Regresi Linear dengan R
Purwoko Haryadi Santoso
Import data
Dataset Cassidy diperoleh dari buku Multilevel Modeling using R yang ditulis oleh Finch, Bollin, & Kelley (2014). Link unduh dataset , pilih “Cassidy”
Cassidy <- read.csv("Cassidy.csv", header = T, sep = ",")
Cassidystr(Cassidy)'data.frame': 486 obs. of 30 variables:
$ Gender : int 2 1 2 2 2 2 2 2 2 2 ...
$ Male : int 1 0 1 1 1 1 1 1 1 1 ...
$ Minority : int 1 1 1 1 1 1 0 1 1 1 ...
$ Age : int 21 20 21 22 21 21 21 21 21 20 ...
$ GPA : num 2.5 2.2 2.8 2.25 3.1 ...
$ Verbal : int NA NA NA NA NA 600 NA 525 NA NA ...
$ Math : int NA NA NA NA NA 600 NA 600 NA NA ...
$ TotSAT : int NA NA NA NA NA 1200 NA 1125 NA NA ...
$ SSH.total : int 20 20 18 18 19 21 22 32 20 31 ...
$ BStotal : int 14 20 23 30 17 NA 15 34 19 10 ...
$ CTA.tot : int 42 NA 40 49 36 45 49 61 36 17 ...
$ PTTtotal : int NA 44 47 47 46 57 50 59 40 35 ...
$ PTT.factor1 : int 25 27 25 26 22 34 31 34 20 23 ...
$ PTT.factor2 : int NA 13 16 13 17 17 13 5 13 7 ...
$ PTT.factor3 : int 11 4 6 8 7 6 6 20 7 5 ...
$ Perf.CM : int 25 31 27 22 33 28 25 42 20 9 ...
$ Perf.D : int 10 12 14 12 16 10 16 19 12 4 ...
$ Perf.PE : int 17 18 18 13 21 19 14 22 18 7 ...
$ Perf.PC : int 10 13 10 10 16 9 12 15 7 4 ...
$ Perf.PS : int 26 28 25 21 26 25 27 31 21 22 ...
$ Perf.O : int 24 30 24 18 25 22 28 30 24 23 ...
$ harvey.negproj: int 32 39 37 32 46 36 37 56 30 12 ...
$ harvey.achexp : int 29 32 29 23 29 27 31 36 23 23 ...
$ harvey.parinf : int 27 31 28 23 37 28 26 37 25 11 ...
$ harvey.org : int 24 30 24 18 25 22 28 30 24 23 ...
$ stoeberORG : int 24 30 24 18 25 22 28 30 24 23 ...
$ stoeberCMD : int 32 39 37 32 46 36 37 56 30 12 ...
$ stoeberPEC : int 27 31 28 23 37 28 26 37 25 11 ...
$ stoeberPS : int 26 29 25 20 25 24 27 32 19 18 ...
