#dataset GaltonFamilies se nalazi u paketu
library(HistData)
GaltonFamilies[1:10,]
## family father mother midparentHeight children childNum gender childHeight
## 1 001 78.5 67.0 75.43 4 1 male 73.2
## 2 001 78.5 67.0 75.43 4 2 female 69.2
## 3 001 78.5 67.0 75.43 4 3 female 69.0
## 4 001 78.5 67.0 75.43 4 4 female 69.0
## 5 002 75.5 66.5 73.66 4 1 male 73.5
## 6 002 75.5 66.5 73.66 4 2 male 72.5
## 7 002 75.5 66.5 73.66 4 3 female 65.5
## 8 002 75.5 66.5 73.66 4 4 female 65.5
## 9 003 75.0 64.0 72.06 2 1 male 71.0
## 10 003 75.0 64.0 72.06 2 2 female 68.0
dim(GaltonFamilies)
## [1] 934 8
#SIMPLE REGRESSION ----
#1. izrada modela
lmmodel=lm(childHeight ~ midparentHeight,data=GaltonFamilies)
summary (lmmodel)
##
## Call:
## lm(formula = childHeight ~ midparentHeight, data = GaltonFamilies)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.9570 -2.6989 -0.2155 2.7961 11.6848
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.63624 4.26511 5.307 1.39e-07 ***
## midparentHeight 0.63736 0.06161 10.345 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.392 on 932 degrees of freedom
## Multiple R-squared: 0.103, Adjusted R-squared: 0.102
## F-statistic: 107 on 1 and 932 DF, p-value: < 2.2e-16
# the fitted model is: Predicted child height=22.6362+.6374⋅Midparent height.
library(ggplot2)
ggplot(GaltonFamilies, aes(x=midparentHeight, y=childHeight)) +
geom_point() +
geom_smooth() #linearna pozitivna veza
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
ggplot(GaltonFamilies, aes(x=midparentHeight, y=childHeight)) +
geom_point() +
geom_smooth(method = "lm", se=F) #linearna pozitivna veza
## `geom_smooth()` using formula = 'y ~ x'
#this is withoud SE, but we know from the previous slide thad se is small, because we have large sample size and small variability
confint(lmmodel)#interval povjerenja
## 2.5 % 97.5 %
## (Intercept) 14.2659135 31.0065676
## midparentHeight 0.5164552 0.7582666
confint(lmmodel, level = 0.9) # manji su intervali jer trazimo i manji nivo pouzdanosti 90 versus 95
## 5 % 95 %
## (Intercept) 15.6137829 29.6586982
## midparentHeight 0.5359246 0.7387972
lmmodel$coefficients
## (Intercept) midparentHeight
## 22.6362405 0.6373609
#2. interpretacija modela
#interpretacija: to znači da u prosjeku za svaki dodatni centimetar
#prosjecnih visina roditelja, ocekujemo da ce se visina djeteta povecati
#u prosjeku za od 0.637, odnosno kretace se u intervalu od 0.516 do 0.758
# “A unit change in x1 will produce a change of ˆβ1 in the response
##intersept je 22.63, sto znaci kad je prosjek visine roditelja nula,
#visina djeteta u prosjeku je 22.636incha. Ovo naravno nema smisla
## t stat= coeff/st.error
#kod simple posmatrmo Rsquare a kod multiple adjRsq te p/value
#3 verifikacija modela
#DIAGNOSTIC PLOT----
#Homeoscesadicity
##**Residuals versus fittet plot----
par(mar = c(4, 4, 2, 2)) # Adjust the numbers as needed
plot (lmmodel,which=1) #which=1 odnosi se na razlicite vrste plotova, a ima ih 6. jedan oyna;ava residuals vs fitted
#ovjde istrazhujemo homoscedasticity or heteroscedasity
#gledamo linear concept of data. Ako je linija zakrivljena nije linearni model.
#ovaj plot mora biti homeoscedastic.
#na ovom plotu vidimo i outlayere. Izbaci nam broj reda i onda odlucimo da li trebmo da ga izbacimo.
#moramo imati argument za to
lmmodel$coefficients
## (Intercept) midparentHeight
## 22.6362405 0.6373609
confint(lmmodel, level=0.99) # ako zelimo da promijenimo nivo pouzdanosti
## 0.5 % 99.5 %
## (Intercept) 11.6275088 33.6449723
## midparentHeight 0.4783446 0.7963772
##**Cook's distance ----
plot(lmmodel,which=4,id.n = 5) #id.n=5 znači da dobijemo pet rednih brojeva koji su najudaljeniji od fitted value)
##**Other plots----
##qq plot
plot(lmmodel,which=2)
##standardized residuals versus fitted values
plot(lmmodel,which=3)
## calculate stand residuals
# Extract standardized residuals
standardized_residuals <- rstandard(lmmodel)
# Display standardized residuals
standardized_residuals
## 1 2 3 4 5 6
## 0.738574554 -0.449022391 -0.508402238 -0.508402238 1.158927030 0.862961935
## 7 8 9 10 11 12
## -1.208793727 -1.208793727 0.719436074 -0.166738752 0.571740269 -0.019042947
## 13 14 15 16 17 18
## -0.462130360 -1.200609381 -1.643696794 1.571878724 0.686894108 0.391899236
## 19 20 21 22 23 24
## -0.050593072 -1.230572560 -1.230572560 -0.036254786 2.035686182 1.295707265
## 25 26 27 28 29 30
## 0.999715698 0.999715698 0.259736781 -1.664208404 0.412090334 -0.327071124
## 31 32 33 34 35 36
## -0.918400291 -0.914608975 -0.963879534 1.901027902 0.720735044 0.130588615
## 37 38 39 40 41 42
## -0.164484600 -0.164484600 -0.459557815 -1.197240851 -1.344777459 -0.652957353
## 43 44 45 46 47 48
## 0.603099864 -2.057153039 -0.283651104 -0.579234759 0.653770724 0.506023049
## 49 50 51 52 53 54
## -0.616859276 1.100992468 0.658082020 0.569499931 0.569499931 0.274226299
## 55 56 57 58 59 60
## 0.126589483 -0.523012506 -1.113559770 -1.408833401 1.742001173 1.446787099
## 61 62 63 64 65 66
## 1.003965989 -1.652960670 -0.472104377 -1.712003485 -0.568807784 -1.011550283
## 67 68 69 70 71 72
## -1.159131116 -1.459719678 1.079489870 1.020301208 0.931518215 0.132471276
## 73 74 75 76 77 78
## -0.163472034 -0.311443689 -0.459415344 -1.051301965 1.186786429 -0.143401659
## 79 80 81 82 83 84
## -0.291200336 1.287775866 0.696924239 -0.484779017 1.844038584 0.751913362
## 85 86 87 88 89 90
## 0.456744383 -0.576347044 -0.723931534 -0.871516023 -0.871516023 -0.774866740
## 91 92 93 94 95 96
## -0.474619743 -1.359870122 0.954631611 0.954631611 0.512091964 -0.668013761
## 97 98 99 100 101 102
## -1.258066624 0.512091964 -0.077960898 -1.258066624 1.692197690 -0.077960898
## 103 104 105 106 107 108
## 0.954631611 0.807118396 -0.225474114 -1.258066624 -0.028232810 -0.116757062
## 109 110 111 112 113 114
## -0.264297482 -0.861416029 1.156601894 0.861594349 0.861594349 -0.318435834
## 115 116 117 118 119 120
## -0.613443380 -0.613443380 2.088562417 1.498566728 0.613573194 0.171076427
## 121 122 123 124 125 126
## -1.008914951 1.498566728 1.351067806 1.351067806 0.908571039 0.318575349
## 127 128 129 130 131 132
## -0.258388695 2.657361661 1.474916826 1.179305617 0.883694409 -0.594361635
## 133 134 135 136 137 138
## 1.440357941 1.381299410 0.200128795 -0.390456512 0.596818809 -0.288710538
## 139 140 141 142 143 144
## -0.288710538 -0.436298763 0.596818809 0.301642360 0.154054136 -0.583886987
## 145 146 147 148 149 150
## -1.026651661 -1.469416335 0.891995258 -0.288710538 2.367877504 1.187171708
## 151 152 153 154 155 156
## 0.891995258 -0.583886987 -0.583886987 0.729394398 1.237769146 1.237769146
## 157 158 159 160 161 162
## 0.942640079 0.352381946 -0.533005254 -0.828134321 1.486091932 -0.816255085
## 163 164 165 166 167 168
## 0.208577207 -0.027523465 0.108026151 0.108026151 -1.662506749 0.209546308
## 169 170 171 172 173 174
## 0.209546308 0.062031468 -0.232998212 -0.232998212 -0.380513052 -0.528027892
## 175 176 177 178 179 180
## -0.675542732 1.273383427 0.978283427 0.830733427 -0.202116571 0.209546308
## 181 182 183 184 185 186
## 0.209546308 0.209546308 1.292131164 0.997045046 0.701958927 -0.478385547
## 187 188 189 190 191 192
## -0.921014725 -0.921014725 -1.658730021 1.634067853 -1.611544737 0.144755912
## 193 194 195 196 197 198
## -0.740251669 1.145332876 -0.034710245 -0.329721026 -0.624731806 -1.067247977
## 199 200 201 202 203 204
## 1.196052713 0.901053726 0.901053726 -0.868940199 -0.573941212 -0.573941212
## 205 206 207 208 209 210
## -0.868940199 -1.163939187 -1.163939187 1.196052713 1.196052713 0.901053726
## 211 212 213 214 215 216
## -1.016439693 1.297573951 1.002577238 -0.619904684 -1.209898110 -1.504894823
## 217 218 219 220 221 222
## 1.592570665 1.150075595 1.150075595 -0.619904684 -1.947389892 0.951804219
## 223 224 225 226 227 228
## -0.818161574 -0.818161574 -0.818161574 -1.260653022 1.150075595 1.002577238
## 229 230 231 232 233 234
## 0.707580525 0.707580525 -0.177409614 -0.619904684 -0.767403040 -1.255977296
## 235 236 237 238 239 240
## 1.852922437 1.114742126 0.681915264 0.386465857 0.091016450 0.091016450
## 241 242 243 244 245 246
## 0.386465857 0.002381628 -0.204432957 -0.795331771 -1.386230585 -1.977129399
## 247 248 249 250 251 252
## 1.964421237 0.589308678 0.294124602 -0.591427625 -1.181795777 -2.362532081
## 253 254 255 256 257 258
## -0.148651511 1.525408017 1.230272381 1.230272381 -0.392973617 0.403892600
## 259 260 261 262 263 264
## -0.186378672 -0.392973617 -0.540541435 -0.540541435 -1.071785580 -1.219353398
## 265 266 267 268 269 270
## 1.335261023 0.804156804 0.450087324 0.302558374 0.155029425 -0.730144275
## 271 272 273 274 275 276
## -1.762846923 -1.910375873 -1.910375873 1.677192446 1.382159361 0.939609735
## 277 278 279 280 281 282
## -0.683072229 -0.683072229 -0.830588771 -1.273138398 -1.568171482 -0.093006061
## 283 284 285 286 287 288
## -0.683072229 -0.830588771 -1.420654940 -1.420654940 0.792093193 0.792093193
## 289 290 291 292 293 294
## -0.093006061 -0.683072229 -0.683072229 -1.273138398 3.447390952 2.267258614
## 295 296 297 298 299 300
## 1.087126277 0.497060108 -0.093006061 -0.476549070 -1.568171482 1.677192446
## 301 302 303 304 305 306
## 1.529675903 -0.683072229 0.497060108 0.497060108 1.412560850 0.822520331
## 307 308 309 310 311 312
## 0.438993993 -0.210050578 -0.505070838 -0.741087046 -0.800091098 1.100037027
## 313 314 315 316 317 318
## 0.893536827 0.303536254 0.008535968 -0.286464318 -0.581464604 0.008535968
## 319 320 321 322 323 324
## 0.893536827 0.303536254 -0.079964118 -0.433964461 1.463252318 0.873243175
## 325 326 327 328 329 330
## -1.339291114 -1.722797057 -2.047302086 2.026612593 0.699058878 0.551552910
## 331 332 333 334 335 336
## 0.256540974 0.256540974 0.256540974 -0.480988868 -0.628494836 -2.154464227
## 337 338 339 340 341 342
## 0.303536254 -0.581464604 -0.876464891 -1.466465463 1.188537113 0.893536827
## 343 344 345 346 347 348
## 0.893536827 0.893536827 0.746036684 0.451036398 0.598536541 -0.581464604
## 349 350 351 352 353 354
## -0.876464891 0.923982875 0.038994907 -0.403499077 -0.934491857 -1.081989852
## 355 356 357 358 359 360
## -1.288487044 -1.376985841 -1.730981028 0.948044195 0.505552592 -0.379430616
## 361 362 363 364 365 366
## -0.969419421 1.685530202 0.653049793 0.063060988 -0.674425018 -0.821922219
## 367 368 369 370 371 372
## 1.239278839 0.206797931 0.206797931 -0.973180249 0.405061931 0.110066024
## 373 374 375 376 377 378
## -0.863420470 -1.364913512 0.995053745 -0.037431930 -1.364913512 -1.659909419
## 379 380 381 382 383 384
## 1.639623134 1.049612570 0.902109928 0.902109928 0.459602005 -0.425413842
## 385 386 387 388 389 390
## -0.720419124 -1.015424406 1.203808026 0.908811894 0.761313827 -0.418670703
## 391 392 393 394 395 396
## -0.772666062 -0.920164128 -1.008662968 1.639623134 1.639623134 -1.900440253
## 397 398 399 400 401 402
## 1.552511743 0.313207599 0.414877904 -0.323005518 -0.175428834 -0.765735572
## 403 404 405 406 407 408
## -0.175428834 -0.175428834 1.896568425 -0.170730118 -0.613722663 2.095570388
## 409 410 411 412 413 414
## 0.323164223 0.323164223 0.027763196 -0.563038859 2.007344064 0.826350051
## 415 416 417 418 419 420
## 0.531101548 -0.649892465 -0.649892465 -0.797516716 -0.945140968 -0.945140968
## 421 422 423 424 425 426
## -1.240389471 -1.240389471 -1.087416570 1.669690894 1.374654249 1.286143256
## 427 428 429 430 431 432
## 1.227135927 -0.543083943 -0.690602266 -1.369186549 -1.428193878 1.138624933
## 433 434 435 436 437 438
## 1.079617604 0.784580959 2.188990050 1.893912047 1.303756041 0.270983030
## 439 440 441 442 443 444
## 0.784580959 0.342025992 0.194507669 -0.690602266 -1.280675556 -1.428193878
## 445 446 447 448 449 450
## 1.619073082 1.028943555 0.881411174 0.881411174 -0.151315497 -0.446380260
## 451 452 453 454 455 456
## -1.921704075 0.834487060 -0.050804376 -0.936095811 -1.083644384 1.028943555
## 457 458 459 460 461 462
## 0.291281648 -0.003783115 -0.446380260 -1.331574549 -1.331574549 1.032696666
## 463 464 465 466 467 468
## 1.032696666 0.885165448 0.885165448 -0.295084297 -0.590146733 -0.885209169
## 469 470 471 472 473 474
## 1.669690894 1.374654249 0.489544314 0.489544314 -0.248047298 -0.543083943
## 475 476 477 478 479 480
## -0.543083943 -0.690602266 -0.985638911 0.886020330 0.443517719 0.001015107
## 481 482 483 484 485 486
## -0.588988375 -0.883990116 -1.031490986 -1.768995339 0.801278231 0.299776541
## 487 488 489 490 491 492
## -2.060231412 -0.526226243 -0.732726939 -0.968727734 -2.060231412 1.470216209
## 493 494 495 496 497 498
## -0.063754225 -0.506245697 -0.948737168 -0.289190130 0.794124550 0.351598768
## 499 500 501 502 503 504
## -0.828469985 1.679176114 1.974193302 1.089141738 1.089141738 -0.680961391
## 505 506 507 508 509 510
## -0.090927014 -1.270995767 1.185823221 0.153313875 -0.141688795 -0.436691465
## 511 512 513 514 515 516
## -1.026696805 -1.321699476 -1.616702146 1.185823221 -0.820194936 -1.026696805
## 517 518 519 520 521 522
## -1.087814391 2.028884378 1.733843679 0.848721583 2.076085171 1.485950066
## 523 524 525 526 527 528
## 1.485950066 0.895814961 -0.874590354 1.733843679 