lm(formula, data)Regression in R
Practice
Starter Pack
First step to get started fitting linear regression in R is to open it on your computer. It’s by default loaded stats library each time R is started and able to run function lm for fitting basic linear regression.
Basic lm
formula defines the linear regression form and data indicates the dataset in the analysis.
Example
Let’s try predicting students mathematics score (MATH) from measure of economic social culture status (ESCS). This model is defined in R as:
Model1.1 <- lm(MATH ~ sex + ESCS, PISA)The code above represents regression equation. Where MATH is dependent variable, followed by the independent variable ESCS separated by ~.
Regression Output
After running regression equation with lm function. The next step is to see the output of Model1.1. Further information on our model can be obtained by requesting a summary of the model.
summary(Model1.1)summary calls the result of the model as the following:
Call:
lm(formula = MATH ~ sex + ESCS, data = PISA)
Residuals:
Min 1Q Median 3Q Max
-164.989 -42.697 -5.302 39.108 240.733
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 404.618 3.447 117.371 < 2e-16 ***
sex -9.218 3.429 -2.688 0.00728 **
ESCS 17.555 1.655 10.606 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 61.7 on 1294 degrees of freedom
Multiple R-squared: 0.08406, Adjusted R-squared: 0.08264
F-statistic: 59.38 on 2 and 1294 DF, p-value: < 2.2e-16Often in a regression model, we are interested in additional information that the model produces, such as predicted values and residuals. Using the R call attributes() we can get a list of the additional information available for the lm function.
Using R call attributes to find the additional information in the model produces in lm function. Such as predicted values and residuals.
attributes(Model1.1)$names
[1] "coefficients" "residuals" "effects" "rank"
[5] "fitted.values" "assign" "qr" "df.residual"
[9] "xlevels" "call" "terms" "model"
$class
[1] "lm"The list of attribute is shown above can be pulled out of the fitted regression model. For example, to obtain the predicted MATH for each individual in the sample, we can type the following:
Model1.1$fitted.values 1 2 3 4 5 6 7 8
405.6453 355.9665 367.2600 370.0753 388.0145 379.3464 376.9713 356.2948
9 10 11 12 13 14 15 16
333.6772 380.7421 379.0493 369.6294 360.5466 407.3792 410.0252 368.4726
17 18 19 20 21 22 23 24
412.3670 383.7632 379.9451 397.5889 352.1190 361.6600 370.1688 375.1877
25 26 27 28 29 30 31 32
360.5852 393.0497 362.8555 358.9087 369.7365 369.1752 366.0926 314.0948
33 34 35 36 37 38 39 40
367.1753 366.7123 393.1581 359.0439 381.0914 357.6996 338.7856 398.5176
41 42 43 44 45 46 47 48
366.2922 391.3855 378.1018 354.6609 420.0139 385.0390 368.2163 378.7439
49 50 51 52 53 54 55 56
355.0256 372.8442 360.7313 369.6382 398.0370 360.8349 362.1230 336.0370
57 58 59 60 61 62 63 64
365.3184 359.2883 360.3236 381.7251 351.8346 345.4214 353.5883 380.8434
65 66 67 68 69 70 71 72
402.5311 401.3373 374.4307 386.2701 353.8464 361.3528 389.6371 372.8529
73 74 75 76 77 78 79 80
382.7657 355.0945 384.9219 373.5705 360.3710 362.1796 356.4107 403.0718
81 82 83 84 85 86 87 88
356.4528 390.0755 347.6811 379.7046 380.4120 371.9150 355.2362 357.6733
89 90 91 92 93 94 95 96
360.7537 392.1224 385.6201 343.6518 402.6066 347.0645 382.4514 391.2398
97 98 99 100 101 102 103 104
