Creates polynomial variables, to be used in regression. Will create polynomials of degree less than
or equal to the degree specified, and will mean center variables by default.
Usage
polynomial(x, degree = 2, center = mean(x, na.rm = TRUE))Arguments
- x
variable used to create the polynomials.
- degree
the maximum degree polynomial to be returned. Polynomials of degree <=
degreewill be returned.- center
the value to center the polynomials at.
Examples
# Reading in a dataset
data(mri)
# Create a polynomial on ldl
polynomial(mri$ldl, degree=3)
#> Linear(ctr) Square(ctr) Cube(ctr)
#> [1,] 9.1972414 8.458925e+01 7.779877e+02
#> [2,] -41.8027586 1.747471e+03 -7.304909e+04
#> [3,] -10.8027586 1.166996e+02 -1.260678e+03
#> [4,] -64.8027586 4.199398e+03 -2.721325e+05
#> [5,] 22.1972414 4.927175e+02 1.093697e+04
#> [6,] 37.1972414 1.383635e+03 5.146740e+04
#> [7,] -24.8027586 6.151768e+02 -1.525808e+04
#> [8,] -9.8027586 9.609408e+01 -9.419870e+02
#> [9,] -1.8027586 3.249939e+00 -5.858855e+00
#> [10,] -15.8027586 2.497272e+02 -3.946378e+03
#> [11,] 10.1972414 1.039837e+02 1.060347e+03
#> [12,] -17.8027586 3.169382e+02 -5.642375e+03
#> [13,] 80.1972414 6.431598e+03 5.157964e+05
#> [14,] 4.1972414 1.761684e+01 7.394211e+01
#> [15,] -4.8027586 2.306649e+01 -1.107828e+02
#> [16,] -30.8027586 9.488099e+02 -2.922596e+04
#> [17,] -47.8027586 2.285104e+03 -1.092343e+05
#> [18,] -15.8027586 2.497272e+02 -3.946378e+03
#> [19,] 10.1972414 1.039837e+02 1.060347e+03
#> [20,] 34.1972414 1.169451e+03 3.999201e+04
#> [21,] 4.1972414 1.761684e+01 7.394211e+01
#> [22,] -42.8027586 1.832076e+03 -7.841791e+04
#> [23,] 28.1972414 7.950844e+02 2.241919e+04
#> [24,] -55.8027586 3.113948e+03 -1.737669e+05
#> [25,] -50.8027586 2.580920e+03 -1.311179e+05
#> [26,] -11.8027586 1.393051e+02 -1.644185e+03
#> [27,] 13.1972414 1.741672e+02 2.298526e+03
#> [28,] -44.8027586 2.007287e+03 -8.993200e+04
#> [29,] -4.8027586 2.306649e+01 -1.107828e+02
#> [30,] -20.8027586 4.327548e+02 -9.002493e+03
#> [31,] -3.8027586 1.446097e+01 -5.499159e+01
#> [32,] 9.1972414 8.458925e+01 7.779877e+02
#> [33,] 10.1972414 1.039837e+02 1.060347e+03
#> [34,] 62.1972414 3.868497e+03 2.406098e+05
#> [35,] 19.1972414 3.685341e+02 7.074838e+03
#> [36,] -26.8027586 7.183879e+02 -1.925478e+04
#> [37,] 45.1972414 2.042791e+03 9.232850e+04
#> [38,] -42.8027586 1.832076e+03 -7.841791e+04
#> [39,] 29.1972414 8.524789e+02 2.489003e+04
#> [40,] 17.1972414 2.957451e+02 5.086000e+03
#> [41,] 22.1972414 4.927175e+02 1.093697e+04
#> [42,] 36.1972414 1.310240e+03 4.742708e+04
#> [43,] 56.1972414 3.158130e+03 1.774782e+05
#> [44,] -43.8027586 1.918682e+03 -8.404355e+04
#> [45,] 25.1972414 6.349010e+02 1.599775e+04
#> [46,] -13.8027586 1.905161e+02 -2.629648e+03
#> [47,] 33.1972414 1.102057e+03 3.658525e+04
#> [48,] -50.8027586 2.580920e+03 -1.311179e+05
#> [49,] -27.8027586 7.729934e+02 -2.149135e+04
#> [50,] 63.1972414 3.993891e+03 2.524029e+05