1.143762282 0.494672744
## 529 530 531 532 533 534
## -0.272433072 -0.419953422 -0.478961561 -0.774002260 -0.774002260 -1.069042959
## 535 536 537 538 539 540
## -1.216563308 -1.364083658 1.435032865 1.139994051 1.139994051 0.844955237
## 541 542 543 544 545 546
## -0.777758240 -1.072797054 -1.072797054 -1.220316461 1.781017619 0.600747409
## 547 548 549 550 551 552
## 0.010612304 0.010612304 1.245584979 1.098031804 0.950478630 -0.820159468
## 553 554 555 556 557 558
## -1.115265818 0.702489904 0.702489904 0.554916707 -0.478095673 -0.773242068
## 559 560 561 562 563 564
## -0.773242068 -0.625668871 -1.068388462 -1.068388462 1.542498893 0.804364438
## 565 566 567 568 569 570
## -0.819531363 1.099618220 0.213856874 -1.055734389 -1.410038927 1.196203583
## 571 572 573 574 575 576
## 0.651894283 -2.096241681 1.615324779 1.025190521 -0.155077995 0.780824929
## 577 578 579 580 581 582
## 0.485786445 0.485786445 0.397274900 0.338267204 0.338267204 0.190747962
## 583 584 585 586 587 588
## 0.190747962 0.190747962 -0.340321309 -1.225436761 0.242521528 -0.199970616
## 589 590 591 592 593 594
## -0.250736142 -0.840727153 1.430738241 1.371739139 1.135742735 -0.398233895
## 595 596 597 598 599 600
## -0.103238389 -0.486732546 -1.578215917 1.569997962 1.569997962 0.390018910
## 601 602 603 604 605 606
## -0.199970616 0.697009143 0.343014894 -0.246975520 -0.246975520 -1.426956348
## 607 608 609 610 611 612
## -1.574453952 -1.721951555 -2.016946762 1.522995723 1.080502912 0.549511539
## 613 614 615 616 617 618
## 0.490512498 0.254516332 -0.836965934 -0.984463538 -1.131961141 1.376625500
## 619 620 621 622 623 624
## 0.491581734 0.491581734 0.196567145 -0.393462033 -0.688476622 -0.983491210
## 625 626 627 628 629 630
## -0.983491210 -1.278505799 -1.573520388 -0.098447444 -0.983491210 -0.245954738
## 631 632 633 634 635 636
## -1.278505799 1.435628418 1.435628418 0.786596323 0.639089028 -1.130998505
## 637 638 639 640 641 642
## -1.329213434 0.786596323 0.196567145 -0.098447444 -0.098447444 -0.098447444
## 643 644 645 646 647 648
## -0.393462033 -0.393462033 -0.393462033 -0.688476622 -0.983491210 1.330872480
## 649 650 651 652 653 654
## 1.183341057 0.593215365 0.003089673 0.003089673 0.003089673 -1.177161710
## 655 656 657 658 659 660
## -1.324693133 2.117931778 1.085376236 0.937868302 -0.242195174 0.298152519
## 661 662 663 664 665 666
## 1.183341057 0.593215365 -0.439504595 -0.587036018 1.478403903 0.593215365
## 667 668 669 670 671 672
## 0.003089673 -0.144441750 -0.291973172 -0.882098864 -1.177161710 -1.177161710
## 673 674 675 676 677 678
## 0.298152519 0.298152519 0.003089673 -0.587036018 -0.734567441 -1.472224556
## 679 680 681 682 683 684
## 0.554347672 1.183341057 1.113621906 0.818595193 0.228541767 -0.213998303
## 685 686 687 688 689 690
## -0.509025016 0.791616758 0.540471697 -1.230047868 0.201421462 0.944435417
## 691 692 693 694 695 696
## 0.796812994 -0.384166392 -0.531788815 -0.679411239 0.494462877 -0.282678676
## 697 698 699 700 701 702
## -1.168814921 -1.168814921 -1.464193669 -1.464193669 -1.464193669 -2.645708662
## 703 704 705 706 707 708
## 0.751146943 0.603457569 0.455768195 -1.464193669 1.249165448 1.001049188
## 709 710 711 712 713 714
## 0.114424993 0.025762573 -0.181116406 -0.181116406 -0.476657804 0.114424993
## 715 716 717 718 719 720
## 0.114424993 -0.772199203 -1.067740601 1.748664812 1.748664812 1.394671664
## 721 722 723 724 725 726
## -0.375294080 -0.965282661 1.216723588 1.857469871 1.267481021 1.178982694
## 727 728 729 730 731 732
## 0.972486596 0.677492171 0.382497746 -0.354988316 -1.387468803 0.985577142
## 733 734 735 736 737 738
## 0.336550422 -0.253473870 -0.400979942 -0.548486015 -0.843498161 1.023269845
## 739 740 741 742 743 744
## 0.728270112 -0.304228954 -0.304228954 -1.041728287 1.023269845 0.344770459
## 745 746 747 748 749 750
## -1.041728287 -1.926727487 -0.400979942 -1.286016379 -1.286016379 1.322033032
## 751 752 753 754 755 756
## 0.732032215 -0.742969830 -0.742969830 -1.037970239 -1.037970239 -1.037970239
## 757 758 759 760 761 762
## -1.037970239 -1.037970239 -1.185470444 -1.332970648 1.618387907 1.175800463
## 763 764 765 766 767 768
## 0.290625577 0.290625577 1.521808624 1.285734990 0.990642947 0.784078516
## 769 770 771 772 773 774
## 0.636532495 0.341440452 -0.101197613 -0.691381699 0.982542241 0.687409326
## 775 776 777 778 779 780
## -0.788255248 1.332459975 1.184867595 1.037275215 0.889682835 0.151720936
## 781 782 783 784 785 786
## 0.595905058 1.112462405 1.112462405 0.079982555 -0.215011687 -0.215011687
## 787 788 789 790 791 792
## -1.394988658 -1.394988658 -1.542485779 1.554953769 -0.510005930 -0.510005930
## 793 794 795 796 797 798
## 0.079982555 -0.805000173 -0.805000173 -1.394988658 -1.984977143 -1.984977143
## 799 800 801 802 803 804
## -0.113488085 -0.408497943 0.181521773 0.034016844 -0.260993014 1.656571065
## 805 806 807 808 809 810
## 0.476531632 -0.113488085 -0.408497943 -1.293527519 -1.588537377 0.737616875
## 811 812 813 814 815 816
## 0.678610880 0.088550929 -0.501509022 -1.091568972 -1.681628923 -1.681628923
## 817 818 819 820 821 822
## -2.566718849 1.707445429 1.412417104 0.232303805 -0.062724519 -0.357752844
## 823 824 825 826 827 828
## 1.372167615 -0.302332878 -1.040266271 0.498404178 0.439368754 -0.150985484
## 829 830 831 832 833 834
## -0.150985484 -0.150985484 -0.741339722 1.375950942 0.785487466 -0.543055354
## 835 836 837 838 839 840
## -0.838287092 -0.838287092 -0.838287092 -0.838287092 1.525642330 1.088291562
## 841 842 843 844 845 846
## 0.792588828 0.201183362 -1.277330304 0.201183362 1.190935451 0.895016435
## 847 848 849 850 851 852
## 0.747056928 0.599097420 0.510321715 0.451137912 0.303178404 0.303178404
## 853 854 855 856 857 858
## 0.007259389 -0.288659627 -0.584578643 -0.880497658 -1.176416674 -1.768254705
## 859 860 861 862 863 864
## -2.064173721 0.026495543 -0.121008321 -0.121008321 -0.416016048 -1.006031502
## 865 866 867 868 869 870
## -0.904625829 -0.904625829 -0.904625829 -1.789774819 0.275572825 -0.019476839
## 871 872 873 874 875 876
## -0.314526502 -0.314526502 -1.494725155 0.967451611 0.672331550 0.672331550
## 877 878 879 880 881 882
## -0.213028634 -0.213028634 -1.098388819 -1.098388819 -1.393508880 -1.983749003
## 883 884 885 886 887 888
## 1.418182976 -0.116239792 1.026475624 0.967451611 0.672331550 0.583795532
## 889 890 891 892 893 894
## -0.360588665 -1.541068911 0.478944885 0.478944885 -0.406712062 -0.406712062
## 895 896 897 898 899 900
## -0.849540536 -1.439978501 1.466842171 -0.600583416 0.285456121 0.285456121
## 901 902 903 904 905 906
## -0.600583416 1.714764548 1.714764548 1.124196732 -0.499864761 1.135779474
## 907 908 909 910 911 912
## 1.135779474 0.839980230 0.839980230 -0.639015990 1.902265067 0.868588778
## 913 914 915 916 917 918
## 0.130248572 -0.312755551 -0.903427716 -0.903427716 -1.198763799 1.606928984
## 919 920 921 922 923 924
## 0.868588778 0.573252696 -0.017419469 -0.312755551 -0.312755551 -1.494099881
## 925 926 927 928 929 930
## -0.063473354 0.686337156 -1.090420627 1.162096747 -0.315726226 -0.327791775
## 931 932 933 934
## -0.918423165 -1.213738860 0.669350299 -2.140295042
##MULTIPLE REGRESSION----