391.8485 398.9674 368.7855 383.2554 359.0439 367.0717 372.5826 392.4735
105 106 107 108 109 110 111 112
398.1669 369.3630 359.3814 366.7452 375.7964 384.0717 403.3509 349.5555
113 114 115 116 117 118 119 120
373.6108 366.6486 363.8105 368.9435 349.3413 375.5265 370.6200 395.4600
121 122 123 124 125 126 127 128
400.8476 406.4107 364.7035 386.9740 357.3082 339.8793 361.6021 357.0409
129 130 131 132 133 134 135 136
370.9131 368.4853 372.8700 384.3596 357.2239 375.2492 388.0461 382.1354
137 138 139 140 141 142 143 144
380.5696 375.3422 375.2299 386.4965 381.1581 374.5026 403.4803 404.2128
145 146 147 148 149 150 151 152
371.4801 368.4726 369.6575 381.2419 390.7689 380.9948 399.8469 380.9259
153 154 155 156 157 158 159 160
363.8087 388.7260 356.0144 377.7854 346.9210 399.1899 374.9455 399.1074
161 162 163 164 165 166 167 168
371.0553 365.6480 323.6113 402.5785 370.5129 370.8600 393.6496 383.0518
169 170 171 172 173 174 175 176
387.0003 345.2656 370.9043 397.3998 361.7526 344.5717 373.8531 352.3612
177 178 179 180 181 182 183 184
366.7474 362.8620 374.4289 364.5701 377.8964 393.2182 349.4436 386.8213
185 186 187 188 189 190 191 192
355.0554 371.8115 330.7736 357.1199 375.2013 383.7435 379.1669 392.7666
193 194 195 196 197 198 199 200
373.6885 379.2231 364.7316 367.8568 363.0832 353.0494 392.1790 354.8641
201 202 203 204 205 206 207 208
385.1975 362.5395 371.7909 399.4186 363.9820 414.4350 392.2400 364.0053
209 210 211 212 213 214 215 216
375.3949 381.0686 362.0106 373.2738 368.4726 369.2748 399.0271 366.2120
217 218 219 220 221 222 223 224
369.0874 371.3081 386.8476 363.9733 387.3971 407.4727 380.3085 364.7918
225 226 227 228 229 230 231 232
368.3765 358.5001 397.6877 389.2017 367.0541 375.1456 384.5176 364.0365
233 234 235 236 237 238 239 240
408.1152 416.5481 413.4027 369.2537 384.8635 368.8224 385.4924 354.4638
241 242 243 244 245 246 247 248
383.1835 337.6586 356.0824 390.2761 368.0003 381.4390 382.3536 377.6910
249 250 251 252 253 254 255 256
380.4278 384.9793 376.7185 360.0726 383.9401 401.6160 381.7054 357.9208
257 258 259 260 261 262 263 264
371.2800 381.4736 410.6695 351.6480 390.6114 357.2761 404.4954 408.4488
265 266 267 268 269 270 271 272
394.2979 361.7192 374.6418 378.2054 373.8711 391.6414 354.6517 376.0163
273 274 275 276 277 278 279 280
354.4445 367.2688 387.8548 350.4473 373.9255 383.2419 372.3298 364.5438
281 282 283 284 285 286 287 288
393.1077 369.3766 404.2075 366.0991 366.7755 391.0046 390.8413 377.1714
289 290 291 292 293 294 295 296
343.9678 368.4484 384.8569 366.3875 386.4210 376.1300 363.2131 381.7304
297 298 299 300 301 302 303 304
388.1291 375.9193 352.5719 369.0769 345.9708 397.0834 416.3221 345.8198
305 306 307 308 309 310 311 312
358.8354 364.9603 396.3267 368.9470 401.3198 393.5584 402.4850 368.4726
313 314 315 316 317 318 319 320
373.1250 383.4946 364.6829 379.4465 360.6085 375.9057 413.4466 414.0575
321 322 323 324 325 326 327 328
366.1659 368.1478 373.1562 380.7210 349.7350 393.0866 356.0038 377.5436
329 330 331 332 333 334 335 336
377.7841 415.4865 363.9504 380.4888 376.1023 383.5240 374.0186 377.6910
337 338 339 340 341 342 343 344
337.5902 364.5267 368.0986 378.2629 352.0623 368.4234 385.0289 408.3452
345 346 347 348 349 350 351 352
375.3053 365.8679 366.2471 370.9618 384.2754 373.3023 368.3027 382.0587
353 354 355 356 357 358 359 360
351.5783 403.5879 363.3360 370.7148 378.5121 372.3175 380.0311 361.1614