$ Harvey4f : int 1 4 1 1 4 1 3 4 1 2 ...Jalankan Pemodelan Regresi Linear
Model regresinya ditulis sebagai berikut. Sesuai dengan contoh yang disajikan dalam Finch, Bollin, & Kelley (2014, p.28), dalam dataset Cassidy GPA akan diprediksi melalui variabel ukuran kecemasan fisik (BSTotal) dan Cognitive Test Anxiety (CTA.tot)
Model1.1 <- lm(GPA ~ CTA.tot + BStotal, Cassidy)
Model1.1
Call:
lm(formula = GPA ~ CTA.tot + BStotal, data = Cassidy)
Coefficients:
(Intercept) CTA.tot BStotal
3.61892 -0.02007 0.01347 Hasil Pemodelan
summary(Model1.1)
Call:
lm(formula = GPA ~ CTA.tot + BStotal, data = Cassidy)
Residuals:
Min 1Q Median 3Q Max
-2.99239 -0.29138 0.01516 0.36849 0.93941
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.618924 0.079305 45.633 < 2e-16 ***
CTA.tot -0.020068 0.003065 -6.547 1.69e-10 ***
BStotal 0.013469 0.005077 2.653 0.00828 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.4852 on 426 degrees of freedom
(57 observations deleted due to missingness)
Multiple R-squared: 0.1066, Adjusted R-squared: 0.1024
F-statistic: 25.43 on 2 and 426 DF, p-value: 3.706e-11ANOVA
anova(Model1.1)Analysis of Variance Table
Response: GPA
Df Sum Sq Mean Sq F value Pr(>F)
CTA.tot 1 10.316 10.3159 43.8125 1.089e-10 ***
BStotal 1 1.657 1.6570 7.0376 0.00828 **
Residuals 426 100.304 0.2355
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Output yang bisa disediakan R dalam packages lm
attributes(Model1.1)$names
[1] "coefficients" "residuals" "effects" "rank" "fitted.values" "assign" "qr" "df.residual"
[9] "na.action" "xlevels" "call" "terms" "model"
$class
[1] "lm"Nilai GPA yang diprediksi
Model1.1$fitted.values 1 3 4 5 8 9 10 11 12 13 14 15 16 17
2.964641 3.125996 3.039668 3.125454 2.852730 3.152391 3.412460 3.011917 2.611103 3.158448 3.298923 3.312121 2.959938 3.205183
19 23 25 26 27 28 29 30 31 34 35 37 38 39
2.945928 2.904979 3.226064 3.245318 2.944573 3.171646 2.917635 3.198584 3.206267 3.073204 3.258787 3.118584 2.972594 2.870630
41 42 43 44 45 46 48 50 51 52 53 54 55 56
3.144980 3.285454 3.386064 2.871713 2.911849 3.166131 3.051511 3.251917 3.080345 3.131782 3.292053 3.138923 3.372324 3.372324
57 58 59 60 61 62 63 65 66 67 68 69 70 71
3.065521 3.212324 3.325590 3.093543 3.172459 2.918177 3.104844 2.985250 3.225251 3.245318 3.151849 2.937703 2.978109 3.058651
72 73 74 75 76 77 79 80 81 83 84 86 87 88
2.852188 3.011375 3.225251 3.253272 3.118313 3.292053 2.664979 2.998448 2.878041 2.737025 3.185928 3.232121 3.225793 3.106199
89 90 91 92 93 94 95 96 97 99 100 101 102 103
2.885995 2.978380 3.231850 3.111443 3.292053 2.924505 3.266741 3.192256 3.012730 3.053407 3.119126 3.053949 3.044912 2.997906
104 106 107 108 109 111 112 113 114 117 118 119 120 121
3.327757 3.058651 3.098245 2.985792 3.486674 2.898109 3.211782 3.185115 3.225793 3.199939 2.891781 3.191714 3.298923 3.118313
122 123 124 125 126 127 128 129 130 131 132 133 134 135
2.885453 3.091375 2.898651 3.118313 2.818922 3.019058 3.032256 2.937703 3.246673 3.084776 2.924234 2.797499 3.078448 2.891781
136 137 138 139 140 141 142 143 144 145 147 148 149 150