# Ovdje cemo raditi i druge testove
#More predictors, x1, x2...xn
lmmodel2=lm(childHeight ~ mother+father,data=GaltonFamilies)
summary(lmmodel2)
##
## Call:
## lm(formula = childHeight ~ mother + father, data = GaltonFamilies)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.117 -2.741 -0.218 2.766 11.694
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.64328 4.26213 5.313 1.35e-07 ***
## mother 0.29051 0.04852 5.987 3.05e-09 ***
## father 0.36828 0.04489 8.204 7.66e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.389 on 931 degrees of freedom
## Multiple R-squared: 0.1052, Adjusted R-squared: 0.1033
## F-statistic: 54.74 on 2 and 931 DF, p-value: < 2.2e-16
#interpretation: “ˆβ1 is the effect of x1 when all the other (specified) predictors are held constant
#fitted model is: Predicted child height=22.6433+.2905*Mother_height+.3683*Father_height.
lmmodel3=lm(childHeight ~ gender,data=GaltonFamilies)
summary (lmmodel3)
##
## Call:
## lm(formula = childHeight ~ gender, data = GaltonFamilies)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.234 -1.604 -0.104 1.766 9.766
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 64.1040 0.1173 546.32 <2e-16 ***
## gendermale 5.1301 0.1635 31.38 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.497 on 932 degrees of freedom
## Multiple R-squared: 0.5137, Adjusted R-squared: 0.5132
## F-statistic: 984.4 on 1 and 932 DF, p-value: < 2.2e-16
#fitted model 3 is Height=64.10+5.13 ⋅Indicator for Male={64.10 if female
#69.23 if male.
#model parents and gender
#plotting the regression
library(ggplot2)
ggplot(aes(x = midparentHeight, y = childHeight, color = gender), data = GaltonFamilies) + geom_smooth(method = "lm") +
geom_point()
## `geom_smooth()` using formula = 'y ~ x'
#graf dokazuje i koeficijente.. nakrivljenost tj slope tj. beta za musko i zensko nisu razliciti da bi bili signifikantni
lmmodel4a <-lm(childHeight ~ midparentHeight+ gender,data=GaltonFamilies)#separatly
summary (lmmodel4a)
##
## Call:
## lm(formula = childHeight ~ midparentHeight + gender, data = GaltonFamilies)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.5317 -1.4600 0.0979 1.4566 9.1110
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 16.51410 2.73392 6.04 2.22e-09 ***
## midparentHeight 0.68702 0.03944 17.42 < 2e-16 ***
## gendermale 5.21511 0.14216 36.69 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.17 on 931 degrees of freedom
## Multiple R-squared: 0.6332, Adjusted R-squared: 0.6324
## F-statistic: 803.6 on 2 and 931 DF, p-value: < 2.2e-16
#INTERACTION TERM
#The interaction effect αβij is interpreted as that part of the mean response
#not attributable to the additive
#effect of αi and βj. For example, you may enjoy strawberries and cream individually,
#but the combination
#is superior. In contrast, you may like fish and ice cream separatly but not together
lmmodel4 <- lm(childHeight ~ midparentHeight+ gender + midparentHeight*gender,data=GaltonFamilies) #together
summary (lmmodel4)
##
## Call:
## lm(formula = childHeight ~ midparentHeight + gender + midparentHeight *
## gender, data = GaltonFamilies)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.5431 -1.4568 0.0769 1.4795 9.0860
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.33348 3.86636 4.742 2.45e-06 ***
## midparentHeight 0.66075 0.05580 11.842 < 2e-16 ***
## gendermale 1.57998 5.46264 0.289 0.772
## midparentHeight:gendermale 0.05252 0.07890 0.666 0.506
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.171 on 930 degrees of freedom
## Multiple R-squared: 0.6334, Adjusted R-squared: 0.6322
## F-statistic: 535.6 on 3 and 930 DF, p-value: < 2.2e-16
#childHeight = 18.5 + 0.66*midparentHeight + 1.58*gendermale + 0.053*midparentHeight*gendermale
#if there are males = 1 and increase in midparent heigh by 1cm then 0.66 + 1.58*1 +0.053*1*1
0.66+1.58+0.053 #2.293 the increase in the hight by 1cm in midpartentHeight will result to the average increse by 2.293 in sons heights (if we have significance)
## [1] 2.293
#and in case of girls 0
#childheight = 0.066*1 + 1.58*0+0.053*1*0
0.066*1 + 1.58*0+0.053*1*0 #0,06. Increase in the height by 1cma in midparetnt height will result to the average incrase by 0.066 cm in doughter higths
## [1] 0.066
summary(lmmodel4)
##
## Call:
## lm(formula = childHeight ~ midparentHeight + gender + midparentHeight *
## gender, data = GaltonFamilies)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.5431 -1.4568 0.0769 1.4795 9.0860
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.33348 3.86636 4.742 2.45e-06 ***
## midparentHeight 0.66075 0.05580 11.842 < 2e-16 ***
## gendermale 1.57998 5.46264 0.289 0.772
## midparentHeight:gendermale 0.05252 0.07890 0.666 0.506
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.171 on 930 degrees of freedom
## Multiple R-squared: 0.6334, Adjusted R-squared: 0.6322
## F-statistic: 535.6 on 3 and 930 DF, p-value: < 2.2e-16
#its is like fish and ice/cream
#Diagnosis of lmmodel4a
ggplot(GaltonFamilies, aes(y = midparentHeight,x= gender)) + geom_boxplot() #we have some outliers we can decide shall we extract them or not
summary (lmmodel4a)
##
## Call:
## lm(formula = childHeight ~ midparentHeight + gender, data = GaltonFamilies)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.5317 -1.4600 0.0979 1.4566 9.1110
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 16.51410 2.73392 6.04 2.22e-09 ***
## midparentHeight 0.68702 0.03944 17.42 < 2e-16 ***
## gendermale 5.21511 0.14216 36.69 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.17 on 931 degrees of freedom
## Multiple R-squared: 0.6332, Adjusted R-squared: 0.6324
## F-statistic: 803.6 on 2 and 931 DF, p-value: < 2.2e-16
#the model is y=16.514 + 0.687midparentHeight + 5.2151gendermale
#f statistics: An F statistic is a value you get when you run a regression analysis to find out if the means between two populations are significantly different.