361 362 363 364 365 366 367 368
375.5142 336.4473 350.5526 359.8378 384.5848 377.8117 367.6387 365.7796
369 370 371 372 373 374 375 376
362.6251 393.9907 391.2679 361.8404 391.7625 357.9783 353.3912 385.3234
377 378 379 380 381 382 383 384
352.6908 369.0940 379.5905 387.4217 378.0943 387.0003 381.4636 371.4867
385 386 387 388 389 390 391 392
409.6267 375.5441 411.8597 370.4409 374.1814 362.0510 371.3994 382.8785
393 394 395 396 397 398 399 400
400.9985 392.1908 386.6400 361.8333 390.9690 376.5289 369.9594 389.1719
401 402 403 404 405 406 407 408
389.4211 362.6396 383.2805 382.4040 349.3273 413.0973 352.0448 343.6185
409 410 411 412 413 414 415 416
395.0646 397.8966 406.1908 350.7685 380.0627 394.8052 365.8872 378.9984
417 418 419 420 421 422 423 424
379.6409 338.9717 396.2530 402.0782 371.7751 388.3551 383.8190 348.9832
425 426 427 428 429 430 431 432
385.3607 352.2383 384.2390 398.2512 360.2797 376.1093 380.1750 371.5346
433 434 435 436 437 438 439 440
386.6826 409.8093 364.5899 388.3398 377.2903 360.8380 364.7931 400.6364
441 442 443 444 445 446 447 448
368.4726 360.0309 370.9377 362.6852 365.5343 386.1362 396.3781 359.0895
449 450 451 452 453 454 455 456
337.9623 363.4822 377.0604 371.1637 373.9268 414.7316 370.0648 350.9283
457 458 459 460 461 462 463 464
369.0418 371.8782 379.3219 397.1202 346.6186 378.2032 369.9226 367.9845
465 466 467 468 469 470 471 472
418.6692 376.8782 348.6519 392.9615 371.9168 371.4692 378.1347 362.8151
473 474 475 476 477 478 479 480
360.9244 356.3211 396.2179 363.6327 370.2232 373.4428 366.4911 380.4906
481 482 483 484 485 486 487 488
336.3227 354.2163 379.6782 362.3178 375.0315 385.2378 330.5208 359.3915
489 490 491 492 493 494 495 496
363.4343 412.8335 392.0293 350.8445 380.1610 392.7754 357.6733 368.4726
497 498 499 500 501 502 503 504
369.2344 357.7067 388.9063 343.6553 403.4176 361.8268 382.8802 348.6168
505 506 507 508 509 510 511 512
362.0457 363.9452 343.5167 345.8238 404.2374 400.6961 378.0825 389.4874
513 514 515 516 517 518 519 520
361.0890 384.9780 343.9648 360.1415 354.6311 379.2815 372.5593 393.3688
521 522 523 524 525 526 527 528
383.1501 379.3113 365.2144 388.7225 387.8056 370.1706 382.7486 369.9897
529 530 531 532 533 534 535 536
391.6524 350.8252 362.5654 389.3527 337.8715 392.1544 364.4332 374.0655
537 538 539 540 541 542 543 544
357.4749 380.7263 381.2511 384.1178 364.5197 409.9967 367.3284 412.7111
545 546 547 548 549 550 551 552
362.3161 377.3224 383.4450 371.3696 396.1323 377.2996 385.3708 374.7782
553 554 555 556 557 558 559 560
360.2832 368.3326 346.3781 402.6552 385.7272 388.9595 349.3365 352.6013
561 562 563 564 565 566 567 568
347.7281 364.4701 398.7142 360.0480 354.9308 412.5865 387.5533 371.6961
569 570 571 572 573 574 575 576
367.2951 408.2996 375.1943 392.1070 376.7641 327.0906 375.2597 392.7601
577 578 579 580 581 582 583 584
345.3283 368.2970 356.9987 359.2651 379.7111 350.1769 342.4669 373.3690
585 586 587 588 589 590 591 592
373.1672 383.7492 377.7929 374.3271 383.4806 389.2065 381.4811 367.9090
593 594 595 596 597 598 599 600
367.5070 375.2645 363.9316 359.3177 370.5094 341.9688 373.8641 372.5896
601 602 603 604 605 606 607 608
356.0367 363.3817 377.3347 355.1981 395.4402 361.1176 363.9509 382.4080
609 610 611 612 613 614 615 616
376.5570 353.0529 366.7065 365.2008 352.9177 370.1074 374.9174 417.2174
617 618 619 620 621 622 623 624
358.9601 360.2376 419.3187 358.0099 405.8981 379.9393 370.9109 371.5082
