Now take some data for Canada: In 1957, GDP per capita in Canada was $12,490 and life expectancy was 70.0 years. In 1977, GDP per capita in Canada was $22,091 and life expectancy was 74.2 years. In 1997, GDP per capita in Canada was $28,955 and life expectancy was 78.0 years.
canada_data <- tibble(
year = c(1957,1977,1997),
gdpPercap = c(12490,22091,28955),
lifeExp = c(70.0,74.2,78.0)
)
canada_data## # A tibble: 3 × 3
## year gdpPercap lifeExp
## <dbl> <dbl> <dbl>
## 1 1957 12490 70
## 2 1977 22091 74.2
## 3 1997 28955 78us_data <- tibble(
year = c(1957, 1977, 1997),
gdpPercap = c(14847, 24073, 35767),
lifeExp = c(69.5, 73.4, 76.8)
)ncol(us_data) == 3## [1] TRUEYou can do that using the function ‘add_row()’. It takes the tibble as the first argument and then variable names and values to construct the new row. Suppose we got a new observation (row) about Canada: In 2007, GDP per capita in Canada was $36,319 and life expectancy was 80.7 years.
add_row(
canada_data,
year = 2007,
gdpPercap = 36319,
lifeExp = 80.7
)## # A tibble: 4 × 3
## year gdpPercap lifeExp
## <dbl> <dbl> <dbl>
## 1 1957 12490 70
## 2 1977 22091 74.2
## 3 1997 28955 78
## 4 2007 36319 80.7gapminder %>%
lm(lifeExp ~ gdpPercap, data = .)##
## Call:
## lm(formula = lifeExp ~ gdpPercap, data = .)
##
## Coefficients:
## (Intercept) gdpPercap
## 5.396e+01 7.649e-04A $1 increase to a country’s GDP per capita can be associated with a 0.0007649 year increase in life expectancy.
broom::tidy(conf.int = TRUE).Is the coefficient on gdpPercap greater than 0 at the 1%
level?
gapminder %>%
lm(lifeExp ~ gdpPercap, data = .) %>%
broom::tidy(conf.int = TRUE)## # A tibble: 2 × 7
## term estimate std.error statistic p.value conf.low conf.high
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 54.0 0.315 171. 0 53.3 54.6
## 2 gdpPercap 0.000765 0.0000258 29.7 3.57e-156 0.000714 0.000815The coefficient on gdpPercap is greater than 0 at the 1%
level.
broom::glance().gapminder %>%
lm(lifeExp ~ gdpPercap, data = .) %>%
broom::glance()## # A tibble: 1 × 12
## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.341 0.340 10.5 880. 3.57e-156 1 -6422. 12850. 12867.
## # ℹ 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>This model explains __% of the variation in lifeExp.
gapminder %>%
lm(lifeExp ~ gdpPercap, data = .) %>%
fitted.values()## 1 2 3 4 5 6 7 8
## 54.55175 54.58342 54.60808 54.59515 54.52156 54.55685 54.70362 54.60754
## 9 10 11 12 13 14 15 16
## 54.45223 54.44152 54.51143 54.70100 55.18018 55.44118 55.72465 56.06679
## 17 18 19 20 21 22 23 24
## 56.48994 56.65789 56.73276 56.81541 55.86581 56.39787 57.47724 58.49669
## 25 26 27 28 29 30 31 32
## 55.82876 56.26090 55.90664 56.43913 57.15481 57.71145 58.34993 58.30113
## 33 34 35 36 37 38 39 40
## 57.79773 57.62493 58.00029 58.71571 56.64841 56.88349 57.22106 58.17984
## 41 42 43 44 45 46 47 48
## 58.14198 56.25682 56.06431 55.81439 55.96555 55.69731 56.07680 57.62488
## 49 50 51 52 53 54 55 56
## 58.47702 59.20025 59.41160 60.11512 61.17838 61.66483 60.83790 60.94634
## 57 58 59 60 61 62 63 64
## 61.07541 62.34424 60.68472 63.73029 61.63467 62.33076 63.30031 65.06634
## 65 66 67 68 69 70 71 72
## 66.79689 67.97907 68.85319 70.69799 71.87276 74.60581 77.42809 80.29458
## 73 74 75 76 77 78 79 80
## 58.64970 60.71911 62.17860 63.77253 66.69975 69.06155 70.47480 72.07397
## 81 82 83 84 85 86 87 88
## 74.63953 76.21053 78.75123 81.58809 61.50272 62.85558 63.71032 65.27940
## 89 90 91 92 93 94 95 96
## 67.92894 68.74847 68.64983 68.12427 68.51555 69.47657 71.85654 76.74604
## 97 98 99 100 101 102 103 104
## 54.47893 54.46164 54.48053 54.50718 54.43762 54.46029 54.47337 54.53074
## 105 106 107 108 109 110 111 112
## 54.59639 54.69962 54.82477 55.01971 60.33706 61.38637 62.36254 64.01303
## 113 114 115 116 117 118 119 120
## 66.70779 68.57857 70.00268 71.18497 73.51787 75.03664 77.27368 79.72645
## 121 122 123 124 125 126 127 128
## 54.76844 54.68954 54.68182 54.74785 54.78607 54.74275 54.93300 54.89320
## 129 130 131 132 133 134 135 136
## 54.86669 54.89864 55.00565 55.05797 56.00340 55.58299 55.62375 55.93423
## 137 138 139 140 141 142 143 144
## 56.23516 56.66944 56.36992 56.06181 56.22091 56.49967 56.56631 56.87905
## 145 146 147 148 149 150 151 152
## 54.70020 54.99120 55.26327 55.61716 56.14326 56.65444 57.11194 57.25535
## 153 154 155 156 157 158 159 160
## 55.90355 57.60126 58.55937 59.65111 54.60666 54.65790 54.70794 54.88467
## 161 162 163 164 165 166 167 168
## 55.68696 56.41455 57.43665 58.70233 60.03952 60.56961 62.37203 63.57002
## 169 170 171 172 173 174 175 176
## 55.56866 55.85810 56.50766 56.57900 57.76905 59.04977 59.33333 59.92707
## 177 178 179 180 181 182 183 184
## 59.27171 60.04248 60.17498 60.88983 55.82515 56.25684 57.20963 58.22131
## 185 186 187 188 189 190 191 192
## 59.00187 59.77803 60.24610 60.25808 58.77633 58.52221 59.84269 62.12511
## 193 194 195 196 197 198 199 200
## 54.37109 54.42763 54.50820 54.56351 54.60933 54.52416 54.57297 54.65318
## 201 202 203 204 205 206 207 208
## 54.66824 54.67937 54.74924 54.88645 54.21508 54.24588 54.22725 54.27144
## 209 210 211 212 213 214 215 216
## 54.31054 54.38091 54.38359 54.43118 54.43874 54.30979 54.29701 54.28451
## 217 218 219 220 221 222 223 224
## 54.23740 54.28755 54.33564 54.35593 54.27805 54.35710 54.43321 54.47866
## 225 226 227 228 229 230 231 232
## 54.47744 54.51720 54.64107 55.26640 54.85251 54.95989 55.02610 55.10935
## 233 234 235 236 237 238 239 240
## 55.24374 55.31968 55.76679 55.94629 55.32712 55.25153 55.43485 55.51752
## 241 242 243 244 245 246 247 248
## 62.65011 63.50891 64.25278 66.25226 68.46582 70.85249 71.47045 74.32172
## 249 250 251 252 253 254 255 256
## 74.10478 76.10268 79.44831 81.73551 54.77499 54.86642 54.86812 54.82451
## 257 258 259 260 261 262 263 264
## 54.77400 54.80410 54.68736 54.60179 54.52762 54.52196 54.52057 54.49558
## 265 266 267 268 269 270 271 272
## 54.85710 54.95641 55.01861 54.87098 54.80007 54.82293 54.56587 54.68402
## 273 274 275 276 277 278 279 280
## 54.76486 54.72424 54.83990 55.25897 56.96918 57.25651 57.41214 57.86155
## 281 282 283 284 285 286 287 288
## 58.15784 57.59393 57.85315 58.19841 59.76571 61.69468 62.20007 64.03032
## 289 290 291 292 293 294 295 296
## 54.26186 54.39612 54.32857 54.42421 54.47331 54.52252 54.69170 55.01026
## 297 298 299 300 301 302 303 304
## 55.22204 55.70656 56.34144 57.74870 55.59556 55.73300 55.86192 56.00447
## 305 306 307 308 309 310 311 312
## 56.45264 56.87421 57.31919 57.70595 58.12008 58.63462 58.35766 59.31477
## 313 314 315 316 317 318 319 320
## 54.79922 54.88195 55.03148 55.39050 55.43758 54.85246 54.92474 54.96213
## 321 322 323 324 325 326 327 328
## 54.90930 54.85324 54.77843 54.70985 54.55258 54.64844 54.64114 54.61458
## 329 330 331 332 333 334 335 336
## 54.64770 54.56422 54.47090 54.47015 54.30566 54.19435 54.14002 54.16786
## 337 338 339 340 341 342 343 344
## 55.58141 55.72631 55.84083 56.00387 56.41325 56.44845 57.68781 57.16898
## 345 346 347 348 349 350 351 352
## 57.02751 56.62054 56.62046 56.73404 55.96491 56.24257 56.60277 57.13879
## 353 354 355 356 357 358 359 360
## 57.87034 58.48893 57.98094 58.26179 58.66756 59.06272 59.86309 61.33290
## 361 362 363 364 365 366 367 368
## 55.01767 55.10357 55.27794 55.52514 55.77461 55.88133 55.94633 55.60538
## 369 370 371 372 373 374 375 376
## 55.21614 55.32184 55.21670 55.13711 56.34141 57.27380 58.14550 59.27937
## 377 378 379 380 381 382 383 384
## 60.96501 62.60285 64.06870 64.52822 60.41713 61.50924 62.84991 65.13755
## 