#It’s similar to a T statistic from a T-Test; A-T test will tell you if a single variable is statistically significant and an F test will tell you if a group of variables are jointly significant.
confint(lmmodel4a)
## 2.5 % 97.5 %
## (Intercept) 11.1487472 21.8794572
## midparentHeight 0.6096139 0.7644165
## gendermale 4.9361179 5.4940929
#Diagnostics
plot(lmmodel4a, which=1) #they are desperzed around zero, we see the data that is "ruining" our model
#lets do correlation
vars <- c("midparentHeight", "childHeight", "mother", "father")
cor(GaltonFamilies[,vars])
## midparentHeight childHeight mother father
## midparentHeight 1.0000000 0.3209499 0.72783397 0.72843929
## childHeight 0.3209499 1.0000000 0.20132195 0.26603854
## mother 0.7278340 0.2013219 1.00000000 0.06036612
## father 0.7284393 0.2660385 0.06036612 1.00000000
#we see that there is a big correlation between midparentHeight and mother and father. This means we can not
#use in one model those variables togeter
#Test the initial correlations
#install.packages("psych")
library(psych)
##
## Attaching package: 'psych'
##
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
vars <- c("midparentHeight", "childHeight", "mother", "father")
corr.test(GaltonFamilies[,vars]) #It allows for all complete data to be used in the correlations
## Call:corr.test(x = GaltonFamilies[, vars])
## Correlation matrix
## midparentHeight childHeight mother father
## midparentHeight 1.00 0.32 0.73 0.73
## childHeight 0.32 1.00 0.20 0.27
## mother 0.73 0.20 1.00 0.06
## father 0.73 0.27 0.06 1.00
## Sample Size
## [1] 934
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## midparentHeight childHeight mother father
## midparentHeight 0 0 0.00 0.00
## childHeight 0 0 0.00 0.00
## mother 0 0 0.00 0.07
## father 0 0 0.07 0.00
##
## To see confidence intervals of the correlations, print with the short=FALSE option
#VARIANCE INFLATION FACTOR
library (SparseM) #prvo sparsM pa car
library (car)
## Loading required package: carData
##
## Attaching package: 'car'
##
## The following object is masked from 'package:psych':
##
## logit
vif(lmmodel4a) #vif je variance Inflation Factors. koristimo da objasnimo koliko multicollinearity (correlation between predictors) postoji u regresionoj analizi.
## midparentHeight gender
## 1.001179 1.001179
#High VIFs are a sign of multicollinearity.vif je na neki nacin mjera nepreciznosti.
#rule of thumb:
##VIF = 1 (Not correlated)
##1 < VIF < 5 (Moderately correlated)
##VIF >=5 (Highly correlated)
## STANDARDISED RESIDUALS FOR LMMODEL4
# Extract standardized residuals
standardized_residuals <- rstandard(lmmodel4)
# Display standardized residuals
standardized_residuals
## 1 2 3 4 5 6
## -0.241020653 0.479301623 0.385881355 0.385881355 0.486008463 0.021700762
## 7 8 9 10 11 12
## -0.698271091 -0.698271091 -0.144300524 0.949215015 -0.375534380 -1.300469804
## 13 14 15 16 17 18
## 0.486825673 -0.669147681 -1.362731693 1.294221034 -0.089280912 -0.550448228
## 19 20 21 22 23 24
## 1.160049331 -0.684756638 -0.684756638 1.140198405 1.859400972 0.698419343
## 25 26 27 28 29 30
## 0.234026692 0.234026692 1.604448134 -1.413175105 1.848858570 0.690777115
## 31 32 33 34 35 36
## -0.235688048 -0.229555294 -0.301654092 1.760364680 -0.085388806 1.428941166
## 37 38 39 40 41 42
## 0.967521096 0.967521096 0.506101026 -0.647449150 -0.878159185 0.209247687
## 43 44 45 46 47 48
## -0.349282677 -2.017127657 -1.738535207 -2.201619383 -0.259940877 -0.491341294
## 49 50 51 52 53 54
## 0.241342228 0.469520117 -0.223612167 -0.362238623 -0.362238623 -0.824326813
## 55 56 57 58 59 60
## 1.412322192 0.395861907 -0.528192897 -0.990220299 1.482070942 1.020174857
## 61 62 63 64 65 66
## 0.327330729 -3.829734037 0.478100574 -1.461650845 0.329458579 -0.363070867
## 67 68 69 70 71 72
## -0.593914015 -1.059394689 0.363220405 0.270372845 0.131101504 1.405610286
## 73 74 75 76 77 78
## 0.941511062 0.709461451 0.477411839 -0.450786607 0.563726912 0.980107967
## 79 80 81 82 83 84
## 0.748595809 0.741227001 -0.183928185 0.450265293 1.649704626 -0.058771293
## 85 86 87 88 89 90
## -0.520521542 0.317271442 0.086417205 -0.144437032 -0.144437032 0.004048636
## 91 92 93 94 95 96
## 0.481742266 -0.902609671 0.296631454 0.296631454 -0.395293429 0.184872157
## 97 98 99 100 101 102
## -0.737692495 -0.395293429 -1.317859940 -0.737692495 1.449839592 -1.317859940
## 103 104 105 106 107 108
## 2.721924950 2.491283787 0.876795646 -0.737692495 1.179996291 1.041563446
## 109 110 111 112 113 114
## 0.810842037 -0.111803055 0.622602266 0.161383514 0.161383514 0.734459013
## 115 116 117 118 119 120
## 0.273230247 0.273230247 2.088344021 1.165976476 -0.217574841 1.502408223
## 121 122 123 124 125 126
## -0.342404666 1.165976476 0.935384590 0.935384590 0.243608931 1.733009834
## 127 128 129 130 131 132
## 0.836820233 2.866429042 1.013738804 0.550566245 0.087393685 0.273359077
## 133 134 135 136 137 138
## 0.997790563 0.905360672 -0.943237153 0.602528735 -0.302836468 0.766814604
## 139 140 141 142 143 144
## 0.766814604 0.535949032 -0.302836468 -0.764610905 -0.995498123 0.305083459
## 145 146 147 148 149 150
## -0.387513258 -1.080109974 0.158937969 0.766814604 2.467810154 0.620712406
## 151 152 153 154 155 156
## 0.158937969 -2.149934215 0.305083459 -0.098309617 0.709406639 0.709406639
## 157 158 159 160 161 162
## 0.247785893 -0.675455599 0.387337120 -0.074250570 1.089045612 -0.058198239
## 163 164 165 166 167 168
## -0.899660280 -1.268948484 -1.047877528 -1.047877528 -1.376304256 1.556559175
## 169 170 171 172 173 174
## 1.556559175 1.325913309 0.864621577 0.864621577 0.633975711 0.403329845
## 175 176 177 178 179 180
## 0.172683979 0.771808127 0.310282071 0.079519043 0.906701812 -0.869758129
## 181 182 183 184 185 186
## -0.869758129 -0.869758129 0.804648482 0.343167804 -0.118312874 0.475652387
## 187 188 189 190 191 192
## -0.216535507 -0.216535507 -1.370181998 1.348127528 -1.293700812 1.459782423
## 193 194 195 196 197 198
## 0.076136900 0.602878418 -1.242041531 0.716187519 0.254949781 -0.436906827
## 199 200 201 202 203 204
## 0.691641148 0.230453062 0.230453062 -2.536675456 0.337212609 0.337212609
## 205 206 207 208 209 210
## -0.123993418 -0.585199444 -0.585199444 0.691641148 0.691641148 0.230453062
## 211 212 213 214 215 216
## -0.354596431 0.869244071 0.408073002 0.271172295 -0.651246512 -1.112455915
## 217 218 219 220 221 222
## 1.330415140 0.638658536 0.638658536 0.271172295 -1.804270020 0.319256967
## 223 224 225 226 227 228
## -0.041712207 -0.041712207 -0.041712207 -0.733507081 0.638658536 0.408073002
## 229 230 231 232 233 234
## -0.053098067 -0.053098067 -1.436611274 0.271172295 0.040567593 -0.717433101
## 235 236 237 238 239 240
## 1.813579355 0.658590833 -0.210358217 -0.673011573 -1.135664929 1.351019352
## 241 242 243 244 245 246
## -0.673011573 -1.274460936 0.888452045 -0.036682569 -0.961817183 -1.886951797
## 247 248 249 250 251 252
## 1.816597346 -0.316028236 -0.777827356 0.292894591 -0.630614026 -2.477631262
## 253 254 255 256 257 258
## 0.985526055 1.157910445 0.696268349 0.696268349 -1.842763183 1.852297552
## 259 260 261 262 263 264
## 0.929082501 0.605957234 0.375153471 0.375153471 -0.455740075 -0.686543838
## 265 266 267 268 269 270
## 0.880178959 0.049680629 -0.503984924 -0.734678904 1.468431210 0.084307495
## 271 272 273 274 275 276
## -1.530503505 -1.761190791 -1.761190791 1.423586748 0.962281172 0.270322807
## 277 278 279 280 281 282
## -2.266857863 -2.266857863 -0.070155340 -0.762107781 -1.223409409 -1.344246710
## 283 284 285 286 287 288
## -2.266857863 -0.070155340 -0.992758595 -0.992758595 0.039670019 0.039670019
## 289 290 291 292 293 294
## 1.083098729 0.160495474 0.160495474 -0.762107781 4.191420207 2.346197901
## 295 296 297 298 299 300
## 0.500975595 2.005701984 1.083098729 0.483406613 -1.223409409 1.423586748
## 301 302 303 304 305 306
## 1.192933960 0.160495474 -0.421635557 -0.421635557 1.015490211 0.092965394
## 307 308 309 310 311 312
## -0.506675737 0.901753925 0.440489350 0.071477691 -0.020775224 0.540132198
## 313 314 315 316 317 318
## 0.217297176 -0.705088601 -1.166281489 -1.627474378 -2.088667267 1.247443884
## 319 320 321 322 323 324
## 0.217297176 -0.705088601 -1.304639356 0.555629906 1.104192471 0.181775879
## 325 326 327 328 329 330
## -0.860931581 -1.460518426 -1.967861142 1.980005836 -0.095547061 -0.326164050
## 331 332 333 334 335 336
## -0.787398027 -0.787398027 -0.787398027 0.479476752 0.248856266 -2.139893323
## 337 338 339 340 341 342
## -0.705088601 0.325025247 -0.136184072 -1.058602710 0.678490065 0.217297176
## 343 344 345 346 347 348
## 0.217297176 0.217297176 -0.013299268 -0.474492157 2.169862522 0.325025247
## 349 350 351 352 353 354
## -0.136184072 0.270578590 -1.112950781 -1.804715466 -0.225173264 -0.455772765
## 355 356 357 358 359 360
## -0.778612066 -0.916971767 -1.470410569 0.312678642 -0.379075070 0.643987862
## 361 362 363 364 365 366
## -0.278405176 1.465601494 -0.148490499 -1.070828781 0.182791343 -0.047806916
## 367 368 369 370 371 372
## 0.767270332 -0.846824508 1.560286380 -0.284499927 -0.527424749 -0.988594025
## 373 374 375 376 377 378
## -0.109984211 -0.894034580 0.394913805 -1.219178663 -0.894034580 -1.355240679
## 379 380 381 382 383 384
## 1.412718748 0.490332070 0.259735400 0.259735400 -0.432054608 0.578002829
## 385 386 387 388 389 390
## 0.116761698 -0.344479432 0.721680343 0.260510580 0.029925698 -1.814753354
## 391 392 393 394 395 396
## 0.032034589 -0.198568931 -0.336931042 1.412718748 1.412718748 -1.728202824
## 397 398 399 400 401 402
## 1.304194293 -0.633640643 -0.456169256 -1.610252404 0.984386470 0.060923088
## 403 404 405 406 407 408
## 0.984386470 0.984386470 1.890076466 -1.345098659 0.308423031 2.211235295
## 409 410 411 412 413 414
## -0.563112811 1.778690719 1.316159141 0.391095984 1.891708578 0.043679800
## 415 416 417 418 419 420
## -0.418327395 0.198396547 0.198396547 -0.032578752 -0.263554051 -0.263554051
## 421 422 423 424 425 426
## -0.725504649 -0.725504649 -0.477798765 1.410461617 0.949144146 0.810748904
## 427 428 429 430 431 432
## 0.718485410 0.378962610 0.148306603 -0.912711026 -1.004973428 0.580090168
## 433 434 435 436 437 438
## 0.487826674 0.026509202 2.209371267 1.747917181 0.825009009 -0.790080294
## 439 440 441 442 443 444
## 0.026509202 -0.665467005 -0.896125741 0.148306603 -0.774317422 -1.004973428
## 445 446 447 448 449 450
## 1.321885954 0.399064788 0.168359496 0.168359496 -1.446577545 -1.907988128
## 451 452 453 454 455 456
## -1.779560506 0.086101199 -1.298449004 -0.240945468 -0.471691282 0.399064788
## 457 458 459 460 461 462
## 1.680901447 1.219506520 0.527414129 -0.856770652 -0.856770652 0.405640298
## 463 464 465 466 467 468
## 0.405640298 0.174938839 0.174938839 0.764197489 0.302809470 -0.158578550
## 469 470 471 472 473 474
## 1.410461617 0.949144146 -0.434808269 -0.434808269 0.840274622 0.378962610
## 475 476 477 478 479 480
## 0.378962610 0.148306603 -0.313005409 0.204141233 -0.487656036 -1.179453306
## 481 482 483 484 485 486
## 0.312838042 -0.148375058 -0.378981608 -1.532014359 0.072360573 -0.711671731
## 487 488 489 490 491 492
## -4.401235516 0.411173857 0.088326053 -0.280642866 -1.987124116 1.132843974
## 493 494 495 496 497 498
## -1.265223646 0.446912344 -0.244885229 0.790321447 0.098226920 1.795267539
## 499 500 501 502 503 504
## -0.049862639 1.481907315 1.943134113 0.559453719 0.559453719 -2.207907071
## 505 506 507 508 509 510
## 1.103343722 -0.741786456 0.701180520 -0.912971368 -1.374157622 0.559705560
## 511 512 513 514 515 516
## -0.362757989 -0.823989763 -1.285221537 0.701180520 -0.039895747 -0.362757989
## 517 518 519 520 521 522
## -0.453282824 2.038840862 1.577545697 0.193660203 2.121464364 1.198714847
## 523 524 525 526 527 528
## 1.198714847 0.275965330 -0.115958232 1.577545697 0.654955367 -0.359893995
## 529 530 531 532 533 534
## 0.822849110 0.592168151 0.499895768 0.038533850 0.038533850 -0.422828067
## 535 536 537 538 539 540
## -0.653509026 -0.884189984 1.109656602 0.648366978 0.648366978 0.187077354
## 541 542 543 544 545 546
## 0.032436506 -0.428919111 -0.428919111 -0.659596919 1.660089605 -0.185409429
## 547 548 549 550 551 552
## 1.268394833 1.268394833 0.832985251 0.602239706 0.371494161 -0.027543691
## 553 554 555 556 557 558
## -0.489122109 -0.007706493 -0.007706493 -0.238512549 -1.854154937 -2.315767048
## 559 560 561 562 563 564
## -2.315767048 0.279571623 -0.412991890 -0.412991890 1.325060550 2.523902941
## 565 566 567 568 569 570
## -0.017410316 0.632151645 -0.753666164 -0.387055881 -0.941524228 0.773866107
## 571 572 573 574 575 576
## -0.263247653 -2.075303680 1.315325901 0.392489163 0.982726693 0.019928548
## 577 578 579 580 581 582
## -0.441395055 -0.441395055 -0.579792136 -0.672056857 -0.672056857 -0.902718658
## 583 584 585 586 587 588
## -0.902718658 -0.902718658 -1.733101143 -0.688159281 -0.784321005 -1.476071741
## 589 590 591 592 593 594
## -1.564909885 -0.078280751 1.063784361 0.971549475 0.602609932 -1.795497100
## 595 596 597 598 599 600
## 1.074714327 0.475156886 -1.231275829 1.290931203 1.290931203 1.848802031
## 601 602 603 604 605 606
## 0.926400118 -0.082572600 -0.635980352 -1.558326607 -1.558326607 -0.994580899
## 607 608 609 610 611 612
## -1.225179641 -1.455778383 -1.916975867 1.208712156 0.516952466 -0.313159163
## 613 614 615 616 617 618
## -0.405393789 -0.774332291 -0.072185930 -0.302784672 -0.533383414 1.007505073
## 619 620 621 622 623 624
## -0.376153085 -0.376153085 -0.837372472 0.629857282 0.168583665 -0.292689951
## 625 626 627 628 629 630
## -0.292689951 -0.753963568 -1.215237184 -1.298591858 -2.682250017 0.860494090
## 631 632 633 634 635 636
## -0.753963568 1.099748950 1.099748950 0.085066301 -0.145543392 -0.523326760
## 637 638 639 640 641 642
## -0.836169926 0.085066301 -0.837372472 -1.298591858 1.091130898 1.091130898
## 643 644 645 646 647 648
## 0.629857282 0.629857282 0.629857282 0.168583665 -0.292689951 0.954834974
## 649 650 651 652 653 654
## 0.724154606 -0.198566868 -1.121288342 -1.121288342 1.256156358 -0.589585550
## 655 656 657 658 659 660
## -0.820303289 2.167150185 0.552869577 0.322258061 0.866598096 -0.659927605
## 661 662 663 664 665 666
## 0.724154606 -0.198566868 0.564003143 0.333285404 1.185515343 -0.198566868
## 667 668 669 670 671 672
## -1.121288342 -1.351968711 -1.582649079 -0.128150073 -0.589585550 -0.589585550
## 673 674 675 676 677 678
## -0.659927605 -0.659927605 -1.121288342 0.333285404 0.102567665 -1.051021027
## 679 680 681 682 683 684
## -0.277331879 0.724154606 0.602257152 0.141002887 -0.781505642 -1.473387040
## 685 686 687 688 689 690
## 0.451074624 0.120991561 -0.274492707 -0.670199975 -0.801938247 0.387979479
## 691 692 693 694 695 696
## 0.157023506 -1.690624272 0.432407447 0.201393405 -0.301340503 -1.514055856
## 697 698 699 700 701 702
## -0.558330030 -0.558330030 -1.020789898 -1.020789898 -1.020789898 -2.870629370
## 703 704 705 706 707 708
## 0.104073820 -0.127087563 -0.358248945 -1.020789898 0.893687988 0.513864461
## 709 710 711 712 713 714
## -0.874609451 -1.013456842 -1.337434089 -1.337434089 -1.800258726 1.458164918
## 715 716 717 718 719 720
## 1.458164918 0.069216127 -0.393766803 1.565069448 1.565069448 1.011667384
## 721 722 723 724 725 726
## 0.650692158 -0.271701034 0.727809189 1.738939576 0.816605915 0.678255866
## 727 728 729 730 731 732
## 0.355439085 -0.105727745 1.836605162 0.683607366 -0.930589548 0.394754905
## 733 734 735 736 737 738
## -0.619912514 0.848287102 0.617654513 0.387021924 -0.074243254 0.444263748
## 739 740 741 742 743 744
## -0.016914768 0.765922846 0.765922846 -0.387129680 0.444263748 -0.616446840
## 745 746 747 748 749 750
## -0.387129680 -1.770792712 -1.772943672 -0.766141020 -0.766141020 0.912024665
## 751 752 753 754 755 756
## -0.010335870 0.080186805 0.080186805 -0.381036713 -0.381036713 -0.381036713
## 757 758 759 760 761 762
## -0.381036713 -0.381036713 -0.611648472 -0.842260231 1.402991488 0.710970679
## 763 764 765 766 767 768
## -0.673070938 -0.673070938 1.261441730 0.892283282 0.430835222 0.107821579
## 769 770 771 772 773 774
## -0.122902451 -0.584350511 -1.276522602 0.172729173 0.427527319 -0.034043974
## 775 776 777 778 779 780
## 0.024308855 0.984910087 0.754045767 0.523181447 0.292317127 1.498313985
## 781 782 783 784 785 786
## -0.140267906 0.572865159 0.572865159 -1.041219312 -1.502386304 -1.502386304
## 787 788 789 790 791 792
## -0.942776289 -0.942776289 -1.173375173 1.264615647 -1.963553295 -1.963553295
## 793 794 795 796 797 798
## 1.363212555 -0.020380751 -0.020380751 -0.942776289 -1.865171826 -1.865171826
## 799 800 801 802 803 804
## -1.324871569 -1.786077598 1.527967289 1.297338675 0.836081446 1.442364604
## 805 806 807 808 809 810
## -0.402459512 1.066710061 0.605452832 -0.778318853 -1.239576081 0.015786969
## 811 812 813 814 815 816
## -0.076465782 -0.998993294 -1.921520805 -0.459373661 -1.382025562 -1.382025562
## 817 818 819 820 821 822
## -2.766003415 1.531361252 1.070102303 -0.774933494 1.149156877 0.687836492
## 823 824 825 826 827 828
## 1.054368427 0.787191127 -0.367300408 -0.321087511 -0.413428590 -1.336839381
## 829 830 831 832 833 834
## 1.024219150 1.024219150 0.100601511 1.060987173 0.137243402 0.414052353
## 835 836 837 838 839 840
## -0.047933355 -0.047933355 -0.047933355 -0.047933355 1.323011032 0.666439318
## 841 842 843 844 845 846
## 0.203114681 -0.723534593 -0.716829817 -0.723534593 