625 626 627 628 629 630 631 632
363.2974 382.8236 345.4552 363.2921 357.9801 375.7947 389.2245 383.8861
633 634 635 636 637 638 639 640
340.7816 388.9502 419.5785 355.3170 360.4974 367.5878 367.1647 363.6608
641 642 643 644 645 646 647 648
376.9906 375.3207 380.7820 345.9568 385.2782 376.9884 365.9991 344.8701
649 650 651 652 653 654 655 656
356.5985 376.0053 347.4805 374.0554 335.9330 354.2461 397.2168 386.8318
657 658 659 660 661 662 663 664
422.4891 330.0170 416.6943 369.8809 355.0098 389.1890 366.4151 368.2132
665 666 667 668 669 670 671 672
408.1762 378.1259 396.8938 346.8350 391.1801 377.5225 402.6311 346.3469
673 674 675 676 677 678 679 680
396.1547 351.1394 345.5026 374.4605 406.2018 402.2555 411.8965 355.7980
681 682 683 684 685 686 687 688
386.6615 343.3609 402.3638 354.7570 361.3036 366.1185 373.8483 364.3880
689 690 691 692 693 694 695 696
365.3127 372.5914 361.8070 370.7599 368.8768 397.6118 357.5798 374.4574
697 698 699 700 701 702 703 704
353.5497 405.8401 356.1109 376.6900 379.6835 398.6282 398.0651 366.3186
705 706 707 708 709 710 711 712
382.1477 355.7265 375.1364 380.7592 373.0965 382.3742 384.1297 358.6985
713 714 715 716 717 718 719 720
357.7962 378.6513 380.9492 367.9253 395.5197 383.4169 376.4218 388.8976
721 722 723 724 725 726 727 728
400.9805 368.7815 337.1671 369.8998 420.9513 366.3625 407.2090 369.9020
729 730 731 732 733 734 735 736
412.5075 375.7267 391.4241 356.4177 395.9866 366.8281 357.8278 411.7772
737 738 739 740 741 742 743 744
357.4095 385.9769 366.1378 371.0325 351.1126 381.8656 405.5452 357.6803
745 746 747 748 749 750 751 752
368.1390 397.8510 369.6948 421.6342 371.2655 345.5289 404.4059 347.1698
753 754 755 756 757 758 759 760
373.9448 407.3867 351.6621 351.9956 382.7341 362.0918 383.2151 370.7775
761 762 763 764 765 766 767 768
365.5830 345.0264 369.5399 387.2128 370.9583 371.9945 371.2537 347.1685
769 770 771 772 773 774 775 776
359.9444 375.0561 343.0304 378.1913 388.3288 367.6036 370.1442 364.1313
777 778 779 780 781 782 783 784
361.8860 398.3565 409.7408 369.0365 369.8265 358.0450 362.6255 394.6314
785 786 787 788 789 790 791 792
362.8186 379.1459 376.6478 374.3675 375.6722 394.0464 363.7784 342.6582
793 794 795 796 797 798 799 800
353.7726 366.1891 378.0123 395.6812 340.2673 371.4714 381.2880 420.3334
801 802 803 804 805 806 807 808
391.3873 348.6923 386.6370 362.6391 376.4411 386.2472 376.0935 374.9771
809 810 811 812 813 814 815 816
352.4362 356.7969 396.6765 393.1476 411.9615 402.0531 371.1145 344.2527
817 818 819 820 821 822 823 824
399.4063 391.1604 401.2180 378.4143 379.6730 379.8661 370.3720 359.5108
825 826 827 828 829 830 831 832
410.9890 415.9271 375.9053 391.9016 371.8716 382.2114 364.9124 360.1182
833 834 835 836 837 838 839 840
349.8417 379.3390 375.2259 356.1228 374.4469 361.7420 408.1481 384.8319
841 842 843 844 845 846 847 848
365.9311 350.5671 406.7354 391.7678 379.0024 355.7945 336.7686 371.9892
849 850 851 852 853 854 855 856
363.0253 376.3498 387.9145 354.8167 371.4714 363.0867 380.6613 409.9304
857 858 859 860 861 862 863 864
399.8289 379.8252 361.0930 377.8227 341.5650 342.3673 359.0807 414.7878
865 866 867 868 869 870 871 872
360.8222 329.8380 409.0614 355.8278 355.9442 358.4159 383.4064 400.1348
873 874 875 876 877 878 879 880
394.9456 369.0957 337.4480 358.7090 349.7943 412.3069 346.5049 372.6405
881 882 883 884 885 886 887 888
