The regression problem Friedman 3 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 $$\mbox{atan}((x2 x3 - (1/(x2 x4)))/x1) + e$$ 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_Friedman2(),
sim_circle()
Other bark functions:
bark(),
bark-package,
bark-package-deprecated,
sim_Friedman1(),
sim_Friedman2(),
sim_circle()
Examples
sim_Friedman3(n=100, sd=0.1)
#> $x
#> [,1] [,2] [,3] [,4]
#> [1,] 30.825952 1127.9017 0.573424780 1.478231
#> [2,] 56.282889 1152.0600 0.870915000 2.033601
#> [3,] 10.283905 413.8673 0.921000510 2.241561
#> [4,] 86.429125 1104.0521 0.973211584 6.799358
#> [5,] 37.058717 1020.2058 0.565367990 2.493783
#> [6,] 56.669640 1049.0497 0.580058141 4.571176
#> [7,] 85.620612 1074.8537 0.451348698 8.135946
#> [8,] 93.787521 137.4751 0.749643839 1.383408
#> [9,] 57.649304 523.8623 0.534890170 8.120493
#> [10,] 96.398831 295.6232 0.395163982 4.895550
#> [11,] 94.458449 410.7939 0.594093726 8.949516
#> [12,] 96.417692 1493.8341 0.346676224 4.511120
#> [13,] 70.495891 1191.4955 0.203333060 4.434715
#> [14,] 91.507220 496.2649 0.871611096 7.487752
#> [15,] 65.914199 1447.5109 0.120421228 6.590462
#> [16,] 70.462228 509.5219 0.254895523 6.631807
#> [17,] 88.310760 707.1107 0.315147347 6.045018
#> [18,] 27.884101 863.0375 0.673826131 10.039038
#> [19,] 4.354110 562.6515 0.241721363 4.982203
#> [20,] 99.230953 367.8261 0.718741739 4.130821
#> [21,] 45.822133 1334.5513 0.105027412 4.170977
#> [22,] 60.809732 145.8603 0.494299243 8.691526
#> [23,] 84.767140 890.9077 0.059236672 8.451566
#> [24,] 94.884000 839.6750 0.493812188 5.903832
#> [25,] 1.986057 559.6768 0.250226249 10.288233
#> [26,] 73.319807 1185.0692 0.891174042 5.008642
#> [27,] 40.755611 649.4596 0.080101752 8.312420
#> [28,] 41.391993 264.0161 0.017509584 10.617382
#> [29,] 82.039428 804.2670 0.294779242 2.655079
#> [30,] 17.574505 960.1463 0.817871663 5.938581
#> [31,] 26.556426 298.4271 0.199264202 1.604306
#> [32,] 3.464958 717.8549 0.441008693 5.314073
#> [33,] 53.889174 1590.9096 0.213425233 2.594641
#> [34,] 37.871453 259.6782 0.594987497 4.236741
#> [35,] 89.704471 850.2740 0.932048126 5.143644
#> [36,] 63.366214 1469.9975 0.090543105 7.923376
#> [37,] 63.607036 194.8063 0.773080538 7.309777
#> [38,] 66.784642 904.3950 0.720907238 10.137250
#> [39,] 2.151921 1162.1605 0.853163768 9.627817
#> [40,] 66.294452 1369.9562 0.240071075 10.613858
#> [41,] 52.770047 390.6047 0.331604818 8.430682
#> [42,] 76.327332 1201.1006 0.413337878 3.661946
#> [43,] 26.010365 413.9119 0.514562150 9.632506
#> [44,] 62.974862 1484.3180 0.143993061 10.936522
#> [45,] 48.456779 1606.1559 0.028128325 9.897014
#> [46,] 2.470620 1030.3406 0.083775715 2.060839
#> [47,] 41.875079 669.4004 0.303986391 2.532628
#> [48,] 19.881345 496.2695 0.218112098 8.412991
#> [49,] 25.576360 1699.0529 0.305153707 2.291095
#> [50,] 73.444774 1470.8927 0.338777487 10.828080
#> [51,] 41.187703 1736.6659 0.509695614 8.165728
#> [52,] 11.476699 1433.8945 0.367414622 10.002884
#> [53,] 35.062301 407.1805 0.145373559 3.248528
#> [54,] 1.898003 1559.2784 0.236825332 3.996812
#> [55,] 53.919572 1456.4783 0.333344291 8.070362
#> [56,] 71.965680 343.9097 0.544956580 1.677744
#> [57,] 31.661532 1443.2678 0.221341793 9.818495
#> [58,] 67.579770 1167.5540 0.347526818 4.580853
#> [59,] 60.254614 316.3190 0.061869972 5.362826