#> [51,] -2.8027586 7.855456e+00 -2.201695e+01
#> [52,] 101.1972414 1.024088e+04 1.036349e+06
#> [53,] -52.8027586 2.788131e+03 -1.472210e+05
#> [54,] -26.8027586 7.183879e+02 -1.925478e+04
#> [55,] 90.1972414 8.135542e+03 7.338035e+05
#> [56,] -21.8027586 4.753603e+02 -1.036417e+04
#> [57,] -45.8027586 2.097893e+03 -9.608927e+04
#> [58,] -36.8027586 1.354443e+03 -4.984724e+04
#> [59,] -17.8027586 3.169382e+02 -5.642375e+03
#> [60,] 21.1972414 4.493230e+02 9.524409e+03
#> [61,] 17.1972414 2.957451e+02 5.086000e+03
#> [62,] 25.1972414 6.349010e+02 1.599775e+04
#> [63,] 25.1972414 6.349010e+02 1.599775e+04
#> [64,] 12.1972414 1.487727e+02 1.814616e+03
#> [65,] -12.8027586 1.639106e+02 -2.098508e+03
#> [66,] 20.1972414 4.079286e+02 8.239032e+03
#> [67,] 23.1972414 5.381120e+02 1.248271e+04
#> [68,] -53.8027586 2.894737e+03 -1.557448e+05
#> [69,] 6.1972414 3.840580e+01 2.380100e+02
#> [70,] -31.8027586 1.011415e+03 -3.216580e+04
#> [71,] -40.8027586 1.664865e+03 -6.793109e+04
#> [72,] -46.8027586 2.190498e+03 -1.025214e+05
#> [73,] 9.1972414 8.458925e+01 7.779877e+02
#> [74,] 13.1972414 1.741672e+02 2.298526e+03
#> [75,] -40.8027586 1.664865e+03 -6.793109e+04
#> [76,] -22.8027586 5.199658e+02 -1.185665e+04
#> [77,] 1.1972414 1.433387e+00 1.716110e+00
#> [78,] 14.1972414 2.015617e+02 2.861620e+03
#> [79,] -24.8027586 6.151768e+02 -1.525808e+04
#> [80,] -4.8027586 2.306649e+01 -1.107828e+02
#> [81,] 20.1972414 4.079286e+02 8.239032e+03
#> [82,] -38.8027586 1.505654e+03 -5.842353e+04
#> [83,] 24.1972414 5.855065e+02 1.416764e+04
#> [84,] 8.1972414 6.719477e+01 5.508117e+02
#> [85,] -45.8027586 2.097893e+03 -9.608927e+04
#> [86,] 3.1972414 1.022235e+01 3.268333e+01
#> [87,] 28.1972414 7.950844e+02 2.241919e+04
#> [88,] -26.8027586 7.183879e+02 -1.925478e+04
#> [89,] -8.8027586 7.748856e+01 -6.821131e+02
#> [90,] 47.1972414 2.227580e+03 1.051356e+05
#> [91,] -5.8027586 3.367201e+01 -1.953905e+02
#> [92,] -0.8027586 6.444214e-01 -5.173148e-01
#> [93,] -15.8027586 2.497272e+02 -3.946378e+03
#> [94,] -40.8027586 1.664865e+03 -6.793109e+04
#> [95,] -55.8027586 3.113948e+03 -1.737669e+05
#> [96,] 41.1972414 1.697213e+03 6.992048e+04
#> [97,] -3.8027586 1.446097e+01 -5.499159e+01
#> [98,] 37.1972414 1.383635e+03 5.146740e+04
#> [99,] -25.8027586 6.657824e+02 -1.717902e+04
#> [100,] 32.1972414 1.036662e+03 3.337767e+04
#> [101,] -10.8027586 1.166996e+02 -1.260678e+03
#> [102,] -28.8027586 8.295989e+02 -2.389474e+04
#> [103,] -41.8027586 1.747471e+03 -7.304909e+04
#> [104,] -44.8027586 2.007287e+03 -8.993200e+04
#> [105,] 25.1972414 6.349010e+02 1.599775e+04
#> [106,] 65.1972414 4.250680e+03 2.771326e+05
#> [107,] 41.1972414 1.697213e+03 6.992048e+04
#> [108,] -8.8027586 7.748856e+01 -6.821131e+02
#> [109,] -21.8027586 4.753603e+02 -1.036417e+04
#> [110,] -12.8027586 1.639106e+02 -2.098508e+03
#> [111,] -7.8027586 6.088304e+01 -4.750557e+02
#> [112,] -5.8027586 3.367201e+01 -1.953905e+02
#> [113,] -27.8027586 7.729934e+02 -2.149135e+04
