e-04 8.468366e-07 1.720969e-05 1.934250e-03 2.335144e-03 1.647439e-03
# 565 566 567 568 569 570
# 2.502536e-04 6.653024e-04 2.663844e-04 8.400234e-05 6.262081e-05 6.106452e-05
# 571 572 573 574 575 576
# 6.271639e-03 8.441752e-05 2.287273e-08 3.125011e-03 4.863026e-06 2.928999e-04
# 577 578 579 580 581 582
# 2.540225e-04 2.979886e-04 1.333432e-03 5.272996e-06 8.759020e-05 1.293530e-04
# 583 584 585 586 587 588
# 7.342273e-06 3.509985e-03 2.019662e-03 8.410665e-04 2.498742e-04 3.103613e-08
# 589 590 591 592 593 594
# 4.820507e-04 1.452900e-03 3.470369e-05 1.002250e-04 1.143857e-04 4.096423e-04
# 595 596 597 598 599 600
# 1.189062e-03 3.913174e-05 4.652351e-04 1.322955e-03 5.610553e-05 2.936843e-05
# 601 602 603 604 605 606
# 1.015027e-02 8.058720e-04 4.205245e-05 8.513408e-03 3.572264e-03 3.343216e-04
# 607 608 609 610 611 612
# 1.768871e-05 2.085399e-04 4.677359e-08 5.287110e-05 1.743867e-05 9.013439e-05
# 613 614 615 616 617 618
# 2.064262e-04 8.242024e-06 6.489838e-06 8.013945e-04 9.719191e-05 1.400797e-04
# 619 620 621 622 623 624
# 3.140498e-04 8.144097e-04 5.364940e-06 4.608256e-04 4.792040e-03 1.531676e-03
# 625 626 627 628 629 630
# 2.163090e-04 2.809024e-04 2.806910e-04 3.576925e-04 8.135362e-05 7.327558e-04
# 631 632 633 634 635 636
# 1.098637e-05 2.063031e-03 2.530280e-06 2.611493e-04 1.184755e-07 4.906597e-02
# 637 638 639 640 641 642
# 1.584843e-03 1.347520e-03 3.252513e-03 9.801511e-05 2.770572e-03 1.769412e-05
# 643 644 645 646 647 648
# 2.036713e-03 3.565046e-04 2.398026e-07 4.103639e-04 8.210783e-04 6.047580e-05
# 649 650 651 652 653 654
# 1.438482e-03 9.673131e-05 4.016773e-03 1.377735e-04 5.285564e-03 8.632848e-06
# 655 656 657 658 659 660
# 1.568621e-03 2.698125e-05 4.515412e-03 2.973097e-04 6.681463e-05 3.082506e-04
# 661 662 663 664 665 666
# 5.529114e-06 1.077364e-07 1.714489e-02 1.795071e-03 1.271018e-04 2.302518e-04
# 667 668 669 670 671 672
# 1.088180e-03 1.908814e-04 1.181343e-04 3.085384e-04 2.328757e-06 3.428290e-07
# 673 674 675 676 677 678
# 1.108826e-03 5.411973e-06 2.278891e-02 3.514741e-07 5.192652e-04 3.645797e-04
# 679 680 681 682 683 684
# 3.886925e-03 5.209815e-08 2.747551e-04 1.347936e-04 6.909379e-07 2.246006e-04
# 685 686 687 688 689 690
# 6.526249e-05 1.543942e-03 1.163792e-05 7.226645e-06 8.701434e-04 2.318997e-05
# 691 692 693 694 695 696
# 6.784884e-05 2.243106e-04 2.548919e-04 1.556602e-04 7.314943e-05 7.577799e-04
# 697 698 699 700 701 702
# 1.106356e-03 6.782817e-04 8.864887e-04 2.058625e-04 5.444202e-04 1.002087e-02
# 703 704 705 706 707 708
# 1.600480e-04 1.803078e-03 2.460335e-05 2.069061e-04 3.165046e-03 2.358445e-03
# 709 710 711 712 713 714
# 7.031996e-04 1.059012e-04 4.403328e-05 1.726870e-02 4.600677e-05 7.334050e-03
# 715 716 717 718 719 720
# 3.839671e-03 6.552220e-04 1.148730e-04 3.271510e-04 1.531447e-03 1.768982e-05
# 721 722 723 724 725 726
# 8.951990e-06 1.100596e-03 6.252350e-04 3.780479e-04 4.012709e-04 7.788258e-07
# 727 728 729 730 731 732
# 7.799883e-04 1.027596e-05 1.981505e-03 1.292803e-04 3.795289e-05 1.038615e-04
# 733 734 735 736 737 738
# 1.147388e-03 2.027998e-05 2.694623e-04 5.660228e-04 3.577965e-04 1.004580e-04
# 739 740 741 742 743 744
# 4.354559e-03 1.688785e-04 2.976606e-04 5.688377e-04 3.401688e-04 2.157617e-06
# 745 746 747 748 749 750
# 9.418815e-04 8.055503e-04 9.429964e-06 8.097102e-04 1.282625e-03 4.039396e-04
# 751 752 753 754 755 756
# 7.221887e-05 