385 386 387 388 389 390 391 392
## 58.22861 58.61536 57.91823 58.30795 58.01360 58.83589 59.55214 59.71736
## 393 394 395 396 397 398 399 400
## 58.23343 58.11040 58.80541 60.79981 59.21500 60.27070 61.70907 62.67480
## 401 402 403 404 405 406 407 408
## 63.98199 65.27595 65.71734 66.43114 64.89110 66.23079 67.41460 71.42036
## 409 410 411 412 413 414 415 416
## 61.36910 62.44550 64.34520 66.14566 68.38600 69.57668 70.54437 73.16649
## 417 418 419 420 421 422 423 424
## 74.15362 76.75239 78.55916 80.93941 55.99744 56.14693 56.26626 56.26555
## 425 426 427 428 429 430 431 432
## 56.78120 56.31275 56.15802 56.15850 55.77381 55.40503 55.41516 55.54841
## 433 434 435 436 437 438 439 440
## 55.02465 55.13685 55.22690 55.22046 55.63056 56.00697 56.14396 56.17360
## 441 442 443 444 445 446 447 448
## 56.28403 56.71992 57.44634 58.56427 56.64956 56.84724 57.08096 57.45802
## 449 450 451 452 453 454 455 456
## 57.99490 59.06469 59.47326 58.91336 59.38906 59.63822 58.37126 59.21280
## 457 458 459 460 461 462 463 464
## 55.04079 55.07146 55.25076 55.34373 55.50369 56.08614 56.63550 56.92748
## 465 466 467 468 469 470 471 472
## 56.85810 57.14756 57.59228 58.22451 56.28715 56.57262 56.84437 57.28937
## 473 474 475 476 477 478 479 480
## 57.41302 57.88623 57.09031 57.12251 57.35488 57.89840 58.04888 58.33708
## 481 482 483 484 485 486 487 488
## 54.24288 54.28147 54.40137 54.65588 54.46988 54.68875 54.66524 54.69512
## 489 490 491 492 493 494 495 496
## 54.82145 56.10831 59.84783 63.25201 54.20716 54.21880 54.24698 54.31413
## 497 498 499 500 501 502 503 504
## 54.34896 54.34240 54.35703 54.35417 54.40138 54.65426 54.54096 54.44613
## 505 506 507 508 509 510 511 512
## 54.23256 54.24538 54.27640 54.35033 54.38867 54.38145 54.39756 54.39441
## 513 514 515 516 517 518 519 520
## 54.27785 54.35016 54.36099 54.48395 58.86956 59.72692 61.12392 62.30933
## 521 522 523 524 525 526 527 528
## 64.93842 65.89188 68.13125 70.12595 69.74822 72.10160 75.52876 79.35508
## 529 530 531 532 533 534 535 536
## 59.33254 60.58161 62.03309 63.89897 66.27567 67.94728 69.47801 70.83380
## 537 538 539 540 541 542 543 544
## 72.85107 73.75821 76.08058 77.26155 57.23957 57.76177 59.02785 60.34903
## 545 546 547 548 549 550 551 552
## 62.67671 70.58837 65.51551 63.03044 64.29842 65.21681 63.53320 64.05697
## 553 554 555 556 557 558 559 560
## 54.32671 54.35401 54.41422 54.51758 54.53388 54.63229 54.59486 54.42341
## 561 562 563 564 565 566 567 568
## 54.46469 54.45559 54.46083 54.53133 59.41997 61.74805 63.82443 65.23423
## 569 570 571 572 573 574 575 576
## 67.73582 69.64554 70.80710 72.80165 74.22901 75.21080 76.92942 78.56212
## 577 578 579 580 581 582 583 584
## 54.65260 54.75376 54.86580 54.81659 54.85676 54.71526 54.62562 54.60342
## 585 586 587 588 589 590 591 592
## 54.66312 54.72446 54.80610 54.97103 56.65612 57.71595 58.55801 60.46708
## 593 594 595 596 597 598 599 600
## 63.68856 64.81347 65.63411 66.28587 67.37275 68.29535 71.17632 75.01921
## 601 602 603 604 605 606 607 608
## 55.81288 55.95738 56.05927 56.43572 57.03912 57.68818 57.64267 57.20362
## 609 610 611 612 613 614 615 616
## 57.35122 57.53851 57.67163 57.92228 54.34580 54.39634 54.48056 54.49768
## 617 618 619 620 621 622 623 624
## 54.52285 54.62459 54.61126 54.57173 54.56314 54.62059 54.67882 54.67658
## 625 626 627 628 629 630 631 632
## 54.18491 54.28583 54.35486 54.50290 54.58294 54.54049 54.59663 54.51883
## 633 634 635 636 637 638 639 640
## 54.52581 54.56492 54.39591 54.39861 55.36323 55.27643 55.32974 55.06621
## 641 642 643 644 645 646 647 648
## 55.22103 55.38918 55.49386 55.34995 55.06947 54.98182 54.92724 54.87467
## 649 650 651 652 653 654 655 656
## 55.63442 55.65397 55.70803 55.89704 55.89059 56.40564 56.34334 56.26788
## 657 658 659 660 661 662 663 664
## 56.31270 56.37294 56.32649 56.66962 56.29183 56.73138 57.54489 58.69628
## 665 666 667 668 669 670 671 672
## 60.31627 62.51165 65.09266 69.28264 72.89222 75.66112 77.06191 84.34051
## 673 674 675 676 677 678 679 680
## 57.98165 58.57559 59.73070 61.08935 61.73339 62.88544 63.55177 63.88869
## 681 682 683 684 685 686 687 688
## 62.01408 62.91446 65.30943 67.73029 59.51449 61.02614 61.87222 64.14372
## 689 690 691 692 693 694 695 696
## 66.03923 68.98930 71.75408 74.54865 73.18807 75.41901 77.79175 81.62962
## 697 698 699 700 701 702 703 704
## 54.37362 54.40689 54.45912 54.49157 54.50936 54.57767 54.61009 54.70248
## 705 706 707 708 709 710 711 712
## 54.84620 55.07139 55.29163 55.83121 54.52898 54.61252 54.60517 54.53873
## 713 714 715 716 717 718 719 720
## 54.80543 55.01317 55.11579 55.29285 55.77838 56.34149 56.15377 56.66374
## 721 722 723 724 725 726 727 728
## 56.27723 56.47222 57.15838 58.47352 61.30900 63.04894 59.77504 59.03659
## 729 730 731 732 733 734 735 736
## 59.48999 60.27624 61.02366 62.83257 57.11435 58.72027 60.33601 60.78708
## 737 738 739 740 741 742 743 744
## 61.28011 65.19034 65.06006 62.86153 56.82054 56.30852 57.31394 57.37540
## 745 746 747 748 749 750 751 752
## 57.94081 58.23820 59.02795 59.81117 61.24548 62.48475 63.60710 64.56668
## 753 754 755 756 757 758 759 760
## 67.38599 72.71197 80.02050 85.06792 57.08127 58.07467 59.39053 60.37579
## 761 762 763 764 765 766 767 768
## 63.73606 64.13356 65.70953 67.05225 67.76286 69.93901 70.71077 73.47787
## 769 770 771 772 773 774 775 776
## 57.72751 58.73505 60.26093 61.62152 63.34012 64.85972 66.60480 68.64684
## 777 778 779 780 781 782 783 784
## 70.79342 72.82906 75.34787 75.80804 56.17260 57.59374 57.96822 58.64024
## 785 786 787 788 789 790 791 792
## 59.64161 59.04218 58.59691 58.81351 59.61946 59.40300 59.30574 59.55518
## 793 794 795 796 797 798 799 800
## 56.41615 57.25809 58.98593 61.48796 65.25960 66.66055 68.78213 71.07053
## 801 802 803 804 805 806 807 808
## 74.47346 75.99687 75.83472 78.16874 55.13876 55.39819 55.75151 56.05271
## 809 810 811 812 813 814 815 816
## 55.57012 56.13728 57.13856 57.35828 56.58033 56.74385 56.89647 57.41242
## 817 818 819 820 821 822 823 824
## 54.60842 54.67795 54.64163 54.76384 54.89052 54.92514 54.98680 54.99728
## 825 826 827 828 829 830 831 832
## 54.98197 54.99617 54.94036 55.07477 54.78797 55.15729 55.19597 55.59512
## 833 834 835 836 837 838 839 840
## 56.78687 57.09640 57.09657 57.09655 56.80556 55.24879 55.21514 55.17407
## 841 842 843 844 845 846 847 848
## 54.74384 55.09340 55.13068 55.50768 56.27383 57.51779 58.25645 60.48237
## 849 850 851 852 853 854 855 856
## 63.21391 66.18873 68.66730 71.81415 136.85534 140.78744 126.96981 115.83065
## 857 858 859 860 861 862 863 864
## 137.59385 99.28670 77.93772 75.46286 80.67514 84.78081 80.81067 90.13986
## 865 866 867 868 869 870 871 872
## 57.65362 58.61353 58.32653 58.55020 59.68177 60.57921 59.79966 58.06840
## 873 874 875 876 877 878 879 880
## 59.22622 60.65208 61.07963 61.95704 54.18414 54.21256 54.27054 54.33696
## 881 882 883 884 885 886 887 888
## 54.33539 54.52568 54.56537 54.54757 54.70322 54.86282 54.93093 55.15592
## 889 890 891 892 893 894 895 896
## 54.39581 54.43053 54.44065 54.50138 54.56977 54.44533 54.39323 54.34268
## 897 898 899 900 901 902 903 904
## 54.44250 54.42151 54.36208 54.27261 55.78175 56.59309 59.12390 68.31451
## 905 906 907 908 909 910 911 912
## 70.02689 70.74566 67.23719 62.95868 61.32914 61.19705 61.24847 63.17813
## 913 914 915 916 917 918 919 920
## 55.05930 55.17111 55.21256 55.20542 55.29301 55.13671 54.95211 54.83934
## 921 922 923 924 925 926 927 928
## 54.75156 54.70996 54.63985 54.75469 54.23793 54.27403 54.28285 54.33457
## 929 930 931 932 