2.784843 2.925047 3.232121 3.158448 2.697160 2.978109 2.991578 2.965995 2.712255 2.924505 2.985521 3.139194 3.104844 3.111443
151 152 153 155 156 158 161 162 163 164 165 166 167 168
3.011104 2.817567 3.286538 3.366267 3.139194 3.091375 2.783759 3.271985 3.171917 3.265657 2.925047 2.985250 2.965453 3.104844
169 171 172 174 175 176 177 178 179 180 181 182 183 185
3.392392 3.131511 3.078448 3.205996 2.851646 3.073204 2.851375 2.964641 3.231850 3.292053 3.332460 2.980277 3.167215 2.737838
186 187 188 189 190 191 192 193 195 196 197 198 199 200
3.185115 3.118855 2.831307 3.004776 3.225793 3.231850 3.266199 3.111443 3.138652 3.040210 2.897838 3.144980 3.059464 3.332189
202 203 204 205 207 209 210 213 214 215 216 217 218 219
3.219194 2.892865 3.231850 3.058110 3.232392 3.205725 2.777973 3.132866 3.178516 3.238720 2.851104 3.171646 3.004505 3.251917
220 221 222 223 224 225 226 227 228 229 230 231 232 233
3.018787 2.925318 3.265386 2.991307 3.098787 3.126267 2.992391 3.151849 3.031172 3.025386 3.252188 3.158448 2.890968 3.426470
234 235 236 237 238 239 240 241 242 243 244 245 246 247
3.165047 2.925589 3.251917 3.225251 3.126267 3.191714 3.118313 2.957771 2.906063 3.258787 3.051511 2.972323 3.225251 3.151579
248 250 251 252 253 254 255 257 258 259 260 261 262 263
3.024573 3.365725 3.132053 2.911849 2.884369 3.252188 3.158448 2.818651 3.005318 3.112527 3.131782 3.225251 3.151579 3.205183
264 265 266 267 268 269 270 271 272 273 274 275 276 277
3.144980 3.125454 3.118584 3.238720 3.360210 2.984708 3.178787 2.811239 3.151579 3.205183 3.118313 3.365725 3.219465 3.278855
279 280 281 282 283 286 287 289 290 291 292 293 294 295
2.930833 3.004505 2.972052 3.111443 3.118313 3.238720 2.924234 3.312121 3.292053 3.038042 3.118313 2.803827 3.265657 3.192527
296 297 298 299 300 301 302 303 304 305 306 307 308 309
3.392392 2.777973 3.145792 3.105386 3.158448 3.086131 3.105386 3.271985 2.958854 2.931917 3.185928 3.158719 3.071307 3.011375
310 311 312 313 315 316 317 318 319 320 321 323 324 325
3.238991 3.238720 3.353069 2.944302 3.085047 3.392392 3.245589 3.171917 2.792526 3.125725 3.278855 3.259058 2.951172 2.817296
326 327 328 329 330 331 332 333 334 335 336 337 338 340
3.251917 3.111443 3.091917 3.234017 3.292053 3.285454 3.119126 3.231850 2.811239 3.305522 3.205183 3.212324 2.892323 3.165860
341 342 343 344 345 346 347 348 349 350 351 352 353 354
2.804640 3.386064 3.099329 3.399533 3.252188 3.091375 3.359126 2.838990 3.399533 3.392392 3.285454 3.392392 3.385793 3.098245
355 356 357 358 360 362 363 364 365 367 369 370 371 372
3.279397 3.018245 3.078448 3.372324 3.120210 3.251917 3.285725 3.111714 3.392663 3.339058 3.078448 3.191985 3.104844 3.231850
373 374 375 376 377 378 379 380 382 384 385 386 387 388
3.245318 2.730426 3.205725 3.245589 3.225251 3.025115 3.285725 3.064979 2.978109 2.977838 3.219465 3.138381 3.059193 2.992933
389 390 391 392 394 395 396 397 398 399 400 401 402 403
3.078177 2.958042 3.211782 2.998448 2.830494 3.131511 3.500414 3.379194 3.385793 3.172188 3.138652 3.386064 3.085589 3.005589