4.944557e-04 1.811121e-02 2.174841e-05 7.114780e-05 2.591806e-04
# 757 758 759 760 761 762
# 5.901567e-04 6.151635e-03 3.190628e-04 2.729119e-03 2.485600e-06 1.534935e-03
# 763 764 765 766 767 768
# 6.175267e-05 1.730799e-03 9.005416e-04 1.745883e-04 6.251554e-04 1.148522e-04
# 769 770 771 772 773 774
# 4.808785e-04 1.308032e-03 4.701841e-04 1.150277e-03 1.128134e-04 4.666687e-06
# 775 776 777 778 779 780
# 2.488478e-03 6.896079e-05 9.256739e-05 1.269279e-03 2.105541e-06 2.498533e-04
# 781 782 783 784 785 786
# 8.468366e-07 3.504641e-05 1.323630e-06 4.530716e-04 1.293002e-05 4.223379e-07
# 787 788 789 790 791 792
# 4.773331e-04 6.832607e-04 1.798748e-04 4.348118e-03 1.458296e-04 7.183720e-03
# 793 794 795 796 797 798
# 1.564156e-04 2.144356e-03 1.704494e-06 2.024022e-04 4.799621e-04 2.244956e-04
# 799 800 801 802 803 804
# 1.545022e-04 1.539064e-03 1.178145e-03 2.258859e-04 8.577806e-04 6.252462e-05
# 805 806 807 808 809 810
# 8.684960e-05 1.954506e-03 6.867399e-03 1.447474e-03 7.233463e-06 2.838495e-05
# 811 812 813 814 815 816
# 3.450252e-04 8.049103e-04 2.048382e-04 1.574569e-04 1.611919e-03 5.668589e-04
# 817 818 819 820 821 822
# 5.175394e-04 4.537397e-04 2.873279e-04 1.831688e-05 2.888562e-06 1.624922e-04
# 823 824 825 826 827 828
# 1.175545e-03 6.731792e-06 6.584022e-05 5.571627e-04 2.312258e-03 1.808312e-04
# 829 830 831 832 833 834
# 1.661190e-03 3.361467e-04 1.178129e-03 1.216249e-03 2.413154e-04 4.678317e-04
# 835 836 837 838 839 840
# 2.927428e-04 1.357345e-03 1.565820e-04 2.538871e-06 7.224042e-04 4.787038e-04
# 841 842 843 844 845 846
# 4.584536e-04 2.761186e-03 1.103406e-03 2.896864e-05 1.007796e-04 1.539240e-04
# 847 848 849 850 851 852
# 1.295321e-03 3.550946e-05 1.504903e-05 5.147707e-03 1.425211e-03 2.978816e-04
# 853 854 855 856 857 858
# 9.658880e-06 5.237535e-04 2.112962e-05 6.986277e-04 5.488686e-04 3.094403e-04
# 859 860 861 862 863 864
# 4.015529e-07 1.856976e-06 4.660315e-04 8.403742e-04 2.163241e-03 1.008769e-04
# 865 866 867 868 869 870
# 5.638730e-05 3.525929e-04 2.006359e-06 2.337344e-03 2.978989e-04 3.970738e-02
# 871 872 873 874 875 876
# 1.079820e-04 2.335804e-04 3.854268e-04 1.365224e-04 7.325721e-04 1.462793e-05
# 877 878 879 880 881 882
# 3.534996e-04 3.498689e-06 1.858280e-03 1.544534e-05 2.396300e-04 1.656366e-04
# 883 884 885 886 887 888
# 2.156032e-03 1.388267e-04 1.975113e-04 5.737835e-06 5.405373e-05 5.326550e-03
# 889 890 891 892 893 894
# 1.176008e-04 1.242068e-04 5.745081e-04 1.386001e-04 6.947351e-05 4.630405e-04
# 895 896 897 898 899 900
# 1.670376e-04 7.488923e-05 6.111467e-03 1.357382e-03 3.857840e-04 7.251249e-03
# 901 902 903 904 905 906
# 2.409060e-06 5.256316e-04 9.719191e-05 6.205035e-08 4.527863e-08 3.255239e-03
# 907 908 909 910 911 912
# 2.201119e-03 7.471355e-03 5.891925e-05 8.942198e-04 1.233727e-03 1.294729e-03
# 913 914 915 916 917 918
# 1.230718e-03 2.170011e-04 2.653200e-03 1.499562e-03 1.882859e-03 1.027551e-04
# 919 920 921 922 923 924
# 2.097703e-03 2.762033e-02 2.888581e-03 6.460248e-03 2.159218e-04 1.710444e-05
# 925 926 927 928 929 930
# 1.105967e-03 1.489553e-04 2.621228e-03 5.913036e-04 6.063600e-05 5.970866e-04
# 931 932 933 934 935 936
# 8.895451e-06 3.343695e-04 1.172793e-03 7.047283e-06 3.605056e-02 2.675004e-02
# 937 938 939 940 941 942
# 1.850290e-03 1.581126e-03 1.776866e-04 2.001583e-03 4.560962e-04 6.846274e-04
# 943 944 945 946 947 948
# 1.796572e-04 5.243167e-03 