#> [60,] 54.028325 268.6651 0.983538146 6.689607
#> [61,] 83.446984 1406.3700 0.232457852 1.697569
#> [62,] 59.118330 646.0840 0.142002595 3.241725
#> [63,] 49.596202 1448.2511 0.977395241 2.890007
#> [64,] 10.458808 1525.4039 0.275599060 4.622639
#> [65,] 44.228854 790.7129 0.944558017 3.884189
#> [66,] 26.763161 1037.2351 0.444347145 2.409515
#> [67,] 67.805727 476.5362 0.016627895 10.148604
#> [68,] 82.057226 1040.8143 0.806981719 2.771745
#> [69,] 30.498487 1095.2270 0.070730513 1.283073
#> [70,] 72.519565 1489.9240 0.967027876 6.343249
#> [71,] 88.149093 1745.3359 0.932933122 4.964997
#> [72,] 88.459378 934.9048 0.596474341 8.683736
#> [73,] 96.992085 989.8979 0.550144838 9.541985
#> [74,] 77.908849 1570.3274 0.129840423 5.800195
#> [75,] 84.016820 1518.6840 0.378134911 5.594849
#> [76,] 21.680225 1390.7443 0.425370500 9.164034
#> [77,] 31.560739 390.4897 0.830497077 1.909209
#> [78,] 4.398040 231.3197 0.111564942 1.372887
#> [79,] 54.870058 185.2058 0.472555966 4.651288
#> [80,] 77.442946 280.1721 0.973888866 1.147488
#> [81,] 48.996267 841.1061 0.436716406 5.406159
#> [82,] 54.964301 1528.7694 0.294627368 8.299121
#> [83,] 7.630711 779.2293 0.169721953 2.274610
#> [84,] 88.413986 1573.9854 0.791205528 3.551065
#> [85,] 33.834462 1218.1433 0.809181832 9.308088
#> [86,] 6.441419 1707.2070 0.950115869 2.746835
#> [87,] 29.304838 1675.8857 0.492245314 7.896159
#> [88,] 62.641159 311.2145 0.460462597 5.304011
#> [89,] 28.528188 874.4557 0.332182426 8.931595
#> [90,] 8.386399 632.0582 0.676949844 2.974928
#> [91,] 90.108014 281.6644 0.174675048 10.877295
#> [92,] 44.483487 139.9396 0.838248761 1.742246
#> [93,] 23.416390 427.4938 0.239468809 5.791856
#> [94,] 23.394862 621.4651 0.816823635 9.557527
#> [95,] 51.664437 1751.4432 0.143833089 1.410754
#> [96,] 14.479299 1269.4888 0.370566186 10.354301
#> [97,] 6.220333 1386.0282 0.956884115 6.977835
#> [98,] 71.859516 159.7813 0.845859981 9.976063
#> [99,] 62.156340 580.9319 0.881534312 4.899534
#> [100,] 28.626160 526.7528 0.005404439 10.791704
#>
#> $y
#> [1] 1.55845593 1.62135963 1.59164799 1.61660710 1.48245246 1.47342289
#> [7] 1.43685486 0.89098999 1.21807163 0.87597717 1.12879908 1.28617670
#> [13] 1.53598528 1.46310158 1.37315462 1.03143303 1.20409573 1.53340144
#> [19] 1.71351951 1.06730746 1.12111759 0.90721157 0.56803291 1.17962792
#> [25] 1.62668378 1.46015556 0.97394053 0.06614486 1.20770422 1.50682298
#> [31] 1.05558016 1.60445814 1.50403672 1.23575106 1.35204559 1.00511700
#> [37] 0.96651611 1.34832957 1.68724931 1.30338894 1.19250371 1.30944982
#> [43] 1.41172915 1.16471093 0.84679889 1.54285974 1.33121444 1.24389417
#> [49] 1.66624222 1.42276030 1.56724967 1.41478802 0.90886807 1.64581436
#> [55] 1.32891832 1.23505317 1.48920327 1.24907667 0.16635414 1.53373651
#> [61] 1.25920313 1.05295061 1.63704348 1.59548563 1.41427255 1.47576587
#> [67] -0.02143759 1.47472971 1.10870813 1.63072137 1.68037500 1.41537110
#> [73] 1.45999089 1.10667827 1.38693292 1.47071790 1.32485388 1.21269998
#> [79] 1.09013858 1.33708294 1.58307448 1.45902861 1.47930360 1.51566074
#> [85] 1.67539290 1.48119998 1.51055379 1.11524523 1.57217760 1.51152985
#> [91] 0.64790509 1.19435007 1.60345166 1.51104608 1.40353431 1.55342898
#> [97] 1.50222820 1.00186983 1.39480412 0.24371478
#>