933 934 935 936
## 54.40273 54.46285 54.43958 54.44166 54.38634 54.48507 54.46453 54.53637
## 937 938 939 940 941 942 943 944
## 55.35616 55.34005 55.51354 55.69777 56.13478 56.88347 57.71906 57.97104
## 945 946 947 948 949 950 951 952
## 59.52231 61.70605 61.76270 63.47962 54.30155 54.33065 54.33508 54.37243
## 953 954 955 956 957 958 959 960
## 54.40024 54.48057 54.42827 54.47887 54.52082 54.56002 54.68328 54.75301
## 961 962 963 964 965 966 967 968
## 54.52396 54.60274 54.76320 55.04257 55.16932 55.10097 55.08847 55.04292
## 969 970 971 972 973 974 975 976
## 54.99685 55.08999 55.16333 55.33476 55.46082 55.51136 55.89000 55.84894
## 977 978 979 980 981 982 983 984
## 55.92550 56.79403 56.77648 57.61444 58.58941 59.63535 60.85619 62.33637
## 985 986 987 988 989 990 991 992
## 56.61592 57.11571 57.45995 58.35726 59.16396 59.82598 61.30696 60.60098
## 993 994 995 996 997 998 999 1000
## 61.20082 61.42640 62.17227 63.11700 54.55719 54.65364 54.76355 54.89334
## 1001 1002 1003 1004 1005 1006 1007 1008
## 55.04303 55.21571 55.48579 55.74386 55.32118 55.41056 55.59298 56.32346
## 1009 1010 1011 1012 1013 1014 1015 1016
## 55.98065 56.77206 57.51195 58.47437 59.90513 61.29532 62.53952 62.92955
## 1017 1018 1019 1020 1021 1022 1023 1024
## 59.31229 58.90100 58.97105 61.03371 55.24684 55.21150 55.15364 55.26431
## 1025 1026 1027 1028 1029 1030 1031 1032
## 55.43193 55.76881 56.02275 56.06285 56.21047 56.23652 56.44793 56.87755
## 1033 1034 1035 1036 1037 1038 1039 1040
## 54.31393 54.33463 54.38136 54.38900 54.51004 54.33978 54.30910 54.25377
## 1041 1042 1043 1044 1045 1046 1047 1048
## 54.26985 54.31685 54.44020 54.58558 54.20874 54.22327 54.25234 54.22250
## 1049 1050 1051 1052 1053 1054 1055 1056
## 54.22862 54.23933 54.27987 54.25004 54.22098 54.27299 54.42290 54.67761
## 1057 1058 1059 1060 1061 1062 1063 1064
## 55.80947 55.96066 56.38270 56.85729 56.82087 56.92062 57.16126 56.78083
## 1065 1066 1067 1068 1069 1070 1071 1072
## 56.86559 56.93824 57.07041 57.63546 54.37308 54.41291 54.45457 54.47296
## 1073 1074 1075 1076 1077 1078 1079 1080
## 54.47169 54.48648 54.50503 54.54883 54.64223 54.72877 54.76420 54.79032
## 1081 1082 1083 1084 1085 1086 1087 1088
## 60.79481 62.58053 63.73906 65.70665 68.33134 70.17800 70.32364 72.04605
## 1089 1090 1091 1092 1093 1094 1095 1096
## 74.44749 77.09030 79.75104 82.10166 62.03010 63.32338 64.03341 65.01876
## 1097 1098 1099 1100 1101 1102 1103 1104
## 66.22890 66.37245 67.44229 68.49383 68.00135 70.05666 71.69304 73.21914
## 1105 1106 1107 1108 1109 1110 1111 1112
## 56.33615 56.60008 56.73542 57.50721 57.54178 58.15199 56.60996 56.21654
## 1113 1114 1115 1116 1117 1118 1119 1120
## 55.61547 55.67886 55.84830 56.05847 54.53831 54.59464 54.71873 54.76204
## 1121 1122 1123 1124 1125 1126 1127 1128
## 54.68542 54.57427 54.65139 54.46673 54.40010 54.39943 54.41531 54.42954
## 1129 1130 1131 1132 1133 1134 1135 1136
## 54.77956 54.79739 54.83589 54.73155 55.25463 55.47152 55.16176 55.01495
## 1137 1138 1139 1140 1141 1142 1143 1144
## 55.19455 55.19845 55.19107 55.49602 61.67737 62.86948 64.24354 66.47048
## 1145 1146 1147 1148 1149 1150 1151 1152
## 68.46160 71.78601 74.07093 78.08071 79.93531 85.53234 88.13356 91.70802
## 1153 1154 1155 1156 1157 1158 1159 1160
## 55.35394 55.67100 56.19257 57.56653 62.07711 63.01815 63.86446 67.81158
## 1161 1162 1163 1164 1165 1166 1167 1168
## 68.19516 69.02532 69.08099 71.02483 54.47920 54.52699 54.57002 54.67639
## 1169 1170 1171 1172 1173 1174 1175 1176
## 54.75864 54.85500 55.05962 55.25945 55.46378 55.52307 55.55624 55.94880
## 1177 1178 1179 1180 1181 1182 1183 1184
## 55.85276 56.22099 56.66060 57.33711 58.05858 58.04915 59.31708 59.33634
## 1185 1186 1187 1188 1189 1190 1191 1192
## 59.01812 59.39670 59.58206 61.45844 55.44885 55.52063 55.59855 55.71431
## 1193 1194 1195 1196 1197 1198 1199 1200
## 55.88562 56.44019 57.21282 57.01423 57.16532 57.20432 56.84963 57.14729
## 1201 1202 1203 1204 1205 1206 1207 1208
## 56.83039 57.20268 57.74711 58.38277 58.49730 58.76001 58.87720 58.82094
## 1209 1210 1211 1212 1213 1214 1215 1216
## 57.35652 58.42121 58.47527 59.62250 54.92917 55.13956 55.21727 55.34316
## 1217 1218 1219 1220 1221 1222 1223 1224
## 55.47720 55.77078 55.94676 55.63037 55.69898 55.89571 55.98320 56.39590
## 1225 1226 1227 1228 1229 1230 1231 1232
## 57.03753 57.57671 58.03908 58.97101 60.07960 61.22817 60.41999 60.90249
## 1233 1234 1235 1236 1237 1238 1239 1240
## 59.87490 61.72645 63.13587 65.72705 56.30247 56.84267 57.57189 58.82138
## 1241 1242 1243 1244 1245 1246 1247 1248
## 60.85652 61.73632 62.94587 63.92910 66.35222 67.44888 69.23096 69.64303
## 1249 1250 1251 1252 1253 1254 1255 1256
## 56.31290 56.94408 57.86285 59.25565 60.93362 61.42887 61.85756 63.34935
## 1257 1258 1259 1260 1261 1262 1263 1264
## 65.15466 66.95813 68.37789 68.73976 56.03519 56.07387 56.38309 57.03129
## 1265 1266 1267 1268 1269 1270 1271 1272
## 57.81643 57.25970 57.98437 58.01202 58.62231 58.59988 58.78669 59.82230
## 1273 1274 1275 1276 1277 1278 1279 1280
## 56.36082 56.97178 57.57728 58.90501 60.08335 61.11211 61.30250 61.37207
## 1281 1282 1283 1284 1285 1286 1287 1288
## 59.00257 59.57481 59.98694 62.22278 54.33290 54.36882 54.41256 54.34639
## 1289 1290 1291 1292 1293 1294 1295 1296
## 54.40729 54.46809 54.62986 54.60417 54.51933 54.40680 54.55649 54.61572
## 1297 1298 1299 1300 1301 1302 1303 1304
## 54.62834 54.61392 54.77517 55.01480 55.12811 55.28459 55.40136 55.11552
## 1305 1306 1307 1308 1309 1310 1311 1312
## 55.04841 54.97980 54.99052 55.17818 58.89636 60.19516 62.84841 66.88441
## 1313 1314 1315 1316 1317 1318 1319 1320
## 72.95328 80.08989 79.72689 70.16974 72.95648 69.70196 68.49945 70.51897
## 1321 1322 1323 1324 1325 1326 1327 1328
## 55.06491 55.15463 55.22143 55.18886 55.17762 55.15013 55.11702 55.05831
## 1329 1330 1331 1332 1333 1334 1335 1336
## 55.00184 55.02056 55.11790 55.26540 56.69496 57.76551 58.76639 60.06828
## 1337 1338 1339 1340 1341 1342 1343 1344
## 62.00371 63.88425 65.56732 66.09492 61.08814 60.00909 59.49031 61.44111
## 1345 1346 1347 1348 1349 1350 1351 1352
## 54.62850 54.72387 54.80966 54.87804 54.99103 54.98684 55.07612 54.94566
## 1353 1354 1355 1356 1357 1358 1359 1360
## 54.77299 54.39510 54.49059 54.61530 55.72637 56.13020 56.76630 57.76270
## 1361 1362 1363 1364 1365 1366 1367 1368
## 60.53184 62.52996 65.55819 68.38242 72.90162 79.59403 81.50901 90.01456
## 1369 1370 1371 1372 1373 1374 1375 1376
## 57.83708 58.61619 59.67773 60.39044 61.35516 62.31012 62.63587 63.16266
## 1377 1378 1379 1380 1381 1382 1383 1384
## 61.22077 63.23070 64.38763 68.24228 57.17957 58.43951 59.61745 61.14966
## 1385 1386 1387 1388 1389 1390 1391 1392
## 63.42747 65.64070 67.62151 68.24245 64.82815 67.08179 69.75805 73.66525
## 1393 1394 1395 1396 1397 1398 1399 1400
## 54.82428 54.91790 55.00306 54.93823 54.91516 55.06540 54.85568 54.79176
## 1401 1402 1403 1404 1405 1406 1407 1408
## 54.66458 54.66736 54.63025 54.66395 57.56986 58.15255 58.36796 59.39730
## 1409 1410 1411 1412 1413 1414 1415 1416
## 59.89561 60.09654 60.50928 59.94140 59.48189 59.67626 59.85353 61.04576
## 1417 1418 1419 1420 1421 1422 1423 1424
## 56.88815 57.44710 58.31068 60.06966 62.09296 64.08025 64.60745 66.01392
## 1425 1426 1427 1428 1429 1430 1431 1432
## 68.18472 69.59382 72.95178 76.00029 54.78434 54.77593 54.77741 54.82410
## 1433 1434 1435 1436 1437 1438 1439 1440
## 54.88367 54.98722 55.21615 55.39107 55.60292 55.99357 56.26197 56.99222
## 1441 1442 1443 1444 1445 1446 1447 