8.985467e-04 3.359145e-04 2.936231e-04 5.159867e-04
# 949 950 951 952 953 954
# 2.033926e-03 7.428518e-06 7.076266e-06 3.545068e-04 2.886557e-04 7.967128e-04
# 955 956 957 958 959 960
# 2.784865e-03 7.501866e-04 3.034125e-04 2.429106e-04 2.072199e-06 1.080548e-03
# 961 962 963 964 965 966
# 3.442114e-05 8.862949e-05 1.285736e-04 2.116088e-03 6.813540e-04 1.924525e-03
# 967 968 969 970 971 972
# 1.361347e-04 7.131638e-05 1.208481e-03 7.242327e-03 2.554560e-04 2.729120e-03
# 973 974 975 976 977 978
# 7.439769e-04 4.683381e-04 1.700287e-03 3.237171e-03 2.456969e-03 4.734591e-05
# 979 980 981 982 983 984
# 8.290908e-04 3.969786e-03 1.567362e-03 1.111097e-03 1.818735e-04 4.633508e-04
# 985 986 987 988 989 990
# 3.908670e-04 5.306012e-05 5.421865e-04 8.648190e-04 2.279865e-04 1.221198e-05
# 991 992 993 994 995 996
# 9.360577e-05 2.680374e-04 1.473071e-03 1.046325e-03 6.445468e-07 3.948441e-05
# 997 998 999 1000
# 5.766960e-06 1.744932e-04 8.057529e-04 1.604166e-02
#
# $influence$influential
# 3 17 70 90 151 167 214 243 275 308 331 362 372 376 380 397
# 3 17 70 90 151 167 214 243 275 308 331 362 372 376 380 397
# 399 400 448 449 462 486 508 509 512 539 558 571 601 604 623 636
# 399 400 448 449 462 486 508 509 512 539 558 571 601 604 623 636
# 651 653 657 663 675 702 712 714 739 753 758 790 792 807 850 870
# 651 653 657 663 675 702 712 714 739 753 758 790 792 807 850 870
# 888 897 900 908 920 922 935 936 944 970 1000
# 888 897 900 908 920 922 935 936 944 970 1000
#
# $influence$cutoff
# [1] 0.004012036
wls_model <- fitWLS(hd$model)
# Re-test after remedy
test(HeteroDiagnostic(wls_model, quakes))
# [INFO] Running White test
# [INFO] White test completed: statistic = 249.2441 df = 5 p = 0
# [INFO] Running Breusch-Pagan test
# $white
#
# White's test for heteroscedasticity
#
# data: model
# X-squared = 249.24, df = 5, p-value < 2.2e-16
# alternative hypothesis: heteroscedasticity present
#
#
# $breusch_pagan
#
# Breusch-Pagan test for heteroscedasticity
#
# data: stations ~ mag + depth
# X-squared = 463.66, df = 2, p-value < 2.2e-16
#
#
# $vif
# mag depth
# 1.056182 1.056182
#
# $reset
#
# RESET test for nonlinearity
#
# data: stations ~ mag + depth
# F = 183.04, df1 = 2, df2 = 995, p-value < 2.2e-16
#
#
# $influence
# $influence$cooks_distance
# 1 2 3 4 5 6
# 1.180793e-05 5.444643e-04 1.291700e-03 6.871808e-04 1.810178e-06 1.334108e-03
# 7 8 9 10 11 12
# 1.498407e-04 4.949897e-04 3.976966e-11 3.068469e-04 2.400998e-03 9.587426e-04
# 13 14 15 16 17 18
# 5.908583e-04 3.993188e-03 2.917379e-05 6.824299e-04 1.043045e-05 1.041763e-03
# 19 20 21 22 23 24
# 2.204389e-03 1.060126e-03 1.917974e-03 1.772672e-04 5.601282e-04 7.968708e-04
# 25 26 27 28 29 30
# 2.968140e-04 1.163766e-03 8.579088e-04 2.769130e-03 3.272599e-04 2.732988e-04
# 31 32 33 34 35 36
# 1.488430e-03 8.580286e-05 2.085964e-05 1.057639e-04 2.636116e-03 1.729989e-03
# 37 38 39 40 41 42
# 5.483802e-04 2.864180e-03 2.144729e-04 1.024388e-03 8.421913e-06 2.893768e-05
# 43 44 45 46 47 48
# 7.212971e-05 1.157678e-03 7.695251e-05 3.070403e-04 7.040164e-05 1.936075e-04
# 49 50 51 52 53 54
# 5.058352e-06 2.294673e-03 5.861289e-04 3.007351e-03 1.045033e-04 1.650123e-03
# 55 56 57 58 59 60
# 4.586793e-05 2.636507e-04 8.227217e-04 1.036140e-05 9.486065e-05 1.331133e-03
# 61 62 63 64 65 66
# 1.071642e-04 5.063863e-06 9.502992e-04 3.376810e-05 3.664347e-04 4.367951e-04
# 67 68 69 70 71 72
# 8.960269e-05 