heteroTests Walkthrough
This vignette demonstrates the main workflow in greater depth. We use
R’s built-in quakes dataset.
## lat long depth mag stations
## 1 -20.42 181.62 562 4.8 41
## 2 -20.62 181.03 650 4.2 15
## 3 -26.00 184.10 42 5.4 43
## 4 -17.97 181.66 626 4.1 19
## 5 -20.42 181.96 649 4.0 11
## 6 -19.68 184.31 195 4.0 12
1. Fit an initial model
base_model <- lm(stations ~ mag + depth, data = quakes)
summary(base_model)
##
## Call:
## lm(formula = stations ~ mag + depth, data = quakes)
##
## Residuals:
## Min 1Q Median 3Q Max
## -46.506 -6.996 -0.453 6.643 47.259
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.920e+02 4.332e+00 -44.335 < 2e-16 ***
## mag 4.791e+01 9.016e-01 53.135 < 2e-16 ***
## depth 1.318e-02 1.685e-03 7.822 1.32e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.17 on 997 degrees of freedom
## Multiple R-squared: 0.7404, Adjusted R-squared: 0.7399
## F-statistic: 1422 on 2 and 997 DF, p-value: < 2.2e-16
2. Diagnose heteroscedasticity
hd <- HeteroDiagnostic(base_model, quakes)
test(hd)
## [INFO] Running White test
## [INFO] White test completed: statistic = 125.558 df = 5 p = 0
## [INFO] Running Breusch-Pagan test
## $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
## $residuals_fitted
## `geom_smooth()` using formula = 'y ~ x'
##
## $spread_level
## `geom_smooth()` using formula = 'y ~ x'
##
## $density
##
## $qq
##
## $bubble_variance
3. Apply a remedy
wls_model <- fitWLS(base_model)
summary(wls_model)
##
## Call:
## lm(formula = stations ~ mag + depth, data = quakes)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -26.519 -6.685 -0.537 6.539 40.074
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.540e+02 4.278e+00 -35.992 < 2e-16 ***
## mag 3.980e+01 9.260e-01 42.975 < 2e-16 ***
## depth 9.189e-03 1.454e-03 6.321 3.91e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.985 on 997 degrees of freedom
## Multiple R-squared: 0.6514, Adjusted R-squared: 0.6507
## F-statistic: 931.6 on 2 and 997 DF, p-value: < 2.2e-16
4. Compare models
compareModelDiagnostics(list(base_model, wls_model))
## [INFO] Running White test
## [INFO] White test completed: statistic = 125.558 df = 5 p = 0
## [INFO] Running Breusch-Pagan test
## [INFO] Running White test
## [INFO] White test completed: statistic = 249.2441 df = 5 p = 0
## [INFO] Running Breusch-Pagan test
## white breusch_pagan
## Model1 125.5580 191.9257
## Model2 249.2441 463.6599
The weighted least squares fit typically reduces the
heteroscedasticity metrics.