1448
## 55.19160 55.30966 55.45442 55.24668 55.22500 55.64059 55.40543 55.10887
## 1449 1450 1451 1452 1453 1454 1455 1456
## 55.09692 55.20401 55.48028 55.94609 54.83393 54.90762 55.37532 55.95428
## 1457 1458 1459 1460 1461 1462 1463 1464
## 56.52927 56.84790 56.93507 57.00350 56.67321 56.92083 57.11309 57.40784
## 1465 1466 1467 1468 1469 1470 1471 1472
## 60.47836 61.53698 63.38614 65.62637 67.59497 68.37798 69.76368 71.99679
## 1473 1474 1475 1476 1477 1478 1479 1480
## 72.22097 73.28154 76.39847 79.85429 65.22552 67.65422 69.58295 71.52197
## 1481 1482 1483 1484 1485 1486 1487 1488
## 74.75663 74.59385 75.67648 77.11751 78.33354 78.53531 80.32945 82.64357
## 1489 1490 1491 1492 1493 1494 1495 1496
## 55.21263 55.57500 55.63298 55.39501 55.92240 56.39973 56.83293 56.33953
## 1497 1498 1499 1500 1501 1502 1503 1504
## 56.51068 57.02598 57.08464 57.15625 54.87873 55.10890 55.34985 55.97780
## 1505 1506 1507 1508 1509 1510 1511 1512
## 57.06291 58.23624 59.63585 62.41100 65.59375 69.41141 71.72793 75.92167
## 1513 1514 1515 1516 1517 1518 1519 1520
## 54.50371 54.48986 54.50781 54.60435 54.65618 54.69175 54.62425 54.59181
## 1521 1522 1523 1524 1525 1526 1527 1528
## 54.58711 54.55920 54.64325 54.80265 54.53519 54.56255 54.72213 54.94644
## 1529 1530 1531 1532 1533 1534 1535 1536
## 55.12152 55.45567 55.78609 56.23694 57.48694 58.43213 58.47846 59.66036
## 1537 1538 1539 1540 1541 1542 1543 1544
## 54.61321 54.66377 54.77210 55.08575 55.21736 55.12796 54.98401 54.87510
## 1545 1546 1547 1548 1549 1550 1551 1552
## 54.74668 54.70690 54.63342 54.63093 56.26801 57.09188 57.77808 58.25525
## 1553 1554 1555 1556 1557 1558 1559 1560
## 59.01874 59.99779 60.93093 59.60697 59.59350 60.68085 62.72158 67.72996
## 1561 1562 1563 1564 1565 1566 1567 1568
## 55.07877 55.02275 55.22550 55.43359 56.06150 56.34267 56.67872 56.87008
## 1569 1570 1571 1572 1573 1574 1575 1576
## 57.26958 57.68574 58.33290 59.38081 55.46169 55.65265 55.73228 56.11739
## 1577 1578 1579 1580 1581 1582 1583 1584
## 56.59494 57.22094 57.19970 57.84808 58.29883 59.00488 58.93348 60.42515
## 1585 1586 1587 1588 1589 1590 1591 1592
## 54.51756 54.54786 54.54243 54.65078 54.68276 54.60092 54.47741 54.42805
## 1593 1594 1595 1596 1597 1598 1599 1600
## 54.44828 54.58013 54.66516 54.76357 61.58871 62.58587 63.49914 64.77318
## 1601 1602 1603 1604 1605 1606 1607 1608
## 66.11346 67.28651 67.90123 70.52658 71.32229 73.89952 76.50354 79.35216
## 1609 1610 1611 1612 1613 1614 1615 1616
## 64.65664 65.31187 66.32612 68.89400 70.63462 72.36830 73.08494 76.81358
## 1617 1618 1619 1620 1621 1622 1623 1624
## 78.43481 81.31345 83.86025 86.80854 58.32822 58.66018 58.24147 58.12006
## 1625 1626 1627 1628 1629 1630 1631 1632
## 58.31800 58.93062 59.24872 59.65577 60.17941 61.01561 59.86581 62.07208
## 1633 1634 1635 1636 1637 1638 1639 1640
## 59.83736 61.45330 60.39815 61.25367 61.99085 64.00914 62.48585 61.51534
## 1641 1642 1643 1644 1645 1646 1647 1648
## 62.16575 61.73097 60.53741 62.68731 54.41837 54.47284 54.54609 54.44289
## 1649 1650 1651 1652 1653 1654 1655 1656
## 54.49060 54.50133 54.49651 54.58338 54.71205 55.01561 55.30516 55.82308
## 1657 1658 1659 1660 1661 1662 1663 1664
## 55.11481 55.35305 55.63750 55.98228 56.35225 56.77249 57.27212 57.86197
## 1665 1666 1667 1668 1669 1670 1671 1672
## 58.55836 59.39439 57.40938 56.26960 54.55348 54.57116 54.58707 54.61523
## 1673 1674 1675 1676 1677 1678 1679 1680
## 54.92317 55.35512 55.46816 55.46371 55.39316 55.57519 55.66494 55.70008
## 1681 1682 1683 1684 1685 1686 1687 1688
## 54.83318 54.95905 55.06673 55.31482 55.31208 55.17072 55.03303 54.88360
## 1689 1690 1691 1692 1693 1694 1695 1696
## 54.88175 54.77502 54.77522 54.92789 54.26678 54.35235 54.35886 54.39139
## 1697 1698 1699 1700 1701 1702 1703 1704
## 54.56698 54.47995 54.55894 54.49569 54.48595 54.56169 54.46959 54.31483Recall that the fitted values plus the residuals will be equal to the observed values for lifeExp.
gapminder %>%
lm(lifeExp ~ gdpPercap, data = .) %>%
residuals()## 1 2 3 4 5 6
## -25.75074507 -24.25141712 -22.61108281 -20.57515356 -18.43355958 -16.11884535
## 7 8 9 10 11 12
## -14.84962486 -13.78554374 -12.77823084 -12.67852245 -12.38242715 -10.87300047
## 13 14 15 16 17 18
## 0.04981907 3.83881961 9.09535049 10.15321238 11.20005998 12.27210573
## 19 20 21 22 23 24
## 13.68724146 15.18459435 15.71519221 16.55212706 18.17375745 17.92630825
## 25 26 27 28 29 30
## -12.75176474 -10.57589884 -7.60363645 -5.03212854 -2.63680782 0.30254655
## 31 32 33 34 35 36
## 3.01806576 7.49786656 9.94626787 11.52707138 12.99370879 13.58529333
## 37 38 39 40 41 42
## -26.63341459 -24.88448612 -23.22105658 -22.19483670 -20.21398390 -16.77382303
## 43 44 45 46 47 48
## -16.12230690 -15.90838505 -15.31855444 -14.73430643 -15.07380022 -14.89387983
## 49 50 51 52 53 54
## 4.00797681 5.19874878 5.73040420 5.51887509 5.88662280 6.81616645
## 55 56 57 58 59 60
## 9.10410352 9.82766306 10.79259116 10.93075546 13.65527639 11.58971337
## 61 62 63 64 65 66
## 7.48532662 7.99924214 7.62969428 6.03365842 5.13310774 5.51092957
## 67 68 69 70 71 72
## 5.88681267 5.62200770 5.68724142 4.22418589 2.94190800 0.94042406
## 73 74 75 76 77 78
## 8.15029580 6.76088932 7.36139908 6.36747444 3.93025080 3.10844868
## 79 80 81 82 83 84
## 2.70520460 2.86603197 1.40046825 1.29947426 0.22877349 -1.75908830
## 85 86 87 88 89 90
## -10.56372281 -9.02358198 -6.78731975 -5.35639815 -4.62894070 -3.15546929
## 91 92 93 94 95 96
## 0.40216588 2.62573453 4.08545491 4.44842757 2.93846272 -1.11104125
## 97 98 99 100 101 102
## -16.99492737 -15.11363589 -13.26453162 -11.05418360 -9.18561564 -7.53728952
## 103 104 105 106 107 108
## -4.46437256 -1.71173687 1.42161267 4.71238420 7.18823380 9.04229324
## 109 110 111 112 113 114
## 7.66294277 7.85363431 7.88745578 6.92696567 4.73220580 4.22143216
## 115 116 117 118 119 120
## 3.92731903 4.16502677 2.94212887 2.49335804 1.04631561 -0.28544990
## 121 122 123 124 125 126
## -16.54544159 -14.33154309 -12.06381624 -9.86285035 -7.77206807 -5.55274846
## 127 128 129 130 131 132
## -4.02900259 -2.55619687 -0.94769496 -0.12164228 -0.59965138 1.67002533
## 133 134 135 136 137 138
## -15.58940134 -13.69299123 -12.19574893 -10.90222513 -9.52116461 -6.64643934
## 139 140 141 142 143 144
## -2.51092095 1.18918828 3.73608642 5.55032991 7.31669372 8.67495279
## 145 146 147 148 149 150
## -0.88019953 3.45879630 6.66673174 9.17284445 11.30674491 13.20556500
## 151 152 153 154 155 156
## 13.57806432 13.88464760 16.27445019 15.64273619 15.53062940 15.20089437
## 157 158 159 160 161 162
## -6.98466045 -5.03990101 -3.18794074 -1.58667094 0.33704226 2.90445016
## 163 164 165 166 167 168
## 4.04734946 4.91966625 2.70547714 -8.01360999 -15.73802748 -12.84202239
## 169 170 171 172 173 174
## -4.65165582 -2.57310396 -0.84265746 1.05299539 1.73495493 2.43922993
## 175 176 177 178 179 180
## 4.00267475 5.27792699 7.78528824 9.34551767 10.83101551 11.50016538
## 181 182 183 184 185 186
## 3.77484668 10.35315909 12.30036993 12.19868645 11.89813013 11.03196849
## 187 188 189 190 191 192
## 10.83389763 11.08191714 12.41367181 11.79779235 12.29730739 10.87988602
## 193 194 195 196 197 198
## -22.39608738 -19.52163380 -16.69419778 -13.86650992 -11.01833359 -8.38716472
## 199 200 201 202 203 204
## -6.45097307 -5.09618215 -4.40824241 -4.35536547 -4.09923770 -2.59144830
## 205 206 207 208 209 210
## -15.18408285 -13.71288327 -12.18224966 -10.72344021 -10.25354253 -8.47091461
## 211 212 213 214 215 216
## -6.91259168 -6.22017930 -9.70273715 -8.98378962 -6.93700718 -4.70451449
## 217 218 219 220 221 222
## -14.82039664 -12.92154927 -10.92064150 -8.94092517 -13.96105378 -23.13710299
## 223 224 225 226 227 228
## -3.47621133 -0.56466073 1.32555726 2.01679714 2.11093140 4.45659954
## 229 230 231 232 233 234
## -16.32951402 -14.53188858 -12.38309632 -10.31035052 -8.19473533 -5.96467774
## 235 236 237 238 239 240
## -2.80579020 -0.96129357 -1.01312035 -3.05253021 -5.57885268 -5.08752409
## 241 242 243 244 245 246
## 6.09989482 6.45109304 7.04721752 5.87773589 4.41417863 3.35750597
## 247 248 249 250 251 252
## 4.28955034 2.53827978 3.84522403 2.50731871 0.32169204 -1.08251355
## 253 254 255 256 257 258
## -19.31198785 -17.40241704 -15.39311846 -13.34651087 -11.31699546 -8.02910206
## 259 260 261 262 263 264
## -6.39236464 -4.11679214 -5.13162084 -8.45596132 -11.21257250 -9.75458068
## 265 266 267 268 269 270
## -16.76510199 -15.07540644 -13.30260826 -11.26998051 -9.23107086 -7.43992629
## 271 272 273 274 275 276
## -5.04886694 -3.63302450 -3.04085590 -3.15123838 -4.31490432 -4.60796965
## 277 278 279 280 281 282
## -2.22418229 -1.18250582 0.51186228 2.66144785 5.28315516 9.45807300
## 283 284 285 286 287 288
## 12.71185282 14.29358631 14.36029418 14.12131581 15.65993438 14.52268111
## 289 290 291 292 293 294
## -10.26185707 -3.84716334 -9.82721427 3.95691117 8.64556999 9.44483944
## 295 296 297 298 299 300
## 10.83329971 12.26373937 13.46795855 14.71944365 15.68655529 15.21229822
## 301 302 303 304 305 306
## -4.95255731 -0.61499944 2.00108301 3.95852515 5.17035730 6.96279389
## 307 308 309 310 311 312
## 9.33380981 10.06205191 10.30092187 11.67837527 13.32434064 13.57422733
## 313 314 315 316 317 318
## -14.08421951 -12.42194739 -10.56448174 -8.91850340 -6.49358042 -3.91346460
## 319 320 321 322 323 324
## -1.99174374 -0.03613177 3.02970131 5.80675890 8.19556953 10.44215172
## 325 326 327 328 329 330
## -15.40958416 -13.99643765 -12.51913639 -10.55857860 -8.65870018 -6.76022181
## 331 332 333 334 335 336
## -6.68689889 -7.05815466 -8.75766234 -11.60734838 -9.17402447 -7.70585548
## 337 338 339 340 341 342
## -13.47041182 -10.67330748 -7.40583075 -3.96387044 -1.50624561 -0.82345033
## 343 344 345 346 347 348
## -0.99281151 0.30101801 -0.59451281 -3.65853775 -3.65045942 -1.41204131
## 349 350 351 352 353 354
## 1.24108516 3.78343174 6.23922844 8.28520571 9.97865734 12.26107377
## 355 356 357 358 359 360
## 15.46906463 16.49021458 17.04544357 18.19728302 18.25990838 17.44909900
## 361 362 363 364 365 366
## -14.54067289 -12.63457013 -10.34794310 -8.17513868 -5.97360564 -3.50733388
## 367 368 369 370 371 372
## -1.96332872 -0.95037915 -3.17214392 -7.33084429 -8.38470002 -6.80911343
## 373 374 375 376 377 378
## 4.86858923 7.49620103 8.98449610 9.22062806 8.64498559 8.03714617
## 379 380 381 382 383 384
## 6.39129701 6.99178451 12.10986740 12.17076058 12.02608618 10.61044933
## 385 386 387 388 389 390
## 1.19239254 3.70964066 7.32776882 9.98205185 12.70939610 13.81310923
## 391 392 393 394 395 396
## 14.16485542 14.45663568 16.18056982 18.04060391 18.35258849 17.47319046
## 397 398 399 400 401 402
## 7.65499876 8.75930492 8.19092534 7.70520152 6.30801041 5.43405307
## 403 404 405 406 407 408
## 5.24266382 5.14886397 7.50889566 7.77920904 8.09540324 5.06563763
## 409 410 411 412 413 414
## 9.41090182 9.36450228 8.00479831 6.81434278 5.08400458 5.11331613
## 415 416 417 418 419 420
## 4.08563327 1.63351204 1.17638200 -0.64238774 -1.37915864 -2.60741125
## 421 422 423 424 425 426
## -21.18543765 -18.81892601 -16.57326315 -14.19154511 -12.41519981 -9.79374641
## 427 428 429 430 431 432
## -7.34601604 -6.11850136 -4.16980640 -2.24802649 -2.04215650 -0.75741489
## 433 434 435 436 437 438
## -9.09665046 -5.30884793 -1.76790090 1.53053509 4.00044212 5.78103235
## 439 440 441 442 443 444
## 7.58303920 9.87240016 12.17297249 13.23707576 13.40066145 13.67073452
## 445 446 447 448 449 450
## -8.29256225 -5.49123541 -2.44095864 -0.78001529 0.80109790 2.24531119
## 451 452 453 454 455 456
## 4.86873535 8.31764037 10.22394027 12.67377723 15.80173755 15.78120003
## 457 458 459 460 461 462
## -13.14779355 -10.62745985 -8.25876409 -6.05073165 -4.36668959 -2.76713659
## 463 464 465 466 467 468
## -0.62950288 2.86951764 6.81589672 10.06944478 12.21372471 13.11349062
## 469 470 471 472 473 474
## -11.02515487 -8.00262462 -4.53737244 -1.43437487 0.79398138 -1.19023343
## 475 476 477 478 479 480
## -0.48631322 6.03148681 9.44312341 11.63660254 12.68511711 13.54092091
## 481 482 483 484 485 486
## -19.76088378 -18.29847463 -16.91636659 -15.66888437 -13.95387734 -12.66475200
## 487 488 489 490 491 492
## -11.00323838 -9.03112347 -7.27645013 -7.86330837 -10.49983123 -11.67301324
## 493 494 495 496 497 498
## -18.27916180 -16.17180433 -14.08897799 -12.12513401 -10.20695854 -9.80740319
## 499 500 501 502 503 504
## -10.46702931 -7.90116733 -4.41037924 -1.27625883 0.69903619 3.59386670
## 505 506 507 508 509 510
## -20.15456028 -17.57837810 -14.21739581 -12.23533107 -10.87367104 -9.87145395
## 511 512 513 514 515 516
## -9.48155654 -7.71040565 -6.18684683 -4.94815573 -3.63598963 -1.53694608
## 517 518 519 520 521 522
## 7.68043596 7.76308182 7.62607936 7.52066905 5.93158409 6.62812197
## 523 524 525 526 527 528
## 6.41874844 4.70404569 5.95178088 5.02840125 2.84123718 -0.04208355
## 529 530 531 532 533 534
## 8.07745995 8.34838702 8.47690698 7.65102767 6.10432766 5.88271990
## 535 536 537 538 539 540
## 5.41198908 5.50620041 4.60893409 4.88179190 3.50941889 3.39545204
## 541 542 543 544 545 546
## -20.23656654 -18.76276846 -18.53884897 -15.75103289 -13.98671338 -17.79837257
## 547 548 549 550 551 552
## -8.95150919 -2.84044103 -2.93242454 -4.75580717 -6.77220259 -7.32197174
## 553 554 555 556 557 558
## -24.32670539 -22.28900868 -20.51822297 -18.66058358 -16.22587858 -12.79029482
## 559 560 561 562 563 564
## -9.01485715 -5.15840813 -1.82068544 1.40541226 3.58016866 4.91667392
## 565 566 567 568 569 570
## 8.08002998 7.35194729 6.47556912 5.56576595 3.26417544 2.85446160
## 571 572 573 574 575 576
## 2.99290200 2.04535353 1.84099263 2.12920380 1.74057535 0.84387792
## 577 578 579 580 581 582
## -11.50359762 -9.97476299 -8.41380268 -6.74458710 -4.98176375 -2.95926065
## 583 584 585 586 587 588
## -0.88162299 1.12557884 2.83787666 3.83154404 3.64690141 5.05097410
## 589 590 591 592 593 594
## 9.20387555 10.14404664 10.95199434 10.53291893 8.65143778 8.86652891
## 595 596 597 598 599 600
## 9.60588891 10.38412667 9.65725294 9.57365011 7.07967628 4.46378570
## 601 602 603 604 605 606
## -13.78987781 -11.81537806 -9.10526692 -6.41971669 -3.30111511 -1.65918266
## 607 608 609 610 611 612
## 0.49432630 3.57837568 6.02178021 8.78348877 11.30637342 12.33671946
## 613 614 615 616 617 618
## -20.73680132 -19.83833752 -18.72755619 -17.30067875 -15.68084851 -13.86259292
## 619 620 621 622 623 624
## -11.72025680 -9.01972928 -5.98714421 -3.16558792 -1.00282135 1.33041927
## 625 626 627 628 629 630
## -21.68491118 -20.79682990 -19.86685591 -19.01089609 -18.09693643 -17.07548650
## 631 632 633 634 635 636
## -15.26962736 -13.27383223 -11.25981139 -9.69191570 -8.89190743 -8.01060519
## 637 638 639 640 641 642
## -17.78422562 -14.58042745 -11.73974065 -8.82321459 -7.17902629 -5.46617961
## 643 644 645 646 647 648
## -4.03286192 -1.71395418 0.01953324 1.68917547 3.20975903 6.04132771
## 649 650 651 652 653 654
## -13.72242185 -10.98897338 -7.66702699 -4.97303907 -2.00659339 0.99636085
## 655 656 657 658 659 660
## 4.56565846 8.22412491 