3.051189e-04 7.419507e-05 2.345477e-03 1.141192e-03 5.227059e-05
# 73 74 75 76 77 78
# 2.905142e-04 1.847798e-03 8.565412e-04 8.364667e-04 2.707758e-09 9.263239e-05
# 79 80 81 82 83 84
# 1.789467e-05 3.172604e-07 5.626189e-04 9.302114e-06 1.263620e-04 2.014537e-04
# 85 86 87 88 89 90
# 1.177137e-04 1.821203e-04 2.499306e-05 1.434091e-04 7.305206e-05 1.173699e-02
# 91 92 93 94 95 96
# 5.180251e-04 7.003875e-04 2.515727e-04 4.228845e-05 5.921090e-04 3.609048e-03
# 97 98 99 100 101 102
# 2.378763e-04 1.392460e-05 9.356878e-05 1.238713e-04 1.384808e-04 8.842172e-04
# 103 104 105 106 107 108
# 7.713872e-04 8.812299e-04 4.470602e-04 1.074168e-05 1.878233e-04 4.378066e-04
# 109 110 111 112 113 114
# 2.217257e-05 5.728828e-04 4.690134e-07 1.019350e-04 1.809392e-03 1.381062e-04
# 115 116 117 118 119 120
# 4.815500e-04 1.042162e-03 3.868187e-04 2.547217e-03 7.796210e-04 9.813884e-05
# 121 122 123 124 125 126
# 5.294470e-04 9.037764e-04 1.383464e-03 5.623386e-04 2.020430e-04 1.966468e-04
# 127 128 129 130 131 132
# 1.761284e-04 2.909377e-03 2.378501e-03 7.846061e-06 1.376634e-04 6.886544e-04
# 133 134 135 136 137 138
# 2.240651e-04 9.899470e-05 1.641414e-03 3.184943e-03 1.668591e-03 1.336234e-03
# 139 140 141 142 143 144
# 5.869245e-04 6.756546e-05 8.738857e-04 6.551957e-04 4.435042e-06 9.151451e-04
# 145 146 147 148 149 150
# 4.812685e-04 4.754431e-04 1.390913e-09 1.617027e-06 1.766820e-05 3.911230e-03
# 151 152 153 154 155 156
# 3.101379e-03 4.966265e-04 2.394067e-04 8.775048e-04 1.714229e-03 2.051054e-06
# 157 158 159 160 161 162
# 1.279982e-06 5.072127e-05 5.909480e-04 4.220211e-09 6.871808e-04 3.886246e-04
# 163 164 165 166 167 168
# 4.043080e-06 5.568920e-05 3.924021e-05 3.619511e-04 2.476020e-03 7.886080e-04
# 169 170 171 172 173 174
# 6.675354e-05 4.236101e-07 2.159402e-05 3.131004e-04 6.477993e-04 6.516183e-04
# 175 176 177 178 179 180
# 1.931665e-04 7.049623e-04 1.513911e-10 1.368706e-04 1.064332e-03 1.037058e-04
# 181 182 183 184 185 186
# 3.790743e-03 1.057850e-03 2.870833e-04 3.521110e-05 2.324020e-07 2.348126e-03
# 187 188 189 190 191 192
# 6.829885e-04 4.902443e-04 7.262974e-04 2.871144e-05 5.827847e-04 4.704363e-08
# 193 194 195 196 197 198
# 4.620398e-03 1.509145e-03 3.073266e-04 4.790910e-04 7.185094e-05 1.008845e-03
# 199 200 201 202 203 204
# 1.096363e-03 1.797236e-03 5.293604e-05 3.106615e-04 8.495069e-06 4.914022e-04
# 205 206 207 208 209 210
# 1.974210e-03 4.068076e-04 4.246618e-04 1.867230e-03 7.339688e-05 9.755089e-04
# 211 212 213 214 215 216
# 1.246331e-04 4.291956e-04 1.776348e-03 2.052074e-03 4.214668e-08 3.215463e-05
# 217 218 219 220 221 222
# 9.103451e-05 4.569259e-04 2.095311e-04 7.309855e-05 9.092645e-05 4.614742e-04
# 223 224 225 226 227 228
# 2.163010e-04 3.723741e-04 1.034155e-04 5.587339e-04 1.613733e-04 1.395485e-04
# 229 230 231 232 233 234
# 2.648225e-04 4.118157e-05 3.471039e-04 8.662950e-05 5.237006e-04 6.000409e-04
# 235 236 237 238 239 240
# 1.826405e-03 1.251806e-04 4.352700e-05 1.359843e-03 2.958252e-04 7.455000e-07
# 241 242 243 244 245 246
# 1.125924e-04 1.097159e-03 7.115329e-03 1.008450e-03 1.069438e-04 4.575107e-04
# 247 248 249 250 251 252
# 2.048264e-04 1.685600e-03 6.522624e-06 1.463976e-04 3.434293e-04 8.354455e-10
# 253 254 255 256 257 258
# 4.215040e-04 7.763420e-05 1.198544e-04 2.434795e-04 1.715205e-05 6.004805e-07
# 259 260 261 262 263 264
# 4.780236e-04 5.735807e-05 1.843167e-03 2.964628e-04 