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 \(N(0,sd^2)\).
Arguments
- n
number of data points to create
- sd
Standard deviation of noise. The default value of 125 gives a signal to noise ratio (i.e., the ratio of the standard deviations) of 3:1. Thus, the variance of the function itself (without noise) accounts for 90% of the total variance.
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-package-deprecated,
bark-package,
bark(),
sim_Friedman1(),
sim_Friedman3(),
sim_circle()
Examples
sim_Friedman2(100, sd=125)
#> $x
#> [,1] [,2] [,3] [,4]
#> [1,] 40.31033018 392.9068 4.234940e-01 8.492036
#> [2,] 85.83408126 852.2963 1.442664e-01 5.029300
#> [3,] 50.59304684 556.1577 6.233667e-01 4.304461
#> [4,] 13.84852058 642.3058 3.472623e-02 7.215476
#> [5,] 37.05942985 285.7109 6.119674e-01 8.506449
#> [6,] 80.38637959 1111.7422 3.933060e-01 8.516819
#> [7,] 36.94892977 866.1329 6.701998e-02 2.235762
#> [8,] 85.30315752 476.1593 9.622922e-01 7.361692
#> [9,] 26.17233112 1369.7858 9.210643e-01 7.689601
#> [10,] 18.21045636 731.1982 1.725161e-01 9.129924
#> [11,] 83.66345980 1480.6888 7.736179e-01 10.958830
#> [12,] 37.39733321 215.4164 7.253227e-01 7.522358
#> [13,] 13.69014531 1661.6196 4.373341e-01 5.697070
#> [14,] 28.52341952 1083.6502 5.281554e-05 2.095540
#> [15,] 82.80846924 873.8537 9.806139e-01 4.496985
#> [16,] 31.44117317 1713.2009 3.355104e-01 6.904515
#> [17,] 15.41426326 1389.3388 1.046550e-01 4.881321
#> [18,] 5.34289824 192.4677 2.320298e-01 6.607259
#> [19,] 11.81400716 1478.6781 3.216293e-01 4.485120
#> [20,] 36.82703609 1367.8765 1.415886e-01 3.135537
#> [21,] 30.52050890 1738.0367 4.256025e-01 3.146900
#> [22,] 60.63664923 369.1924 9.130099e-01 5.122639
#> [23,] 75.98668458 397.9552 5.281590e-01 1.862510
#> [24,] 76.83549840 1547.0915 8.298280e-01 3.171977
#> [25,] 5.16630823 208.5042 6.320202e-01 2.742757
#> [26,] 1.55121456 993.8004 6.030199e-01 5.721088
#> [27,] 61.89282371 346.8844 8.656386e-01 3.132223
#> [28,] 27.16715944 437.9407 1.908079e-01 10.128243
#> [29,] 4.24223798 290.0046 2.642196e-01 4.755193
#> [30,] 0.37476788 1627.5438 6.430273e-01 10.049531
#> [31,] 46.03025834 462.2176 3.540388e-01 3.152695
#> [32,] 2.35659701 940.3333 5.999537e-01 9.818145
#> [33,] 6.89610131 1312.3817 7.341556e-01 8.321876
#> [34,] 28.83316854 484.3093 2.935392e-01 6.780161
#> [35,] 79.87668863 998.4419 9.084195e-01 1.479679
#> [36,] 47.91614835 1037.6755 6.433106e-01 8.232159
#> [37,] 44.34666105 1029.2295 7.667393e-01 8.315256
#> [38,] 68.57045353 1258.3297 1.843836e-01 4.162148
#> [39,] 27.46232273 360.6011 8.232718e-01 5.148551
#> [40,] 93.25197928 761.8242 6.868438e-01 1.055510
#> [41,] 75.17115991 1500.3825 5.351089e-01 1.826496
#> [42,] 57.99147671 1045.8018 1.532441e-01 8.788244
#> [43,] 90.91170665 1500.9688 4.851869e-01 8.808681
#> [44,] 87.79961099 434.3643 3.328602e-01 4.744891
#> [45,] 45.32646656 513.7015 8.812874e-01 6.490534
#> [46,] 23.73316356 1482.9461 1.126794e-01 3.515720
#> [47,] 28.91706980 1291.0490 4.289537e-01 7.499692
#> [48,] 46.86446693 410.9832 2.225182e-01 9.219056
#> [49,] 76.24004970 1691.7291 6.671319e-01 8.805002
#> [50,] 41.24804994 454.7849 6.816068e-01 7.538328
#> [51,] 67.20454623 977.1106 2.850808e-02 4.576211
#> [52,] 59.21448714 1523.5920 3.762219e-01 3.676311
#> [53,] 75.85058238 396.5897 9.619086e-02 3.300054
#> [54,] 85.43704432 126.5850 8.306405e-01 8.513437
#> [55,] 22.73612176 264.6511 7.398675e-01 4.403511
#> [56,] 0.08090667 1715.9546 4.322950e-01 5.191691
#> [57,] 53.80831901 1437.5885 6.308986e-01 7.670706