10.08630439 11.28606200 12.23851046 13.52838243
## 661 662 663 664 665 666
## 4.66816534 8.01862151 10.10511388 11.30372491 11.68372998 11.08835377
## 667 668 669 670 671 672
## 10.35734198 6.91735905 4.70877816 4.33888065 4.43308759 -2.13250779
## 673 674 675 676 677 678
## 6.04834635 7.83441024 8.22929986 8.41065044 8.02661050 7.06455859
## 679 680 681 682 683 684
## 5.83822856 5.69130592 7.15591965 8.12553938 7.28057037 5.60771000
## 685 686 687 688 689 690
## 12.97551035 12.44386284 11.80778205 9.58628203 8.42077438 7.12069937
## 691 692 693 694 695 696
## 5.23592010 2.68134579 5.58192996 3.53099089 2.70824666 0.12738125
## 697 698 699 700 701 702
## -17.00061953 -14.15788906 -10.85411919 -7.29856816 -3.85836079 -0.36966848
## 703 704 705 706 707 708
## 1.98591104 3.85052152 5.37680456 6.69361497 7.58736548 8.86678593
## 709 710 711 712 713 714
## -17.06097937 -14.69451879 -12.08716789 -8.57473171 -5.60242804 -2.31116569
## 715 716 717 718 719 720
## 1.04320929 4.84415122 6.90261600 9.69951345 12.43423304 13.98625618
## 721 722 723 724 725 726
## -11.40822907 -9.29122186 -7.83337679 -6.00451755 -6.07500392 -5.34694097
## 727 728 729 730 731 732
## -0.15504400 4.00341442 6.25201355 7.76576229 8.42734063 8.13142948
## 733 734 735 736 737 738
## -11.79434728 -10.28327003 -8.87901139 -6.32807951 -4.33010588 -4.77733702
## 739 740 741 742 743 744
## -3.02205612 2.18247241 2.64046355 2.50247668 -0.26794436 2.16960145
## 745 746 747 748 749 750
## 8.96918611 10.66180161 11.26204540 11.26882726 10.03451631 9.54524714
## 751 752 753 754 755 756
## 9.49290402 9.79332423 8.08100578 3.41002725 -2.23750468 -6.18292471
## 757 758 759 760 761 762
## 8.30872925 9.76533308 9.99946549 10.37421197 7.89393653 8.92643698
## 763 764 765 766 767 768
## 8.74046512 8.54775137 9.16714275 8.32998530 8.98522949 7.26712733
## 769 770 771 772 773 774
## 8.21249365 9.07495039 8.97906603 9.43847826 8.84988450 8.62028375
## 775 776 777 778 779 780
## 8.37520494 7.77315848 6.64658413 5.99094106 4.89212611 4.73795624
## 781 782 783 784 785 786
## 2.35740315 5.01625509 7.64178250 8.86975972 9.35838619 11.06781992
## 787 788 789 790 791 792
## 12.61309193 12.95648777 12.14654148 12.85900249 12.74125720 13.01182484
## 793 794 795 796 797 798
## 6.61384503 8.24190962 9.74407406 9.94203649 8.16040187 8.71944996
## 799 800 801 802 803 804
## 8.32787300 7.59946942 4.88654230 4.69313327 6.16528310 4.43426194
## 805 806 807 808 809 810
## -11.98076382 -9.72919119 -7.62551234 -4.42371326 0.95788176 4.99672490
## 811 812 813 814 815 816
## 6.60044426 8.51072105 11.43467269 13.02815154 14.36652868 15.12258169
## 817 818 819 820 821 822
## -12.33841952 -9.99194536 -6.69263489 -4.10984026 -1.33152281 1.22986378
## 823 824 825 826 827 828
## 3.77920461 4.34171725 4.30302648 -0.58917226 -3.94835855 -0.96477486
## 829 830 831 832 833 834
## -4.73196565 -1.07629451 1.46003383 4.34688210 7.19613306 10.06260055
## 835 836 837 838 839 840
## 12.00342918 13.55045440 13.17243780 12.47820857 11.44686239 12.12293098
## 841 842 843 844 845 846
## -7.29084299 -2.41239536 0.16131596 2.20831773 6.33817416 7.24821157
## 847 848 849 850 851 852
## 8.86654800 9.32762756 9.03008635 8.45826709 8.37769530 6.80885216
## 853 854 855 856 857 858
## -81.29034205 -82.75443547 -66.49981425 -51.20665346 -69.88184703 -29.94369601
## 859 860 861 862 863 864
## -6.62871878 -1.28886008 -5.48514494 -8.62480582 -3.90667149 -12.55185653
## 865 866 867 868 869 870
## -1.72561862 0.87546676 3.76747087 5.31980202 5.73923364 5.51978727
## 871 872 873 874 875 876
## 7.18333831 9.85759527 10.06578052 9.61291918 9.94836892 10.03595685
## 877 878 879 880 881 882
## -12.04614316 -9.16555924 -6.52354003 -5.84496122 -4.56838752 -2.31768111
## 883 884 885 886 887 888
## 0.51262641 2.63242514 4.98177683 0.69517510 -10.33792743 -12.56391527
## 889 890 891 892 893 894
## -15.91580667 -14.94453005 -13.93864575 -12.96538393 -11.95576581 -10.68133240
## 895 896 897 898 899 900
## -9.54122640 -8.31567858 -13.64050270 -12.20050746 -10.60908252 -8.59461035
## 901 902 903 904 905 906
## -13.05875496 -11.30409378 -11.31589650 -18.08751291 -17.25389052 -13.30366187
## 907 908 909 910 911 912
## -5.08219382 3.27531922 7.42586445 10.35795391 11.48852977 10.77386714
## 913 914 915 916 917 918
## -18.37829550 -16.30611449 -14.36455916 -12.32441529 -10.44200636 -8.25571453
## 919 920 921 922 923 924
## -5.98311016 -5.48933837 -2.53755604 0.26803851 2.64614674 4.68831258
## 925 926 927 928 929 930
## -17.98192884 -17.06703492 -15.87285499 -14.84757153 -12.63672808 -10.69584916
## 931 932 933 934 935 936
## -8.79758162 -6.98465708 -4.96634280 -6.99007063 -9.45553147 -6.23337445
## 937 938 939 940 941 942
## -6.89316265 -3.23804971 0.22346117 3.67323349 6.87521596 8.37252833
## 943 944 945 946 947 948
## 10.28094423 11.52895616 11.17068990 10.23195236 11.28129880 10.76138365
## 949 950 951 952 953 954
## -20.61654558 -19.02364570 -17.39907602 -15.88542948 -14.42323984 -12.76657271
## 955 956 957 958 959 960
## -10.51226911 -8.11487183 -6.13282015 -4.65701550 -2.86527769 -0.28601342
## 961 962 963 964 965 966
## -13.98095734 -12.26474358 -10.51519743 -8.75357018 -6.73231627 -4.24896669
## 967 968 969 970 971 972
## -1.48946696 1.10207921 3.33615100 5.34001403 7.08367447 8.82923983
## 973 974 975 976 977 978
## -4.47481605 2.57763876 4.35599929 5.70805813 7.01849598 8.13597265
## 979 980 981 982 983 984
## 9.93452305 11.12555650 11.15558587 11.10064599 11.09780869 10.46462673
## 985 986 987 988 989 990
## -5.82691874 -1.92570921 0.83904560 1.75274303 3.19704210 5.20601902
## 991 992 993 994 995 996
## 6.09803913 8.89701935 10.25417673 12.24360272 12.72973276 13.07799986
## 997 998 999 1000 1001 1002
## -12.31319222 -9.40564067 -6.51254769 -3.64033846 -1.28902664 0.27528604
## 1003 1004 1005 1006 1007 1008
## 2.00321250 4.47813714 5.94981610 8.21443950 9.44002476 10.47953663
## 1009 1010 1011 1012 1013 1014
## 3.18334684 4.67594242 6.21604551 8.70362645 10.73086521 11.77067884
## 1015 1016 1017 1018 1019 1020
## 11.56147658 11.93544567 16.12270661 16.54400366 15.00995499 13.50929455
## 1021 1022 1023 1024 1025 1026
## -12.37383849 -9.78849996 -7.22963749 -4.92930933 -2.56993352 -0.03880696
## 1027 1028 1029 1030 1031 1032
## 3.62725171 6.61415148 9.18252893 11.42348116 13.16707239 14.28645337
## 1033 1034 1035 1036 1037 1038
## -23.02792831 -20.55562665 -18.22036061 -16.27599628 -14.18203793 -11.84477652
## 1039 1040 1041 1042 1043 1044
## -11.51409837 -11.39277041 -9.98584873 -7.97285019 -10.41420425 -12.50358372
## 1045 1046 1047 1048 1049 1050
## -17.88973703 -12.31826980 -9.14433534 -4.84350492 -1.15862398 1.81966766
## 1051 1052 1053 1054 1055 1056
## 3.77612888 4.08895930 5.09902484 6.05501282 5.48509583 7.39138990
## 1057 1058 1059 1060 1061 1062
## -14.08446848 -10.73466101 -7.99669843 -5.69829217 -2.95387319 -0.48361772
## 1063 1064 1065 1066 1067 1068
## 1.80673906 4.05416811 5.13341402 1.97076068 -5.59141142 -4.72945752
## 1069 1070 1071 1072 1073 1074
## -18.21608410 -16.72691202 -15.06156791 -13.00095980 -10.50069461 -7.73847544
## 1075 1076 1077 1078 1079 1080
## -4.91103199 -2.01182868 1.08477310 4.69722527 6.57580036 8.99467697
## 1081 1082 1083 1084 1085 1086
## 11.33518596 10.40947442 9.49094023 8.11335473 5.41866427 5.06199774
## 1087 1088 1089 1090 1091 1092
## 5.72636312 4.78395207 2.97250662 0.93969861 -1.22104294 -2.33966158
## 1093 1094 1095 1096 1097 1098
## 7.35989757 6.93661895 7.20659164 6.50123850 5.66110363 5.84755013
## 1099 1100 1101 1102 1103 