1.466803e-03 6.086700e-06
# 265 266 267 268 269 270
# 1.009506e-07 1.129634e-04 1.234410e-03 8.051075e-04 7.469292e-05 7.385406e-04
# 271 272 273 274 275 276
# 5.896598e-04 1.135479e-03 8.529999e-05 8.130896e-04 2.993136e-03 6.115142e-04
# 277 278 279 280 281 282
# 5.817373e-04 3.598128e-04 1.253081e-03 3.701910e-05 5.079445e-05 8.967548e-04
# 283 284 285 286 287 288
# 1.045303e-03 6.747454e-05 3.876212e-05 5.602857e-04 3.858391e-04 1.766938e-05
# 289 290 291 292 293 294
# 1.986686e-04 1.412232e-07 3.412210e-05 2.225504e-03 7.961065e-05 1.098119e-05
# 295 296 297 298 299 300
# 4.907787e-04 1.840118e-06 1.739239e-04 1.614586e-03 4.707214e-03 2.847282e-04
# 301 302 303 304 305 306
# 4.981866e-04 2.205290e-06 9.474112e-05 3.191885e-03 8.811555e-05 4.878281e-04
# 307 308 309 310 311 312
# 7.474764e-04 5.899835e-03 3.595731e-05 7.947299e-04 4.599639e-03 4.058017e-05
# 313 314 315 316 317 318
# 1.409246e-03 4.222941e-04 5.297129e-04 1.032950e-03 1.540370e-05 1.437522e-04
# 319 320 321 322 323 324
# 1.477739e-04 1.413696e-03 5.120788e-04 8.380332e-04 1.468460e-04 7.285531e-04
# 325 326 327 328 329 330
# 9.205490e-04 1.669061e-03 9.507267e-04 6.949976e-04 1.462391e-03 2.973312e-05
# 331 332 333 334 335 336
# 9.907926e-04 3.104584e-03 1.697283e-03 1.545532e-03 1.129693e-04 1.423084e-03
# 337 338 339 340 341 342
# 7.644559e-07 1.590555e-04 1.000338e-03 1.924346e-03 1.803043e-06 3.408229e-03
# 343 344 345 346 347 348
# 1.702340e-03 6.671760e-04 2.848083e-04 8.767407e-04 2.787976e-03 1.881797e-03
# 349 350 351 352 353 354
# 1.375997e-03 3.153335e-03 1.753571e-03 1.139603e-03 2.249216e-04 2.369135e-05
# 355 356 357 358 359 360
# 1.053238e-03 1.585067e-05 7.972405e-06 7.708497e-04 6.000777e-04 1.223913e-03
# 361 362 363 364 365 366
# 5.176063e-04 1.486399e-02 3.260582e-06 2.983622e-05 3.624612e-04 4.841327e-04
# 367 368 369 370 371 372
# 1.971813e-04 1.247102e-03 2.229926e-04 3.136607e-03 1.554211e-04 6.865713e-03
# 373 374 375 376 377 378
# 3.446210e-04 5.072798e-06 3.702261e-05 7.192244e-03 1.683189e-03 2.180304e-04
# 379 380 381 382 383 384
# 1.470338e-06 2.948428e-03 1.282514e-03 5.465957e-05 2.038075e-03 1.944612e-05
# 385 386 387 388 389 390
# 2.489170e-04 6.163509e-04 4.498212e-04 4.886664e-04 2.612717e-03 1.656279e-04
# 391 392 393 394 395 396
# 1.497738e-04 6.715777e-04 3.139573e-04 1.265613e-04 1.824854e-05 1.135899e-04
# 397 398 399 400 401 402
# 4.664185e-03 1.213306e-03 4.952860e-03 6.870052e-03 6.372749e-04 2.312305e-04
# 403 404 405 406 407 408
# 5.760469e-06 5.221404e-06 6.742841e-04 7.790989e-04 2.014640e-05 2.061636e-04
# 409 410 411 412 413 414
# 2.034210e-06 9.305501e-04 6.499948e-04 1.913546e-03 2.397710e-06 4.619288e-04
# 415 416 417 418 419 420
# 5.527112e-04 3.075461e-08 2.903862e-04 2.118791e-03 1.293409e-04 2.082674e-03
# 421 422 423 424 425 426
# 3.183720e-04 6.309338e-05 6.897794e-03 1.043008e-04 7.342317e-04 3.683560e-05
# 427 428 429 430 431 432
# 2.945424e-04 2.927201e-03 5.417897e-04 4.790407e-04 1.309568e-04 1.875680e-03
# 433 434 435 436 437 438
# 2.297719e-03 5.998059e-04 1.403177e-04 2.874858e-04 3.860110e-05 2.425397e-03
# 439 440 441 442 443 444
# 3.356707e-06 1.143933e-04 5.834744e-06 1.453583e-04 1.356768e-04 2.956263e-03
# 445 446 447 448 449 450
# 1.530080e-03 1.334711e-03 1.017330e-04 8.786799e-03 6.074281e-03 1.180445e-04
# 451 452 453 454 455 456
# 7.703508e-04 1.618040e-05 7.739856e-04 1.786185e-05 2.582717e-05 