The regression problem Friedman 2 as described in Friedman (1991) and Breiman (1996). Inputs are 4 independent variables uniformly distributed over the ranges $$0 \le x1 \le 100$$ $$40 \pi \le x2 \le 560 \pi$$ $$0 \le x3 \le 1$$ $$1 \le x4 \le 11$$ The outputs are created according to the formula $$y = (x1^2 + (x2 x3 - (1/(x2 x4)))^2)^{0.5} + e$$ where e is \(N(0,sd^2)\).
Value
Returns a list with components
- x
input values (independent variables)
- y
output values (dependent variable)
References
Breiman, Leo (1996) Bagging predictors. Machine Learning 24,
pages 123-140.
Friedman, Jerome H. (1991) Multivariate adaptive regression
splines. The Annals of Statistics 19 (1), pages 1-67.
See also
Other bark simulation functions:
sim_Friedman1(),
sim_Friedman3(),
sim_circle()
Other bark functions:
bark(),
bark-package,
bark-package-deprecated,
sim_Friedman1(),
sim_Friedman3(),
sim_circle()
Examples
sim_Friedman2(100, sd=125)
#> $x
#> [,1] [,2] [,3] [,4]
#> [1,] 18.262463 491.5231 0.07114439 6.978089
#> [2,] 5.607791 482.1103 0.01440722 7.477066
#> [3,] 7.704316 938.0194 0.63228474 7.580063
#> [4,] 10.147811 430.6193 0.36903048 6.600625
#> [5,] 62.153368 414.8822 0.85641368 3.859618
#> [6,] 51.718262 361.9174 0.53191017 7.673378
#> [7,] 59.719055 429.7168 0.77955279 9.740183
#> [8,] 87.474530 1442.6427 0.93296497 2.933012
#> [9,] 89.619381 259.8091 0.31156134 2.110618
#> [10,] 37.487429 650.6089 0.76978253 6.213695
#> [11,] 38.101307 125.9915 0.59951651 1.681106
#> [12,] 39.971403 254.9086 0.36559866 3.498771
#> [13,] 78.740243 1166.3633 0.96247087 5.035825
#> [14,] 72.517907 1424.6209 0.50298157 3.598552
#> [15,] 89.934109 1023.5085 0.50777279 10.886831
#> [16,] 74.971386 445.2254 0.64873961 10.519389
#> [17,] 86.015524 480.2190 0.08254605 10.578331
#> [18,] 58.866572 1588.9600 0.12493271 1.217222
#> [19,] 62.322241 156.3314 0.83155279 6.854086
#> [20,] 86.518436 1553.0864 0.45329176 2.425176
#> [21,] 32.615805 452.3908 0.36575743 1.131676
#> [22,] 64.928966 394.8766 0.91697840 4.042177
#> [23,] 57.656540 1503.3392 0.40876946 3.806401
#> [24,] 24.656280 1609.3011 0.46578712 3.304635
#> [25,] 80.270074 1130.0013 0.09705467 7.091302
#> [26,] 86.285008 1417.0428 0.71410556 3.516569
#> [27,] 66.537688 1559.7374 0.36151383 3.212030
#> [28,] 33.995277 362.3922 0.09457859 1.686985
#> [29,] 84.163848 775.6468 0.71676187 5.814709
#> [30,] 95.633813 1678.1716 0.87053314 2.235394
#> [31,] 82.801383 881.0271 0.70067009 9.192320
#> [32,] 19.797151 713.8181 0.49444926 10.784887
#> [33,] 94.382804 602.9954 0.23320481 1.529075
#> [34,] 9.588987 745.0397 0.82251561 4.589201
#> [35,] 69.347271 1511.6083 0.57814760 10.714830
#> [36,] 28.618559 1577.8851 0.82281658 6.468201
#> [37,] 4.622148 200.8398 0.57575076 2.056239
#> [38,] 62.884142 1296.8160 0.32929867 2.739424
#> [39,] 13.311413 536.4444 0.06095796 8.825691
#> [40,] 89.977071 1427.6955 0.48881298 4.816399
#> [41,] 36.681397 226.3136 0.70115230 6.243887
#> [42,] 83.000138 1431.5814 0.99965129 2.595934
#> [43,] 62.176392 707.6541 0.77052128 9.200219
#> [44,] 30.191458 1146.3607 0.56836875 6.407920
#> [45,] 45.645724 1224.4550 0.24446183 4.314882
#> [46,] 74.341682 488.5715 0.84033147 5.489354
#> [47,] 36.742740 482.0334 0.54786029 3.233426
#> [48,] 84.673994 1135.7622 0.05184123 3.941269
#> [49,] 88.429746 1237.4162 0.24467223 1.805190
#> [50,] 83.701030 1630.7357 0.70819886 6.926104
#> [51,] 76.682258 1516.3766 0.99561037 5.057091
#> [52,] 28.001987 1448.0801 0.49741377 4.026803
#> [53,] 86.592753 1577.8522 0.99795629 2.957071