0.846124420 0.382126826
## 847 848 849 850 851 852
## 0.150128029 -0.081870767 -0.221070046 -0.313869564 -0.545868361 1.768702623
## 853 854 855 856 857 858
## 1.304506766 0.840310910 0.376115054 -0.088080803 -0.552276659 -1.480668372
## 859 860 861 862 863 864
## -1.944864228 -1.107412939 -1.338012981 -1.338012981 0.593252201 -0.329247335
## 865 866 867 868 869 870
## -2.544643971 -0.164721716 -0.164721716 -1.548897078 -0.699357516 -1.160679130
## 871 872 873 874 875 876
## -1.622000744 0.758061859 -1.087505291 0.401155389 -0.060377054 -0.060377054
## 877 878 879 880 881 882
## 0.923151657 0.923151657 -0.461717982 -0.461717982 -0.923341195 -1.846587622
## 883 884 885 886 887 888
## 1.096599623 1.071313871 0.493461878 0.401155389 -0.060377054 -0.198836787
## 889 890 891 892 893 894
## 0.692340050 -1.154152802 -0.344365930 -0.344365930 0.626673800 0.626673800
## 895 896 897 898 899 900
## -0.066242873 -0.990131771 1.220047500 0.329847182 -0.628847022 -0.628847022
## 901 902 903 904 905 906
## 0.329847182 1.599183059 1.599183059 0.675120052 0.484438156 0.749543652
## 907 908 909 910 911 912
## 0.749543652 0.285919070 0.285919070 0.286928956 1.900063507 0.282392966
## 913 914 915 916 917 918
## 1.473410153 0.779926473 -0.144718434 -0.144718434 -0.607040888 1.437871924
## 919 920 921 922 923 924
## 0.282392966 2.166893833 1.242248926 0.779926473 0.779926473 -1.069363341
## 925 926 927 928 929 930
## -1.158444911 0.070467932 -0.411776633 3.100518364 0.785231044 -1.592531201
## 931 932 933 934
## -0.169132772 -0.631389516 0.014419231 -2.068227579
# Residuals vs. Fitted values plot
plot(lmmodel4$fitted.values, standardized_residuals,
xlab = "Fitted Values", ylab = "Standardized Residuals",
main = "Residuals vs Fitted")
abline(h = 0, col = "red")
#sa nasim rezultatom smo ok VIF je oko 1
##DISPLAYING REGRESSION RESULTS
#displaying regression results
library(xtable)
library(texreg)
## Version: 1.39.4
## Date: 2024-07-23
## Author: Philip Leifeld (University of Manchester)
##
## Consider submitting praise using the praise or praise_interactive functions.
## Please cite the JSS article in your publications -- see citation("texreg").
screenreg(list(lmmodel, lmmodel2, lmmodel3, lmmodel4, lmmodel4a))
##
## ======================================================================================
## Model 1 Model 2 Model 3 Model 4 Model 5
## --------------------------------------------------------------------------------------
## (Intercept) 22.64 *** 22.64 *** 64.10 *** 18.33 *** 16.51 ***
## (4.27) (4.26) (0.12) (3.87) (2.73)
## midparentHeight 0.64 *** 0.66 *** 0.69 ***
## (0.06) (0.06) (0.04)
## mother 0.29 ***
## (0.05)
## father 0.37 ***
## (0.04)
## gendermale 5.13 *** 1.58 5.22 ***
## (0.16) (5.46) (0.14)
## midparentHeight:gendermale 0.05
## (0.08)
## --------------------------------------------------------------------------------------
## R^2 0.10 0.11 0.51 0.63 0.63
## Adj. R^2 0.10 0.10 0.51 0.63 0.63
## Num. obs. 934 934 934 934 934
## ======================================================================================
## *** p < 0.001; ** p < 0.01; * p < 0.05
#displaying for descriptive statistics- also stargazer good and regreesion
library(stargazer)
##
## Please cite as:
##
## Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.
## R package version 5.2.3. https://CRAN.R-project.org/package=stargazer
stargazer(GaltonFamilies, type = "text", title = "Descriptive statistics", digits = 2, out = "Descriptive statistics.txt")
##
## Descriptive statistics
## ==============================================
## Statistic N Mean St. Dev. Min Max
## ----------------------------------------------
## father 934 69.20 2.48 62.00 78.50
## mother 934 64.09 2.29 58.00 70.50
## midparentHeight 934 69.21 1.80 64.40 75.43
## children 934 6.17 2.73 1 15
## childNum 934 3.59 2.36 1 15
## childHeight 934 66.75 3.58 56.00 79.00
## ----------------------------------------------
#the dabase HAS TO BE in dataframe format. Then, it will give the descriptive statistics for all numeric variables
stargazer(lmmodel, lmmodel2, lmmodel3, lmmodel4, lmmodel4a, type = "text", title="Results", align=TRUE, out = "regressions.txt")
##
## Results
## ======================================================================================================================================================
## Dependent variable:
## ---------------------------------------------------------------------------------------------------------------------------
## childHeight
## (1) (2) (3) (4) (5)
## ------------------------------------------------------------------------------------------------------------------------------------------------------
## midparentHeight 0.637*** 0.661*** 0.687***
## (0.062) (0.056) (0.039)
##
## mother 0.291***
## (0.049)
##
## father 0.368***
## (0.045)
##
## gendermale 5.130*** 1.580 5.215***
## (0.164) (5.463) (0.142)
##
## midparentHeight:gendermale 0.053
## (0.079)
##
## Constant 22.636*** 22.643*** 64.104*** 18.333*** 16.514***
## (4.265) (4.262) (0.117) (3.866) (2.734)
##
## ------------------------------------------------------------------------------------------------------------------------------------------------------
## Observations 934 934 934 934 934
## R2 0.103 0.105 0.514 0.633 0.633
## Adjusted R2 0.102 0.103 0.513 0.632 0.632
## Residual Std. Error 3.392 (df = 932) 3.389 (df = 931) 2.497 (df = 932) 2.171 (df = 930) 2.170 (df = 931)
## F Statistic 107.029*** (df = 1; 932) 54.742*** (df = 2; 931) 984.402*** (df = 1; 932) 535.585*** (df = 3; 930) 803.636*** (df = 2; 931)
## ======================================================================================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01
#otvorite folder u kojem se nalayite i otvorite file regression