404 405 406 407 408 409 410 411 412 413 414 415 416 417
3.259600 3.352256 3.118584 3.372324 3.085047 3.191985 3.285454 3.312392 3.231850 3.159803 3.191714 3.258787 2.944573 3.124912
418 419 420 421 422 423 424 425 426 427 428 429 430 431
3.105115 3.211782 3.278855 3.399262 3.051240 3.025115 2.959396 3.199668 3.258787 3.266199 3.238720 3.392392 3.305522 3.178516
432 433 434 435 436 437 438 439 440 441 442 445 446 447
3.312121 3.238720 3.198584 3.272256 3.292053 3.206267 3.179329 3.365725 3.292053 3.372324 3.345657 3.158990 3.131511 3.071307
448 449 450 451 452 453 454 455 456 457 458 459 460 461
3.305793 3.171646 3.312121 3.071307 3.065521 3.339058 3.113069 3.426200 2.925860 3.231850 3.251917 2.984437 3.312392 2.931375
462 463 464 465 466 467 468 469 470 471 472 473 475 476
3.392392 3.379194 3.447080 3.198855 3.392392 3.379465 3.205454 3.412460 3.225251 3.305522 3.091375 3.392392 3.024573 3.318991
477 478 479 480 481 482 483 484 485
3.392392 3.425929 3.386064 3.459736 3.199397 3.312121 3.192256 2.864031 3.245318 Residu
Model1.1$residuals 1 3 4 5 8 9 10 11 12
-0.4646405061 -0.3259956916 -0.7896675749 -0.0254537419 0.4492704297 -0.0283914353 -0.1124596847 -0.5119169570 0.0888967457
13 14 15 16 17 19 23 25 26
-0.6584484215 -0.7989228998 -0.4221207716 -0.5799383942 -0.3051829226 -0.1459275978 -0.8649791080 0.0989363702 -0.2453184879
27 28 29 30 31 34 35 37 38
-0.4445727235 0.7783537067 -0.8176350301 0.1014160133 0.3937331779 -0.1232042042 0.3412126654 0.4814161689 0.9394056837
39 41 42 43 44 45 46 48 50
-0.6706295541 -0.5449795748 -0.4194540531 -0.4960639410 -0.0717134535 -0.4118490187 0.4338687432 0.7484894275 0.4480825762
51 52 53 54 55 56 57 58 59
0.1496549101 -0.3317817030 -0.0920529890 0.1910774114 0.4276758805 0.6276758805 0.5244786311 0.0156761917 0.3744103817
60 61 62 63 65 66 67 68 69
0.7564570383 0.2275407821 0.1818230202 0.1951559904 -0.0142502384 -0.2252507053 -0.3453184879 0.0481505144 -0.1377028127
70 71 72 73 74 75 76 77 79
-0.7281093528 -0.5586514581 0.3478123794 -0.1113750073 0.5747492947 0.1467277019 0.2116871437 0.1579470110 -0.0849786411
80 81 83 84 86 87 88 89 90
0.6015518897 -0.0780414146 0.2209750135 -0.8859280646 0.3778793840 0.6642073450 -0.6061988838 -0.0859952248 -0.0783803277
91 92 93 94 95 96 97 99 100
-0.4318496412 -0.6114429455 -0.1220529890 -0.9245049409 0.1932588552 -0.1922560257 -0.1127298815 -0.1534073965 0.6808742192
101 102 103 104 106 107 108 109 111
-0.0539493462 -0.2449116366 0.1020938394 -0.6277574172 0.3413485419 0.4017549264 0.0142078119 -0.4866738290 0.0018908028
112 113 114 117 118 119 120 121 122
-0.5017818586 0.5148848600 -0.3257926550 -0.4999388610 -0.6417812361 0.4682859240 0.2010771002 -0.2183128563 0.1145467249
123 124 125 126 127 128 129 130 131
0.8086248371 -0.9986511469 0.1816871437 -0.3189219661 -0.0190578426 -0.5322557144 -0.7877028127 0.0533266379 -0.7507762269
132 133 134 135 136 137 138 139 140
-0.4742339660 0.4025006907 -0.0784482659 -0.1917812361 0.0151566129 0.3749531094 -0.1321206160 0.6415515785 0.0028396038