6.309872e-04
# 457 458 459 460 461 462
# 7.221964e-04 1.037028e-03 2.538289e-03 2.119635e-04 1.685199e-03 2.282987e-02
# 463 464 465 466 467 468
# 1.407463e-03 2.415690e-03 9.867772e-09 9.781361e-04 1.901835e-05 8.777052e-04
# 469 470 471 472 473 474
# 2.301582e-04 9.050514e-05 7.908978e-05 4.279192e-04 6.519148e-04 1.776540e-04
# 475 476 477 478 479 480
# 4.258679e-04 6.860542e-05 4.654225e-05 3.568448e-04 1.715024e-03 9.236717e-04
# 481 482 483 484 485 486
# 2.148715e-03 9.068290e-05 2.079696e-03 3.313777e-05 9.800678e-05 2.731769e-03
# 487 488 489 490 491 492
# 2.502620e-03 2.983423e-04 1.061983e-04 2.871502e-03 7.423259e-04 3.358200e-04
# 493 494 495 496 497 498
# 2.103157e-05 5.454910e-04 4.244275e-04 1.110934e-04 1.009434e-04 1.856284e-03
# 499 500 501 502 503 504
# 4.781399e-04 4.299084e-05 1.039989e-04 9.041252e-04 2.751754e-04 2.898968e-05
# 505 506 507 508 509 510
# 3.014985e-04 4.492581e-06 2.110665e-04 1.318959e-02 6.565687e-03 3.973807e-05
# 511 512 513 514 515 516
# 7.372207e-07 2.491689e-03 8.851828e-05 3.406558e-05 1.713531e-05 2.111114e-04
# 517 518 519 520 521 522
# 5.518747e-04 6.313121e-04 3.928330e-05 2.502940e-04 1.044247e-03 1.961977e-03
# 523 524 525 526 527 528
# 8.851828e-05 7.924078e-04 8.757321e-04 2.047225e-03 1.082320e-03 1.556476e-03
# 529 530 531 532 533 534
# 6.060760e-05 1.499769e-05 1.992410e-04 7.737495e-04 2.874723e-03 2.572874e-04
# 535 536 537 538 539 540
# 7.297167e-05 3.493347e-05 2.087829e-04 6.776307e-04 2.533119e-03 3.777829e-08
# 541 542 543 544 545 546
# 1.522694e-03 2.299753e-05 1.400981e-04 2.196494e-04 1.825470e-03 9.243417e-04
# 547 548 549 550 551 552
# 1.269731e-03 2.565277e-06 1.215212e-03 3.713937e-04 5.827469e-05 2.204345e-06
# 553 554 555 556 557 558
# 7.781372e-04 3.184249e-05 6.569110e-04 2.224044e-04 1.095482e-04 3.124378e-03
# 559 560 561 562 563 564
# 4.240857e-04 6.969761e-06 5.934670e-05 1.938379e-03 1.469249e-03 1.448527e-03
# 565 566 567 568 569 570
# 2.462247e-04 8.685772e-04 4.747113e-04 5.434222e-04 1.018047e-04 2.867470e-04
# 571 572 573 574 575 576
# 4.364723e-03 3.673044e-05 8.755758e-09 1.536643e-03 7.732188e-06 6.293908e-04
# 577 578 579 580 581 582
# 5.575921e-04 3.807041e-04 1.520862e-03 8.910376e-05 1.306590e-04 4.199709e-04
# 583 584 585 586 587 588
# 1.025219e-04 3.389203e-03 2.279493e-03 9.635622e-04 3.585937e-04 2.195505e-06
# 589 590 591 592 593 594
# 4.605741e-04 1.973086e-04 1.485097e-04 2.041642e-04 1.044385e-04 4.961170e-04
# 595 596 597 598 599 600
# 1.214183e-03 4.315276e-05 2.472348e-04 2.688132e-03 4.290820e-05 2.127279e-05
# 601 602 603 604 605 606
# 5.613964e-03 1.068400e-03 4.483603e-06 5.277899e-03 1.915707e-03 3.442784e-04
# 607 608 609 610 611 612
# 1.909218e-04 6.950836e-05 2.810038e-05 7.013829e-05 1.907416e-04 4.056452e-05
# 613 614 615 616 617 618
# 2.086870e-04 1.059277e-05 9.198877e-05 1.379294e-03 1.702169e-04 8.668945e-07
# 619 620 621 622 623 624
# 4.888747e-04 8.982284e-04 2.486188e-06 5.171244e-04 3.615407e-03 1.952716e-03
# 625 626 627 628 629 630
# 7.974196e-05 3.720400e-04 3.339428e-04 4.793712e-04 1.222829e-06 1.224232e-03
# 631 632 633 634 635 636
# 6.661334e-06 2.088215e-03 3.791547e-05 2.996669e-04 2.957867e-05 1.272210e-02
# 637 638 639 640 641 642
# 3.051154e-03 6.626173e-04 5.650803e-03 6.323741e-05 3.198146e-03 9.154375e-06
# 643 644 645 646 647 648
# 9.184455e-04 4.225592e-04 2.224401e-05 5.919049e-04 1.037335e-03 3.084302e-04