#> [54,] 74.597069 813.5721 0.94435804 10.698488
#> [55,] 82.197207 290.3845 0.60513483 3.842885
#> [56,] 90.184483 675.9599 0.77718189 4.879202
#> [57,] 91.013115 706.7436 0.78288535 7.031318
#> [58,] 87.341718 1267.1097 0.39707278 8.704094
#> [59,] 15.962643 1601.2012 0.60478401 5.627293
#> [60,] 89.524400 904.2673 0.50216681 8.312079
#> [61,] 24.281698 640.5242 0.99602080 8.826385
#> [62,] 80.375353 790.0304 0.51258570 4.077453
#> [63,] 82.094168 390.1152 0.72745769 2.179077
#> [64,] 66.407117 797.4422 0.81472102 8.970994
#> [65,] 67.402452 1593.9706 0.72260843 1.611694
#> [66,] 49.845640 1158.2204 0.94623656 2.165398
#> [67,] 42.826414 716.8947 0.31894380 7.312426
#> [68,] 38.562026 1523.8975 0.89945890 4.182647
#> [69,] 37.278056 1268.5095 0.53605594 2.699829
#> [70,] 18.550458 434.6745 0.47007538 7.557141
#> [71,] 26.849755 345.5153 0.81768650 10.380134
#> [72,] 16.185893 1299.1987 0.17191988 9.355192
#> [73,] 5.315435 899.5591 0.33210020 5.269765
#> [74,] 10.338490 1324.4634 0.44689802 10.551321
#> [75,] 14.286200 643.3956 0.70963288 8.274537
#> [76,] 19.563285 889.4581 0.40360962 3.172217
#> [77,] 5.595757 186.1946 0.09469529 7.964189
#> [78,] 72.080033 380.7959 0.09920605 9.726578
#> [79,] 29.588607 945.5775 0.17765886 6.160170
#> [80,] 17.596138 977.9291 0.56791720 9.589185
#> [81,] 54.466443 1541.0992 0.69310552 9.400745
#> [82,] 29.280815 1159.3930 0.46378592 6.635512
#> [83,] 9.171389 857.0365 0.69600253 2.929414
#> [84,] 49.406546 772.3389 0.98230391 10.426093
#> [85,] 81.975772 572.1705 0.43780839 3.062772
#> [86,] 55.720458 283.5028 0.26466661 7.504752
#> [87,] 51.573961 1398.6325 0.29028419 3.675866
#> [88,] 13.762274 760.9968 0.99238614 5.326755
#> [89,] 63.072191 1107.2621 0.18165608 9.320026
#> [90,] 27.509516 797.0533 0.84727654 3.877584
#> [91,] 81.651935 1010.3020 0.60210431 8.817648
#> [92,] 40.656011 1663.5780 0.81782936 7.735521
#> [93,] 10.524811 826.3836 0.77276366 9.164330
#> [94,] 29.507558 1342.7608 0.58130633 3.310590
#> [95,] 85.806083 1680.0849 0.05593927 3.066666
#> [96,] 78.676377 843.4041 0.60383202 10.650448
#> [97,] 19.536995 127.2035 0.29153471 3.677354
#> [98,] 55.490650 1315.4058 0.49786227 8.004522
#> [99,] 54.204656 1742.0479 0.12102541 10.091623
#> [100,] 73.133351 135.1225 0.55348738 9.503634
#>
#> $y
#> [1] -130.386781 247.044660 576.417589 224.869373 327.095616 221.757782
#> [7] 175.159848 1397.780048 210.407995 599.053550 399.926705 240.318452
#> [13] 892.095663 725.848794 650.437591 579.310812 158.155312 180.538552
#> [19] 198.188255 883.979583 393.573330 574.211369 616.407128 982.886958
#> [25] 53.632263 881.139662 698.387337 -31.464549 484.055242 1437.760021
#> [31] 507.178161 270.324496 233.551586 354.221262 647.788709 1182.165628
#> [37] -37.883774 159.487213 97.355775 492.450107 236.026694 1621.991485
#> [43] 859.234827 508.744184 376.732335 451.598132 511.821178 205.008436
#> [49] 37.651928 1474.628395 1599.380608 874.315417 1643.415718 811.304368
#> [55] 187.362744 495.098991 317.745885 590.402769 580.114554 375.817764
#> [61] 705.211496 264.224872 192.677088 608.723279 1031.272492 1007.107962
#> [67] 230.364812 1352.862952 612.542698 291.583626 323.749882 256.941235
#> [73] 277.978273 468.119474 459.740296 117.919284 125.712886 272.468931
#> [79] 44.836861 468.021192 1113.493503 592.913090 594.934042 621.066562
#> [85] 388.368959 2.399765 359.798479 725.813365 144.097278 569.469726
#> [91] 582.150312 1625.025977 621.652475 906.138188 -51.275749 394.028874
#> [97] -61.744053 684.652265 498.292681 116.713696
#>