141 142 143 144 145 147 148 149 150
0.2218906472 0.8304218005 0.0340046196 0.7877449080 -0.9245049409 0.5904787867 -0.2391935634 -0.5048440096 0.0885570545
151 152 153 155 156 158 161 162 163
-0.5111040324 0.2824329081 -0.2865379525 0.1297328667 0.2608064366 -0.2913751629 0.9212405123 0.2280147936 -0.3719172682
164 165 166 167 168 169 171 172 174
0.3343427547 0.2749531094 -0.3852502384 -0.5654534307 0.6951559904 -0.8923919021 0.0684892719 -1.0784482659 -0.6409958472
175 176 177 178 179 180 181 182 183
-0.1516456709 0.4267957958 0.1486253040 0.0353594939 -0.4318496412 -0.0920529890 -0.0324595291 0.6197228484 -0.1672151562
185 186 187 188 189 190 191 192 193
-0.0378379111 -0.1851151400 0.3811451940 0.5016930866 0.6452239287 0.5342073450 -0.0318496412 0.0338008049 -0.4114429455
195 196 197 198 199 200 202 203 204
0.5313483863 -1.0402095246 -0.3978382223 -0.4449795748 -0.0374643827 -0.1321885543 -1.3191937190 -0.1778651355 -0.5318496412
205 207 209 210 213 214 215 216 217
-0.0781095084 -0.9323915909 0.4942751276 -0.0779734763 -0.1328656024 -0.8785162041 0.3612804480 -0.4511037212 0.4283537067
218 219 220 221 222 223 224 225 226
-0.0045050965 0.1580825762 0.1812131323 -0.0423178654 0.3346137295 0.1086927754 -0.0987870234 -0.6262666665 -2.9923911241
227 228 229 230 231 232 233 234 235
-0.6168494856 0.2688281850 0.4746141963 0.3478116013 0.1415515785 -0.5909683116 -0.7264704811 -0.0650473574 0.0644111597
236 237 238 239 240 241 242 243 244
-1.1519174238 -0.9252507053 -0.9262666665 -0.1917140760 -0.0183128563 0.0422294047 0.2939369926 -0.2587873346 -0.0715105725
245 246 247 248 250 251 252 253 254
-0.1723233414 0.0747492947 -0.2515785107 0.0754271209 -0.4657251836 0.1679473222 -0.2118490187 0.2156306244 0.2178116013
255 257 258 259 260 261 262 263 264
0.2415515785 0.5813490087 0.1946819790 0.3764731551 0.3682182970 0.1747492947 -0.3785785107 -0.1051829226 0.7210204252
265 266 267 268 269 270 271 272 273
-0.6254537419 -0.9185838311 -0.0387195520 -0.1602101471 0.5152917113 0.0912128210 -0.5112391308 0.4484214893 -0.9051829226
274 275 276 277 279 280 281 282 283
-0.6183128563 -0.9657251836 -0.6194646939 0.5211448828 0.0691670981 -0.2045050965 0.9279476334 0.3485570545 -0.0183128563
286 287 289 290 291 292 293 294 295
0.2112804480 -0.4242339660 -0.6121207716 -1.4920529890 -0.2380417258 -0.1183128563 0.1761727297 -0.7656572453 -1.1925270005
296 297 298 299 300 301 302 303 304
0.0486080979 -0.7779734763 0.3542075006 -0.6353859593 0.5915515785 0.2438688988 -0.0053859593 -0.1719852064 0.3411455053
305 306 307 308 309 310 311 312 313
0.0680831986 -0.6859280646 0.2412806037 -0.5713073803 -0.1493750073 -0.0389905268 -0.1387195520 0.2969307386 -0.1443017486
315 316 317 318 319 320 321 323 324
0.2149527982 -0.3923919021 0.0544105373 0.4980827318 0.4074737775 -0.0257247167 -0.3988551172 0.0409416906 0.0358283406
325 326 327 328 329 330 331 332 333
0.5827038830 0.0480825762 0.7885570545 0.7080828874 0.2099825600 0.4679470110 -0.2854540531 0.4608742192 -0.3418496412
334 335 336 337 338 340 341 342 343