# 649 650 651 652 653 654
# 9.127722e-04 5.949937e-04 3.107371e-03 4.311230e-09 1.899341e-03 9.849467e-06
# 655 656 657 658 659 660
# 1.180644e-03 5.351067e-05 4.396855e-03 3.974638e-04 4.793698e-05 4.807692e-04
# 661 662 663 664 665 666
# 4.454704e-05 5.622965e-05 7.095794e-03 5.733968e-04 1.264422e-04 8.444703e-04
# 667 668 669 670 671 672
# 4.947977e-04 2.097020e-04 1.684239e-05 3.556946e-04 1.407743e-04 2.055916e-05
# 673 674 675 676 677 678
# 1.162114e-03 2.818433e-05 6.487254e-03 1.389169e-05 6.472835e-04 1.518019e-04
# 679 680 681 682 683 684
# 3.858251e-03 1.160492e-04 2.553455e-06 1.157091e-04 4.874404e-07 6.747665e-04
# 685 686 687 688 689 690
# 3.053204e-04 2.528915e-03 6.649293e-05 2.801749e-05 1.466536e-03 5.651790e-04
# 691 692 693 694 695 696
# 2.410407e-04 5.423887e-04 1.161767e-03 3.499645e-04 9.437586e-05 1.411206e-03
# 697 698 699 700 701 702
# 1.795440e-03 5.862753e-04 8.141198e-04 3.044904e-06 6.033841e-04 7.235992e-03
# 703 704 705 706 707 708
# 6.772280e-04 2.602631e-03 1.932515e-04 4.580271e-04 3.915128e-03 1.991761e-03
# 709 710 711 712 713 714
# 9.149683e-04 3.467477e-04 6.239129e-05 4.880269e-03 1.087445e-04 3.503655e-03
# 715 716 717 718 719 720
# 4.641436e-03 1.224914e-03 3.629112e-04 1.653087e-04 2.094679e-03 6.857835e-05
# 721 722 723 724 725 726
# 4.396361e-06 2.302632e-03 1.166050e-04 3.068120e-06 6.667090e-04 3.272084e-06
# 727 728 729 730 731 732
# 1.120401e-03 1.214382e-05 1.839085e-03 2.530129e-04 1.947527e-04 7.849790e-05
# 733 734 735 736 737 738
# 1.787900e-03 2.411487e-04 4.875638e-04 6.568010e-04 6.516483e-04 1.721541e-05
# 739 740 741 742 743 744
# 5.250389e-03 1.640125e-04 2.251005e-04 6.048636e-04 4.766781e-04 1.005613e-05
# 745 746 747 748 749 750
# 1.311263e-03 8.881207e-05 6.797818e-05 1.073733e-03 1.813681e-03 3.198393e-04
# 751 752 753 754 755 756
# 4.049579e-05 5.507118e-04 3.934469e-03 1.370881e-07 1.337365e-04 5.543373e-04
# 757 758 759 760 761 762
# 6.329168e-04 3.264214e-03 2.821535e-05 4.703156e-03 4.158649e-05 2.176580e-03
# 763 764 765 766 767 768
# 4.514930e-05 1.662159e-03 7.743499e-04 1.282039e-04 6.496459e-04 8.421848e-05
# 769 770 771 772 773 774
# 5.153643e-04 1.165800e-03 5.760497e-04 2.139070e-03 4.888308e-05 4.455503e-05
# 775 776 777 778 779 780
# 7.321090e-03 9.526551e-04 2.703534e-04 3.286413e-03 1.595548e-04 1.078484e-04
# 781 782 783 784 785 786
# 6.969761e-06 2.525586e-05 2.739225e-05 3.426275e-04 1.044042e-04 1.235274e-07
# 787 788 789 790 791 792
# 5.437314e-04 1.216011e-03 1.319299e-04 4.748466e-03 6.933744e-05 4.119155e-03
# 793 794 795 796 797 798
# 8.116934e-05 4.243578e-03 2.994319e-06 3.689889e-04 5.910148e-04 3.849443e-04
# 799 800 801 802 803 804
# 2.894340e-05 2.959545e-03 4.538483e-04 3.950360e-04 1.489505e-03 1.538947e-04
# 805 806 807 808 809 810
# 2.371702e-04 3.662786e-03 7.913396e-03 1.201858e-03 6.797666e-05 1.213826e-05
# 811 812 813 814 815 816
# 7.169835e-04 8.852197e-05 4.701680e-04 8.573673e-04 2.643160e-03 7.437288e-04
# 817 818 819 820 821 822
# 6.733081e-04 3.315678e-04 2.173334e-04 5.294838e-04 1.247123e-04 2.110977e-04
# 823 824 825 826 827 828
# 2.566539e-03 1.908839e-06 3.048758e-04 5.352864e-04 2.381125e-03 1.134005e-04
# 829 830 831 832 833 834
# 2.095643e-03 4.439724e-04 1.923658e-03 1.246531e-03 1.424651e-04 4.092227e-04
# 835 836 837 838 839 840
# 1.951174e-04 1.794978e-03 1.506075e-04 3.498056e-05 1.417173e-04 1.655396e-04
# 841 842 