1104
## 6.39771435 5.82616830 8.32865050 7.49334288 7.41696244 6.98486265
## 1105 1106 1107 1108 1109 1110
## -14.02215406 -11.16807834 -8.10342315 -5.62321202 -2.39078451 -0.68199093
## 1111 1112 1113 1114 1115 1116
## 2.68803768 5.79145797 10.22752772 12.74714092 14.98769967 16.84053122
## 1117 1118 1119 1120 1121 1122
## -17.09430919 -15.99663823 -15.23173486 -14.64404158 -14.13941896 -13.28327221
## 1123 1124 1125 1126 1127 1128
## -12.05339155 -9.91173197 -7.00909746 -3.08642626 0.08068767 2.43745902
## 1129 1130 1131 1132 1133 1134
## -18.45555508 -16.99538503 -15.47588533 -13.69154511 -12.43362903 -10.95752142
## 1135 1136 1137 1138 1139 1140
## -9.33576074 -8.12894596 -7.72255467 -7.73445026 -8.58306541 -8.63701717
## 1141 1142 1143 1144 1145 1146
## 10.99262622 10.57051736 9.22646039 7.60952371 5.87839723 3.58399246
## 1147 1148 1149 1150 1151 1152
## 1.89906929 -2.19070523 -2.61530575 -7.21233696 -9.08355822 -11.51201923
## 1153 1154 1155 1156 1157 1158
## -17.77594252 -15.59099880 -13.02756582 -10.57852802 -9.93411433 -5.65115356
## 1159 1160 1161 1162 1163 1164
## -1.13645574 -0.07758073 3.00184303 3.47367849 5.11200952 4.61517041
## 1165 1166 1167 1168 1169 1170
## -11.04319735 -8.96999211 -6.90002380 -4.87639260 -2.82964099 -0.81200259
## 1171 1172 1173 1174 1175 1176
## 1.09838469 2.98555393 5.37422098 6.29492647 8.05375969 9.53419504
## 1177 1178 1179 1180 1181 1182
## -0.66176076 2.98000900 5.15640081 6.73388599 8.15741763 10.63185439
## 1183 1184 1185 1186 1187 1188
## 11.15491649 12.18665861 13.44387741 14.34129935 15.12993793 14.07856323
## 1189 1190 1191 1192 1193 1194
## 7.20015207 7.67537089 8.76245043 9.23668608 9.92938169 9.91281474
## 1195 1196 1197 1198 1199 1200
## 9.66118361 10.36376849 11.05967710 12.19567636 13.90537235 14.60470739
## 1201 1202 1203 1204 1205 1206
## -12.92839024 -10.93968406 -8.65111322 -6.93777303 -3.04930194 -0.31301126
## 1207 1208 1209 1210 1211 1212
## 2.52880035 5.31306385 9.10147950 9.96478830 11.43073220 11.79849581
## 1213 1214 1215 1216 1217 1218
## -7.17716546 -3.80555703 -0.46027470 1.04984453 2.58780142 4.28921634
## 1219 1220 1221 1222 1223 1224
## 6.13524019 8.52062531 10.75902373 12.66828757 14.31979560 15.29209555
## 1225 1226 1227 1228 1229 1230
## 4.27247475 8.19329113 9.60092024 10.63898674 10.77040085 9.44182670
## 1231 1232 1233 1234 1235 1236
## 10.90000970 10.07750630 11.11510314 11.02354985 11.53413470 9.83595277
## 1237 1238 1239 1240 1241 1242
## 3.51753450 4.66733469 6.81810846 7.77862439 8.40347862 8.67368130
## 1243 1244 1245 1246 1247 1248
## 9.82412863 10.13089810 8.50778209 8.52112018 8.05903821 8.45496541
## 1249 1250 1251 1252 1253 1254
## 7.96710156 11.59592315 11.75715495 11.84435483 11.22638279 12.01113414
## 1255 1256 1257 1258 1259 1260
## 11.89244478 11.28065379 8.75634319 7.95886755 9.40011312 10.00624498
## 1261 1262 1263 1264 1265 1266
## -3.31118906 -0.98386654 1.28291321 3.51071157 6.45757267 9.80429595
## 1267 1268 1269 1270 1271 1272
## 11.90063443 13.90097770 14.99269441 16.17211649 16.95731396 16.61969546
## 1273 1274 1275 1276 1277 1278
## 4.68917906 7.12822366 9.22272163 7.89498558 9.12664726 8.34789322
## 1279 1280 1281 1282 1283 1284
## 8.35750107 8.15792792 10.35742988 10.14519237 11.33506402 10.25322367
## 1285 1286 1287 1288 1289 1290
## -14.33289575 -12.86881886 -11.41255766 -10.24638816 -9.80728578 -9.46809390
## 1291 1292 1293 1294 1295 1296
## -8.41185897 -10.58417464 -30.92033186 -18.31979919 -11.14349381 -8.37372227
## 1297 1298 1299 1300 1301 1302
## -8.15733910 -5.66892360 -2.88217173 -0.58980142 1.35188530 3.26540836
## 1303 1304 1305 1306 1307 1308
## 4.94964408 6.61247512 7.69359176 8.32620310 9.34648223 10.34982386
## 1309 1310 1311 1312 1313 1314
## -19.02136228 -17.32716088 -16.93440761 -16.98340966 -19.06727909 -21.39988964
## 1315 1316 1317 1318 1319 1320
## -16.71488601 -3.87474318 -4.18848328 0.83103700 3.12654650 2.25803391
## 1321 1322 1323 1324 1325 1326
## -17.78691377 -15.82563146 -13.76743303 -11.62586120 -9.36262311 -6.27113097
## 1327 1328 1329 1330 1331 1332
## -2.73801987 0.71069196 3.19415663 5.16644073 6.48209648 7.79659890
## 1333 1334 1335 1336 1337 1338
## 1.30104293 3.91948913 5.76461091 6.84572105 6.69629227 6.41575021
## 1339 1340 1341 1342 1343 1344
## 4.59468473 5.12307953 10.57085623 12.22291285 13.72269072 12.56088853
## 1345 1346 1347 1348 1349 1350
## -24.29749525 -23.15387359 -22.04265934 -20.76504260 -19.59102823 -18.19884080
## 1351 1352 1353 1354 1355 1356
## -16.63112221 -14.93966153 -16.43998812 -14.49809928 -13.47858842 -12.04730333
## 1357 1358 1359 1360 1361 1362
## 4.66963006 7.04879789 9.03169765 10.18329805 8.98916459 8.26503619
## 1363 1364 1365 1366 1367 1368
## 6.20181099 5.17758148 2.88637913 -2.43602692 -2.73900915 -10.04256099
## 1369 1370 1371 1372 1373 1374
## 6.52292043 8.83380800 10.65226973 10.58955605 8.99483616 8.13988292
## 1375 1376 1377 1378 1379 1380
## 8.16413331 7.91734201 10.15922597 9.47929570 9.41237420 6.42072057
## 1381 1382 1383 1384 1385 1386
## 8.39042683 9.41048545 9.53254570 8.03034348 6.39252540 5.32930382
## 1387 1388 1389 1390 1391 1392
## 3.44149367 4.00755186 8.81184888 8.04820588 6.90194879 4.26074600
## 1393 1394 1395 1396 1397 1398
## -21.84627622 -19.94089600 -18.02205874 -15.96123099 -13.94216439 -13.09139987
## 1399 1400 1401 1402 1403 1404
## -11.90068016 -10.29076498 -15.00657672 -10.87235794 -8.69424996 -6.50495011
## 1405 1406 1407 1408 1409 1410
## -12.56085744 -10.16755169 -8.41696214 -7.47030163 -6.19961095 -4.56953706
## 1411 1412 1413 1414 1415 1416
## -2.34827904 0.89260259 2.40610901 0.55973781 -6.48853002 -11.70676129
## 1417 1418 1419 1420 1421 1422
## 8.05185247 9.21290097 11.37931674 11.37034027 10.96704284 10.30974780
## 1423 1424 1425 1426 1427 1428
## 11.69255335 10.88607707 9.38527786 9.17618470 6.82821778 4.94070758
## 1429 1430 1431 1432 1433 1434
## 2.80866427 6.68006684 7.41459416 9.44190392 10.15833394 10.96178403
## 1435 1436 1437 1438 1439 1440
## 13.54085149 13.61993274 14.77608136 14.46342670 14.55302817 15.40378203
## 1441 1442 1443 1444 1445 1446
## -16.55660445 -15.68566099 -14.58442015 -12.38868098 -10.14200049 -7.84058850
## 1447 1448 1449 1450 1451 1452
## -5.06742965 -3.36486559 -1.54091650 0.16898943 0.88872334 2.60991235
## 1453 1454 1455 1456 1457 1458
## -13.42693423 -11.48361671 -10.38332238 -9.32127700 -6.97726603 -4.31089625
## 1459 1460 1461 1462 1463 1464
## -1.37407252 0.67450429 1.80079394 -2.63183380 -13.24408590 -17.79484391
## 1465 1466 1467 1468 1469 1470
## 11.38163871 10.95301545 9.98386293 8.53363252 7.12503288 7.06202208
## 1471 1472 1473 1474 1475 1476
## 6.65631781 5.19320619 5.93902860 6.10845902 3.64153474 1.02970512
## 1477 1478 1479 1480 1481 1482
## 4.39448015 2.90578118 1.73705082 1.24803382 -0.97663097 0.79615328
## 1483 1484 1485 1486 1487 1488
## 0.53351956 0.29248871 -0.30354139 0.83468814 0.29055286 -0.94257004
## 1489 1490 1491 1492 1493 1494
## -9.32963431 -7.29099711 -5.32797693 -1.74001161 1.37360228 4.79526841
## 1495 1496 1497 1498 1499 1500
## 7.75707473 10.63447255 12.73831592 14.50101739 15.96836132 16.98675090
## 1501 1502 1503 1504 1505 1506
## 3.62126561 7.29110219 9.85015058 11.52219749 12.32708508 12.35375822
## 1507 1508 1509 1510 1511 1512
## 12.52414921 10.98899665 8.66624641 5.83859237 5.26206701 2.47832747
## 1513 1514 1515 1516 1517 1518
## -13.28871408 -11.51585864 -10.26180906 -8.84734861 -7.03618195 -4.77275453
## 1519 1520 1521 1522 1523 1524
## -4.01625388 -3.05680715 -4.14711106 -6.09319573 -4.99224714 -2.28565478
## 1525 1526 1527 1528 1529 1530
## -3.68718697 -0.93255447 1.33887437 3.33856374 5.28348342 7.03833243
## 1531 1532 1533 1534 1535 1536
## 8.81090684 9.84705901 9.81105507 9.08886743 10.08554458 10.95564119
## 1537 1538 1539 1540 1541 1542
## -16.01721360 -13.45577208 -10.85009973 -8.31674900 -5.45835733 -2.24095541
## 1543 1544 1545 1546 1547 1548
## 0.48699478 2.06589616 3.31432184 3.68310490 2.92758438 3.78907073
## 1549 1550 1551 1552 1553 1554
## 2.83199088 4.70811936 7.12191975 7.14475192 6.88125910 8.30220718
## 1555 1556 1557 1558 1559 1560
## 7.90106993 9.97502885 10.26849606 8.78415250 6.25442486 2.08904288
## 1561 1562 1563 1564 1565 1566
## -10.47877241 -7.92274998 -5.64649799 -3.38058964 -0.45950156 3.49433460
## 1567 1568 1569 1570 1571 1572
## 7.36927854 10.02391552 12.73141665 14.28726048 14.70909554 14.54218537
## 1573 1574 1575 1576 1577 1578
## -11.87669205 -7.57364751 -3.63428376 -1.78139184 0.41006134 2.28606153
## 1579 1580 1581 1582 1583 1584
## 3.83629925 5.25991791 7.84716906 9.83011992 11.91151728 11.35185028
## 1585 1586 1587 1588 1589 1590
## -14.53956107 -11.97686387 -9.19843372 -6.59977688 -3.66676225 -4.25091771
## 1591 1592 1593 1594 1595 1596
## -4.62841448 -2.91904756 -5.62327594 -10.00213275 -6.85215857 -3.22156770
## 1597 1598 1599 1600 1601 1602
## 7.59128624 7.83413209 7.26086288 6.58681787 5.89654038 5.47349184
## 1603 1604 1605 1606 1607 1608
## 6.13877396 4.48041894 5.09770780 3.31848251 1.96746414 0.07284069
## 1609 1610 1611 1612 1613 1614
## 3.78336213 4.17812921 3.88388048 1.86600137 0.70538059 1.01170050
## 1615 1616 1617 1618 1619 1620
## 1.56506128 -1.79358198 -2.34481334 -4.50344979 -6.55025394 -8.56653506
## 1621 1622 1623 1624 1625 1626
## 7.74278343 8.38381960 10.01152803 10.34794405 10.35500062 10.55038257
## 1627 1628 1629 1630 1631 1632
## 11.55628059 12.26222846 12.57258536 13.20738816 15.44118936 14.31191520
## 1633 1634 1635 1636 1637 1638
## -4.74935529 -3.54629744 0.37185233 2.22533107 3.72114829 3.44685911
## 1639 1640 1641 1642 1643 1644
## 6.07115414 8.67465672 8.98424514 10.41502824 12.22858735 11.05968743
## 1645 1646 1647 1648 1649 1650
## -14.00636574 -11.58583988 -9.18308788 -6.60488543 -4.23659755 1.26266696
## 1651 1652 1653 1654 1655 1656
## 4.31948674 8.23662387 12.94995248 15.65639073 17.71183683 18.42591970
## 1657 1658 1659 1660 1661 1662
## -11.95481115 -9.68205329 -7.51050440 -4.35128191 0.17974874 3.99250522
## 1663 1664 1665 1666 1667 1668
## 7.13388342 9.18403246 11.15963941 11.70161284 14.96062103 17.15240156
## 1669 1670 1671 1672 1673 1674
## -22.00548309 -20.60116173 -19.40706574 -17.63122791 -15.07517340 -11.18011651
## 1675 1676 1677 1678 1679 1680
## -6.35515992 -2.54171177 0.20584473 2.44481195 4.64306345 6.99791780
## 1681 1682 1683 1684 1685 1686
## -12.79517868 -10.88205384 -9.04372561 -7.54681648 -5.20507893 -3.78472099
## 1687 1688 1689 1690 1691 1692
## -3.21203467 -4.06260456 -8.78174552 -14.53702082 -15.58221978 -12.54388857
## 1693 1694 1695 1696 1697 1698
## -5.81577948 -3.88335466 -2.00086222 -0.39638724 1.06802087 3.19404500
## 1699 1700 1701 1702 1703 1704
## 5.80405759 7.85531165 5.89105360 -7.75269210 -14.48059156 -10.82783337lm(log(y) ~ log(x), data = gapminder).
gapminder %>%
lm(log(lifeExp) ~ log(gdpPercap), data = .) %>%
broom::tidy(conf.int = TRUE)## # A tibble: 2 × 7
## term estimate std.error statistic p.value conf.low conf.high
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 2.86 0.0233 123. 0 2.82 2.91
## 2 log(gdpPercap) 0.147 0.00282 51.9 0 0.141 0.152gapminder %>%
lm(lifeExp ~ log(gdpPercap), data = .) %>%
broom::glance()## # A tibble: 1 × 12
## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.652 0.652 7.62 3192. 0 1 -5877. 11760. 11777.
## # ℹ 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>You’ll need to wrap the transformation in I(), which “inhibits the interpretation” of arithmetic operators like “+”, “-”, “*“, and”^” in formulas. So the formula will look like: lm(y ~ I(x^2), data = gapminder). What’s the R-squared now? Does a log transformation, square transformation, or no transformation at all of gdpPercap seem to be the best fit?
gapminder %>%
lm(lifeExp ~ I(gdpPercap^2), data = .) %>%
broom::glance()## # A tibble: 1 × 12
## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.0489 0.0483 12.6 87.5 2.56e-20 1 -6734. 13475. 13491.
## # ℹ 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>lm(y ~ 0 + x, data = gapminder). Take the simple regression and omit the intercept.
gapminder %>%
lm(lifeExp ~ 0 + gdpPercap, data = .) %>%
broom::tidy(conf.int = TRUE)## # A tibble: 1 × 7
## term estimate std.error statistic p.value conf.low conf.high
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 gdpPercap 0.00337 0.0000888 38.0 3.25e-229 0.00320 0.00355gapminder %>%
lm(lifeExp ~ gdpPercap + year, data = .) %>%
broom::tidy(conf.int = TRUE)## # A tibble: 3 × 7
## term estimate std.error statistic p.value conf.low conf.high
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -418. 27.6 -15.2 9.76e- 49 -473. -364.
## 2 gdpPercap 0.000670 0.0000245 27.4 5.77e-137 0.000622 0.000718
## 3 year 0.239 0.0140 17.1 1.18e- 60 0.212 0.266Every year, a country’s life expectancy is expected to increase by 0.2389 years.
This variable is different from the numerical variables we’ve been working with (lifeExp, gdpPercap, and year are all numeric). ‘continent’ is a “factor” variable, which means the data is categorical rather than numeric. When you add ‘continent’, lm() lets different continents have different intercepts.
gapminder %>%
lm(lifeExp ~ gdpPercap + continent, data = .) %>%
broom::tidy(conf.int = TRUE)## # A tibble: 6 × 7
## term estimate std.error statistic p.value conf.low conf.high
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 47.9 0.340 141. 0 47.2 48.6
## 2 gdpPercap 0.000445 0.0000235 18.9 8.55e- 73 0.000399 0.000491
## 3 continentAmericas 13.6 0.601 22.6 2.82e- 99 12.4 14.8
## 4 continentAsia 8.66 0.555 15.6 2.72e- 51 7.57 9.75
## 5 continentEurope 17.6 0.626 28.1 7.60e-143 16.3 18.8
## 6 continentOceania 18.1 1.79 10.2 1.50e- 23 14.6 21.7What happened to Africa? One level has to be omitted to avoid the dummy variable trap. So the intercept is the OLS prediction for the intercept for Africa. It’s saying that if a country in Africa has a GDP per capita of $0 (which is nonsense), the life expectancy of the people in that country is expected to be 47.9 years. The intercept for a country in the Americas is 47.9 + 13.6 = 61.5 years.
Our model predicts that a country in Asia with $0 GDP per capita will have a life expectancy of 47.88 + 8.65 years.
Hint: an interaction between x and z is done like this: lm(y ~ x:z, data = gapminder)
gapminder %>%
lm(lifeExp ~ gdpPercap:continent, data = .) %>%
broom::tidy(conf.int = TRUE)## # A tibble: 6 × 7
## term estimate std.error statistic p.value conf.low conf.high
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 5.37e+1 0.317 170. 0 5.31e+1 54.4
## 2 gdpPercap:continent… 2.47e-5 0.000121 0.204 8.38e- 1 -2.13e-4 0.000262
## 3 gdpPercap:continent… 1.21e-3 0.0000633 19.2 3.22e- 74 1.09e-3 0.00134
## 4 gdpPercap:continent… 4.38e-4 0.0000317 13.8 3.08e- 41 3.76e-4 0.000500
## 5 gdpPercap:continent… 1.02e-3 0.0000334 30.5 1.26e-163 9.54e-4 0.00109
## 6 gdpPercap:continent… 1.05e-3 0.000102 10.3 2.32e- 24 8.53e-4 0.00125According to our model, a $1 larger GDP per capita can be associated with a 0.00101 year higher life expectancy in Europe.