0.2887608692 0.1944781643 -0.4551829226 -0.2123238083 0.1076768142 -0.1858602820 -0.6366401949 0.3959360590 0.0006710269
344 345 346 347 348 349 350 351 352
0.3334672123 0.6478116013 0.5786248371 0.4408737523 -0.0389897488 -0.1995327877 -0.4923919021 0.2145459469 0.1076080979
353 354 355 356 357 358 360 362 363
0.2372070338 -0.4982450736 0.6806029331 0.4717550820 0.5275517341 -0.2723241195 0.5797903198 0.6680825762 -0.2857250280
364 365 367 369 370 371 372 373 374
-0.1117139203 -0.1926628770 0.0809415350 0.2215517341 -0.4419850508 0.5951559904 -0.0238496412 0.2546815121 0.4095739494
375 376 377 378 379 380 382 384 385
-0.5057248724 0.3544105373 -0.3252507053 -0.3251148288 -1.0857250280 -0.1649794192 -0.0881093528 -0.0278383779 0.2805353061
386 387 388 389 390 391 392 394 395
0.7716193611 0.7408065922 0.3070669262 -0.0781772910 -0.1580415702 -0.4117818586 0.5675518897 0.1695060111 0.3684892719
396 397 398 399 400 401 402 403 404
-0.0004136505 0.2208059697 0.2142070338 0.4078117570 0.5613483863 0.5139360590 0.0504108485 0.6944110041 -0.1496002591
405 406 407 408 409 410 411 412 413
-0.0522563369 -0.5185838311 -0.0723241195 0.7149527982 -0.1919850508 0.7145459469 -0.1123917465 0.1681503588 -0.0598032958
414 415 416 417 418 419 420 421 422
-0.4917140760 0.0412126654 0.2554272765 -0.5249117922 -0.2051149844 0.2832181414 0.3211448828 -0.0992618129 0.5487604024
423 424 425 426 427 428 429 430 431
0.2748851712 0.6376035555 0.7003321139 -0.7587873346 0.1338008049 0.5612804480 0.0066080979 -0.0055218357 0.5214837959
432 433 434 435 436 437 438 439 440
0.1878792284 0.2612804480 -0.2085839867 0.4747438187 0.4969470110 -0.9062668221 0.5206708713 -0.2257251836 -0.1820529890
441 442 445 446 447 448 449 450 451
0.0276758805 0.5543425990 0.6310096288 0.0014892719 0.1286926197 0.4442071894 -0.1716462933 -0.5121207716 -0.3713073803
452 453 454 455 456 457 458 459 460
0.1534786311 0.2609415350 0.6369312054 0.5338004937 0.5741401849 -0.0318496412 0.2480825762 -0.2844373139 0.4876082535
461 462 463 464 465 466 467 468 469
0.7686251484 0.4076080979 0.4208059697 -0.4470802135 0.8011450384 0.4076080979 -0.5484650051 0.6945461025 0.4505403153
470 471 472 473 475 476 477 478 479
0.7047492947 0.6804781643 0.4856248371 0.5776080979 0.8434271209 -0.0189906824 -0.0923919021 0.5740714686 0.4139360590
480 481 482 483 484 485
0.5202638644 -0.2993969113 0.6018792284 0.8077439743 0.0359693818 -0.7453184879 Model Regresi dengan Interaksi (Mediation Analysis)
Model1.2 <- lm(GPA ~ CTA.tot + BStotal + CTA.tot*BStotal,
Cassidy)
summary(Model1.2)
Call:
lm(formula = GPA ~ CTA.tot + BStotal + CTA.tot * BStotal, data = Cassidy)
Residuals:
Min 1Q Median 3Q Max
-2.98711 -0.29737 0.01801 0.36340 0.95016
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.8977792 0.2307491 16.892 < 2e-16 ***
CTA.tot -0.0267935 0.0060581 -4.423 1.24e-05 ***
BStotal -0.0057595 0.0157812 -0.365 0.715
CTA.tot:BStotal 0.0004328 0.0003364 1.287 0.199
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.4849 on 425 degrees of freedom
(57 observations deleted due to missingness)