843 844 845 846
# 1.590239e-04 3.810289e-03 4.629424e-04 3.143114e-05 5.071091e-05 7.836166e-05
# 847 848 849 850 851 852
# 2.012279e-03 4.057661e-05 1.082109e-04 4.829491e-03 1.701679e-03 3.483750e-04
# 853 854 855 856 857 858
# 1.272242e-04 6.139618e-04 7.131407e-05 6.117561e-04 1.245921e-03 2.121774e-04
# 859 860 861 862 863 864
# 4.861781e-05 6.583107e-05 5.581070e-04 1.606260e-03 5.373093e-03 6.131389e-04
# 865 866 867 868 869 870
# 1.999105e-05 2.878710e-04 4.516055e-05 4.118654e-03 6.645314e-05 4.541676e-03
# 871 872 873 874 875 876
# 7.513313e-05 2.424940e-04 1.666927e-04 2.576070e-04 1.176364e-03 8.629204e-05
# 877 878 879 880 881 882
# 4.784774e-04 1.667318e-07 1.173545e-03 2.876219e-05 1.410944e-04 8.660388e-04
# 883 884 885 886 887 888
# 1.047548e-03 7.474156e-06 3.833149e-04 6.875543e-07 7.530711e-05 2.781931e-03
# 889 890 891 892 893 894
# 2.186858e-04 3.191602e-04 5.078145e-04 1.387518e-04 7.882392e-05 4.917019e-04
# 895 896 897 898 899 900
# 9.325331e-05 1.505726e-04 5.502764e-03 2.447270e-03 6.603377e-04 2.574653e-02
# 901 902 903 904 905 906
# 5.389888e-06 1.508597e-04 1.702169e-04 5.833024e-06 7.385335e-05 7.275363e-03
# 907 908 909 910 911 912
# 4.380243e-03 2.467776e-03 1.821067e-05 2.207114e-04 2.063224e-03 1.691112e-03
# 913 914 915 916 917 918
# 1.635273e-03 4.221817e-04 2.572188e-03 4.267766e-04 3.204144e-03 9.092645e-05
# 919 920 921 922 923 924
# 3.542754e-03 8.453222e-03 2.012548e-03 5.736252e-03 3.504116e-04 5.161596e-04
# 925 926 927 928 929 930
# 1.181048e-03 3.654724e-04 1.896258e-03 7.391186e-07 1.113815e-04 4.308114e-04
# 931 932 933 934 935 936
# 4.126002e-06 4.794775e-04 1.937932e-03 2.000090e-05 8.448091e-03 9.132308e-03
# 937 938 939 940 941 942
# 4.884987e-03 1.352355e-03 9.157322e-04 3.204650e-03 1.273963e-03 5.967519e-04
# 943 944 945 946 947 948
# 1.367769e-04 2.564409e-03 6.660906e-04 4.667562e-04 3.377130e-04 6.000922e-06
# 949 950 951 952 953 954
# 2.070413e-03 1.294243e-05 3.017209e-05 4.949189e-04 3.345964e-04 1.460623e-03
# 955 956 957 958 959 960
# 8.093812e-03 1.215171e-03 2.917353e-04 3.463391e-04 1.450908e-06 1.573269e-03
# 961 962 963 964 965 966
# 1.358161e-04 1.315700e-04 3.898396e-05 4.136442e-03 3.189778e-06 4.790373e-03
# 967 968 969 970 971 972
# 2.064322e-05 3.962796e-05 9.316945e-04 1.025562e-03 6.602298e-04 1.873183e-03
# 973 974 975 976 977 978
# 7.426093e-04 2.704835e-04 1.098324e-03 6.099478e-03 3.526164e-03 3.121672e-04
# 979 980 981 982 983 984
# 2.146646e-03 2.556378e-03 2.222093e-03 1.104693e-03 2.761280e-04 3.512971e-04
# 985 986 987 988 989 990
# 7.761293e-04 4.084796e-07 4.087679e-05 6.524471e-04 8.062744e-05 6.248306e-06
# 991 992 993 994 995 996
# 3.218546e-04 3.194652e-04 1.975096e-03 2.280609e-03 4.195435e-04 8.823188e-05
# 997 998 999 1000
# 4.466584e-07 2.123072e-04 1.484386e-03 2.294804e-03
#
# $influence$influential
# 90 193 243 299 308 311 362 372 376 397 399 400 423 448 449 462 508 509 571 601
# 90 193 243 299 308 311 362 372 376 397 399 400 423 448 449 462 508 509 571 601
# 604 636 639 657 663 675 702 712 715 739 760 775 790 792 794 807 850 863 868 870
# 604 636 639 657 663 675 702 712 715 739 760 775 790 792 794 807 850 863 868 870
# 897 900 906 907 920 922 935 936 937 955 964 966 976
# 897 900 906 907 920 922 935 936 937 955 964 966 976
#
# $influence$cutoff
# [1] 0.004012036
The drop in test statistics or diagnostic plots indicates whether the
remedy helped.