337.0109 369.1361 369.9805 376.0075 388.5535 397.5819 374.0467 373.9501
889 890 891 892 893 894 895 896
359.0584 378.5157 396.1214 367.8200 392.6986 431.2876 359.8005 414.2068
897 898 899 900 901 902 903 904
411.5134 356.2193 371.0799 340.9015 351.6621 370.8846 383.7246 407.9169
905 906 907 908 909 910 911 912
338.0922 364.5315 343.6681 373.9338 377.6910 369.9072 407.4903 361.8386
913 914 915 916 917 918 919 920
365.9148 395.4104 364.3226 368.4555 401.4093 359.6008 343.5979 419.9682
921 922 923 924 925 926 927 928
370.8934 356.7389 407.0791 334.1968 361.2014 374.4662 375.0719 392.3839
929 930 931 932 933 934 935 936
397.3032 351.2992 388.5201 350.8914 364.9269 355.1221 354.0746 338.1660
937 938 939 940 941 942 943 944
360.3346 387.8237 367.7076 341.8086 342.9361 370.7231 357.5816 364.0158
945 946 947 948 949 950 951 952
356.6621 366.5134 378.5969 360.4641 367.5878 334.1143 337.1074 411.6806
953 954 955 956 957 958 959 960
348.8152 361.2580 374.9099 373.2426 378.0171 376.1831 409.5192 340.7500
961 962 963 964 965 966 967 968
371.5288 366.2361 355.8717 381.5706 363.0025 419.8857 367.0598 378.1492
969 970 971 972 973 974 975 976
369.3064 387.3146 374.7664 350.5052 388.8418 402.9734 408.5804 392.3962
977 978 979 980 981 982 983 984
372.5598 356.9939 414.7580 367.8968 369.2665 344.5739 365.8183 389.2000
985 986 987 988 989 990 991 992
353.0208 345.7571 377.6910 350.6474 413.9570 365.6502 377.6910 383.4982
993 994 995 996 997 998 999 1000
405.7647 398.3965 355.0102 397.2536 366.9365 365.5795 382.1864 352.4836
1001 1002 1003 1004 1005 1006 1007 1008
371.0759 370.6463 356.8706 380.3120 374.8660 391.9332 372.8700 387.3391
1009 1010 1011 1012 1013 1014 1015 1016
408.9241 371.2445 372.6704 354.5060 371.0847 383.4859 368.8803 361.4283
1017 1018 1019 1020 1021 1022 1023 1024
351.9382 339.7986 396.4834 398.3929 388.0220 339.1174 394.2048 378.3599
1025 1026 1027 1028 1029 1030 1031 1032
386.3363 390.7513 385.8237 373.2655 377.4716 381.3600 405.6312 395.3805
1033 1034 1035 1036 1037 1038 1039 1040
372.1011 386.3416 371.3906 358.4650 371.6552 363.7766 374.7817 350.2459
1041 1042 1043 1044 1045 1046 1047 1048
382.6568 363.7170 341.7107 355.4364 401.3105 394.6542 364.7531 381.7392
1049 1050 1051 1052 1053 1054 1055 1056
370.1267 376.1124 385.6188 380.1101 387.2737 377.1341 372.6664 364.8602
1057 1058 1059 1060 1061 1062 1063 1064
342.7166 410.5413 357.0062 353.6721 381.9498 375.2347 378.1698 388.3218
1065 1066 1067 1068 1069 1070 1071 1072
367.2209 405.0976 353.0634 379.7414 362.1989 387.0245 352.9998 353.0072
1073 1074 1075 1076 1077 1078 1079 1080
353.3092 345.9133 388.3481 359.1246 399.0899 351.6516 354.5937 389.1666
1081 1082 1083 1084 1085 1086 1087 1088
363.5871 395.6285 373.5968 417.8213 405.0853 388.5798 384.9618 379.2512
1089 1090 1091 1092 1093 1094 1095 1096
353.5282 372.2350 345.0913 354.5661 412.8814 379.5040 376.7391 377.0762
1097 1098 1099 1100 1101 1102 1103 1104
358.6998 353.3105 364.4525 370.3742 399.0934 374.4184 371.8506 375.4370
1105 1106 1107 1108 1109 1110 1111 1112
358.4246 380.7118 382.1201 385.9611 357.3270 404.8641 386.2415 371.1220
1113 1114 1115 1116 1117 1118 1119 1120
369.7194 380.5735 385.2062 355.9705 348.5514 389.0854 397.3010 358.8056
1121 1122 1123 1124 1125 1126 1127 1128
386.0976 408.2539 346.7788 351.0266 362.8568 368.6183 367.5544 365.0235
1129 1130 1131 1132 1133 1134 1135 1136