#> [58,] 30.44114781 189.6070 7.869683e-01 2.674233
#> [59,] 14.76664240 860.6449 3.506726e-01 6.910719
#> [60,] 21.20272305 244.0436 2.643117e-01 5.508392
#> [61,] 99.56628431 1673.4203 2.345411e-01 2.742866
#> [62,] 89.70391413 978.2079 3.164071e-01 3.150918
#> [63,] 14.30061234 1368.1915 5.529929e-01 3.430588
#> [64,] 36.21285867 1687.3594 7.531868e-01 10.253146
#> [65,] 44.18814897 838.3010 9.012047e-01 9.354260
#> [66,] 87.40188607 1647.2802 5.395599e-01 9.610504
#> [67,] 97.45918962 275.4555 2.024721e-01 8.346496
#> [68,] 81.87260139 863.3771 1.278682e-01 3.526732
#> [69,] 85.03514479 477.1280 8.309138e-01 10.562176
#> [70,] 38.91721342 371.7449 6.520063e-02 9.046101
#> [71,] 79.33953984 325.6327 8.413347e-01 8.343739
#> [72,] 82.22308545 1529.6128 6.025897e-01 10.067588
#> [73,] 41.47189143 175.2934 5.764747e-02 8.072306
#> [74,] 99.89077931 1655.8989 6.473664e-01 10.009166
#> [75,] 63.07461711 1417.8543 9.218605e-01 3.519825
#> [76,] 97.55246902 1628.5366 8.257336e-01 8.030802
#> [77,] 11.65834414 1105.7170 4.079828e-01 2.519754
#> [78,] 91.45692517 1552.5930 2.983137e-01 4.413569
#> [79,] 50.74741349 1410.7695 6.923392e-02 7.303725
#> [80,] 93.36117711 686.3985 8.743553e-01 7.881417
#> [81,] 51.96310114 634.1457 7.707882e-01 9.140969
#> [82,] 98.49658618 884.3117 7.486028e-01 2.556467
#> [83,] 38.71217181 1443.0351 8.662715e-01 8.542493
#> [84,] 88.50824367 1447.8898 7.110395e-01 3.483382
#> [85,] 41.33270294 645.6988 3.710737e-01 6.034954
#> [86,] 24.77983322 1619.5769 3.767196e-01 4.311213
#> [87,] 24.55436361 959.9580 7.480623e-01 2.260164
#> [88,] 90.11276301 1495.8486 8.915209e-01 7.282821
#> [89,] 14.15408393 850.3424 3.837797e-01 1.578305
#> [90,] 15.11031894 1302.5998 8.554977e-01 9.616837
#> [91,] 18.81693676 1317.3113 7.381299e-01 6.766259
#> [92,] 2.52145468 941.9654 6.717267e-01 3.349248
#> [93,] 55.98446950 558.1767 4.447505e-01 6.716263
#> [94,] 63.92070991 660.4935 9.838993e-01 5.322187
#> [95,] 32.15269595 1142.1360 6.458190e-01 6.945927
#> [96,] 78.36734289 1127.1643 6.475675e-01 4.341003
#> [97,] 71.83093901 373.2856 6.136161e-01 7.884168
#> [98,] 98.93729149 1102.7284 8.470273e-01 3.257250
#> [99,] 16.40526105 1192.0949 6.763981e-01 4.582068
#> [100,] 4.68827116 311.7199 4.522710e-01 6.762997
#>
#> $y
#> [1] 286.577360 164.257028 336.715002 66.833563 120.559018 538.687678
#> [7] 137.400229 475.275051 1211.910339 110.650646 1099.164586 188.840342
#> [13] 742.472986 -65.774555 1075.444462 510.055972 75.310446 15.509392
#> [19] 570.617536 371.373014 542.682288 430.513324 212.319324 1499.545946
#> [25] 239.684563 563.283100 395.517683 171.539845 3.969427 904.995145
#> [31] 270.815353 502.739446 748.510784 278.770141 817.452291 796.456259
#> [37] 868.519967 107.287813 141.692919 457.952289 833.662775 273.227996
#> [43] 977.576357 15.787150 467.613514 36.728221 559.499044 106.319826
#> [49] 1126.924666 216.539024 44.192958 402.381721 18.978338 20.159805
#> [55] 275.361760 822.991073 1038.011971 185.159136 280.951634 186.427092
#> [61] 96.432573 200.044602 499.567860 1389.338935 754.057929 882.701357
#> [67] 70.248076 318.750407 295.096853 100.185334 392.761457 999.654909
#> [73] 57.309942 1279.683289 1320.467894 1418.757321 628.424827 228.462055
#> [79] 163.774504 771.739322 381.373706 733.236598 1518.855082 1114.267528
#> [85] 291.399357 618.530204 840.041342 1306.768278 326.351650 899.969575
#> [91] 1053.978365 759.885223 212.781460 544.336490 839.121054 714.488545
#> [97] 271.782007 878.478943 986.118566 227.459800
#>