Multiple R-squared: 0.1101, Adjusted R-squared: 0.1038
F-statistic: 17.53 on 3 and 425 DF, p-value: 9.558e-11Model Regresi dengan Variabel Bebas Kategori
Disini kita memasukkan variabel Male (0 : Perempuan, 1 : Laki-laki)
Model1.4 <- lm(GPA~CTA.tot + Male, Cassidy)
summary(Model1.4)
Call:
lm(formula = GPA ~ CTA.tot + Male, data = Cassidy)
Residuals:
Min 1Q Median 3Q Max
-3.01149 -0.29005 0.03038 0.35374 0.96294
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.740318 0.080940 46.211 < 2e-16 ***
CTA.tot -0.015184 0.002117 -7.173 3.16e-12 ***
Male -0.222594 0.047152 -4.721 3.17e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.4775 on 437 degrees of freedom
(46 observations deleted due to missingness)
Multiple R-squared: 0.1364, Adjusted R-squared: 0.1324
F-statistic: 34.51 on 2 and 437 DF, p-value: 1.215e-14GPAmodel1.5 <- lm(GPA~CTA.tot + Minority, Cassidy)
summary(GPAmodel1.5)
Call:
lm(formula = GPA ~ CTA.tot + Minority, data = Cassidy)
Residuals:
Min 1Q Median 3Q Max
-2.95593 -0.27885 0.01024 0.37506 1.11245
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.331752 0.118509 28.114 < 2e-16 ***
CTA.tot -0.014555 0.002137 -6.812 3.21e-11 ***
Minority 0.322835 0.096014 3.362 0.000841 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.4833 on 437 degrees of freedom
(46 observations deleted due to missingness)
Multiple R-squared: 0.1152, Adjusted R-squared: 0.1112
F-statistic: 28.46 on 2 and 437 DF, p-value: 2.403e-12Uji Asumsi Regresi Linear
Fungsi residualPlots melakukan uji lack-of-fit
dimana t-test dari kuadrat prediktor di-plot terhadap residual (sumbu
y) dan dibuat garis kecocokan untuk memeriksa pola nonlinear di
dalam data.
Uji Tukey untuk non-additivity juga dihitung pada
residualPlots terhadap nilai y-pred untuk menambah
informasi tentang kecukupan dari model fit along with uji lack-of-fit
untuk setiap prediktor.
Statistik Tukey diperoleh dengan menambahkan kuadrat dari nilai y-pred
pada model regresi awal. Ini akan menguji hipotesis nol bahwa model
aditif dan tidak ada interaksi diantara variabel bebas (Tukey,
1949).
Hasil nonsignifikan (Ho diterima) berarti bahwa tidak ada interaksi
variabel bebas di dalam model.
library(car)
residualPlots(Model1.1) Test stat Pr(>|Test stat|)
CTA.tot 1.1085 0.2683
BStotal 0.5973 0.5506
Tukey test 0.4988 0.6179
Melalui residualPlots kita bisa menguji asumsi dalam
model regresi. Pertama, asumsi homogenitas varians melalui fitted plot.
Jika asumsi dipenuhi, plot kita seharusnya tidak berbentuk awan dari
titik data dengan jarak yang sama untuk semua nilai x.
Kemudian asumsi linearitas, jika garis pad variabel bebas datar, seperti
dalam kasus kita disini, kita dapat menyimpulkan bahwa hubungan BSTotal
dan CTA.tot adalah linear terhadap GPA.
Asumsi normalitas residu
QQplots (quantile–quantile plots) digunakan untuk mengevaluasi normalitas residu. Semakin dekat data amatan pada garis (distribusi normal), maka asumsi normalitas residu terpenuhi.
qqPlot(Model1.1)[1] 226 290
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