345.4723 377.7696 349.9211 350.0054 391.4079 396.7573 349.2852 356.5423
1137 1138 1139 1140 1141 1142 1143 1144
396.1635 370.8570 385.3888 402.5995 397.2887 396.1236 364.1400 364.5473
1145 1146 1147 1148 1149 1150 1151 1152
423.0649 408.9280 357.8484 399.9518 382.7784 405.4873 382.8153 365.9552
1153 1154 1155 1156 1157 1158 1159 1160
403.6704 365.6221 380.5590 360.4483 360.1428 341.6839 381.9446 409.6179
1161 1162 1163 1164 1165 1166 1167 1168
376.2230 353.6370 343.4504 405.0076 365.4250 365.6638 371.9805 371.7676
1169 1170 1171 1172 1173 1174 1175 1176
370.9952 332.1166 357.6430 394.0714 392.7895 392.5384 371.9331 376.2884
1177 1178 1179 1180 1181 1182 1183 1184
392.0930 380.1469 347.4191 399.1741 352.3665 382.5309 377.4224 341.9209
1185 1186 1187 1188 1189 1190 1191 1192
349.7311 328.7812 359.6513 367.1243 381.5579 382.3150 379.7059 388.4117
1193 1194 1195 1196 1197 1198 1199 1200
392.7425 358.4475 371.8786 368.7411 356.9057 376.5500 396.3851 370.9219
1201 1202 1203 1204 1205 1206 1207 1208
400.4820 336.0524 368.4726 394.4664 382.3553 408.5102 355.3894 372.4123
1209 1210 1211 1212 1213 1214 1215 1216
387.6955 376.8098 364.2717 367.1437 379.3021 371.1848 349.2729 359.1685
1217 1218 1219 1220 1221 1222 1223 1224
354.2865 349.3190 360.5834 396.6094 372.4347 397.6930 391.0779 363.6525
1225 1226 1227 1228 1229 1230 1231 1232
370.8126 403.9653 362.5693 369.6615 408.1890 374.7945 371.3515 354.7535
1233 1234 1235 1236 1237 1238 1239 1240
352.6860 396.4817 354.5428 348.9920 376.6588 373.2409 377.5330 374.7085
1241 1242 1243 1244 1245 1246 1247 1248
378.2914 379.3530 368.8675 408.0516 377.3996 375.4054 356.2456 404.7711
1249 1250 1251 1252 1253 1254 1255 1256
358.8196 403.9144 342.9694 351.0148 368.0780 359.6359 393.1902 380.6069
1257 1258 1259 1260 1261 1262 1263 1264
359.3498 389.0275 355.5347 381.6040 376.5061 366.2466 348.1792 373.6201
1265 1266 1267 1268 1269 1270 1271 1272
374.2288 375.1311 384.4461 350.9511 347.1558 379.9042 363.3097 382.4168
1273 1274 1275 1276 1277 1278 1279 1280
413.3097 383.6017 371.5451 373.3616 355.0800 375.6384 343.2621 351.7902
1281 1282 1283 1284 1285 1286 1287 1288
380.9211 337.9535 379.2494 380.5402 380.9277 356.9443 380.2154 372.5703
1289 1290 1291 1292 1293 1294 1295 1296
366.3594 335.4770 355.2889 369.8927 342.7991 373.0315 359.2532 348.8217
1297
377.0972 We can obtain another attributes in the same regression by typing the model following by $ then typing the list of attributes.
Interaction Terms in Regression
More complicated regression relationships can also be easily modeled using the lm() function. An interaction is simply computed as the product of the interacting variables, so that the moderation model using lm() is defined as:
Model1.2 <- lm(MATH ~ sex + ESCS + sex*ESCS, PISA)
summary(Model1.2)
Call:
lm(formula = MATH ~ sex + ESCS + sex * ESCS, data = PISA)
Residuals:
Min 1Q Median 3Q Max
-165.103 -42.686 -5.276 39.156 240.895
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 404.7758 4.1301 98.006 < 2e-16 ***
sex -9.5613 6.0216 -1.588 0.113
ESCS 17.6592 2.2390 7.887 6.53e-15 ***
sex:ESCS -0.2304 3.3261 -0.069 0.945
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 61.72 on 1293 degrees of freedom
Multiple R-squared: 0.08406, Adjusted R-squared: 0.08194
F-statistic: 39.56 on 3 and 1293 DF, p-value: < 2.2e-16The slope for interaction is denoted sex:ESCS, takes the value -0.8908, and is non-significant (t=-0.284, p=0.7765).