#> [114,] 0.1972414 3.890416e-02 7.673511e-03
#> [115,] 16.1972414 2.623506e+02 4.249356e+03
#> [116,] 20.1972414 4.079286e+02 8.239032e+03
#> [117,] -42.8027586 1.832076e+03 -7.841791e+04
#> [118,] 7.1972414 5.180028e+01 3.728191e+02
#> [119,] 2.1972414 4.827870e+00 1.060800e+01
#> [120,] 4.1972414 1.761684e+01 7.394211e+01
#> [121,] -35.8027586 1.281838e+03 -4.589332e+04
#> [122,] 10.1972414 1.039837e+02 1.060347e+03
#> [123,] -18.8027586 3.535437e+02 -6.647597e+03
#> [124,] -2.8027586 7.855456e+00 -2.201695e+01
#> [125,] -21.8027586 4.753603e+02 -1.036417e+04
#> [126,] -23.8027586 5.665713e+02 -1.348596e+04
#> [127,] -25.8027586 6.657824e+02 -1.717902e+04
#> [128,] 51.1972414 2.621158e+03 1.341960e+05
#> [129,] -39.8027586 1.584260e+03 -6.305790e+04
#> [130,] NA NA NA
#> [131,] 38.1972414 1.459029e+03 5.573089e+04
#> [132,] 30.1972414 9.118734e+02 2.753606e+04
#> [133,] -17.8027586 3.169382e+02 -5.642375e+03
#> [134,] -72.8027586 5.300242e+03 -3.858722e+05
#> [135,] 24.1972414 5.855065e+02 1.416764e+04
#> [136,] 69.1972414 4.788258e+03 3.313343e+05
#> [137,] 8.1972414 6.719477e+01 5.508117e+02
#> [138,] 16.1972414 2.623506e+02 4.249356e+03
#> [139,] -37.8027586 1.429049e+03 -5.402198e+04
#> [140,] 4.1972414 1.761684e+01 7.394211e+01
#> [141,] 48.1972414 2.322974e+03 1.119609e+05
#> [142,] 25.1972414 6.349010e+02 1.599775e+04
#> [143,] 22.1972414 4.927175e+02 1.093697e+04
#> [144,] -6.8027586 4.627752e+01 -3.148148e+02
#> [145,] 35.1972414 1.238846e+03 4.360395e+04
#> [146,] 10.1972414 1.039837e+02 1.060347e+03
#> [147,] 30.1972414 9.118734e+02 2.753606e+04
#> [148,] -26.8027586 7.183879e+02 -1.925478e+04
#> [149,] -11.8027586 1.393051e+02 -1.644185e+03
#> [150,] 12.1972414 1.487727e+02 1.814616e+03
#> [151,] -21.8027586 4.753603e+02 -1.036417e+04
#> [152,] -12.8027586 1.639106e+02 -2.098508e+03
#> [153,] 7.1972414 5.180028e+01 3.728191e+02
#> [154,] -44.8027586 2.007287e+03 -8.993200e+04
#> [155,] -47.8027586 2.285104e+03 -1.092343e+05
#> [156,] -10.8027586 1.166996e+02 -1.260678e+03
#> [157,] 15.1972414 2.309561e+02 3.509896e+03
#> [158,] NA NA NA
#> [159,] -47.8027586 2.285104e+03 -1.092343e+05
#> [160,] -24.8027586 6.151768e+02 -1.525808e+04
#> [161,] 29.1972414 8.524789e+02 2.489003e+04
#> [162,] 10.1972414 1.039837e+02 1.060347e+03
#> [163,] 5.1972414 2.701132e+01 1.403843e+02
#> [164,] 12.1972414 1.487727e+02 1.814616e+03
#> [165,] 14.1972414 2.015617e+02 2.861620e+03
#> [166,] -10.8027586 1.166996e+02 -1.260678e+03
#> [167,] 18.1972414 3.311396e+02 6.025827e+03
#> [168,] 0.1972414 3.890416e-02 7.673511e-03
#> [169,] 91.1972414 8.316937e+03 7.584817e+05
#> [170,] 19.1972414 3.685341e+02 7.074838e+03
#> [171,] 1.1972414 1.433387e+00 1.716110e+00
#> [172,] -49.8027586 2.480315e+03 -1.235265e+05
#> [173,] NA NA NA
#> [174,] -74.8027586 5.595453e+03 -4.185553e+05
#> [175,] 6.1972414 3.840580e+01 2.380100e+02
#> [176,] -11.8027586 1.393051e+02 -1.644185e+03
#> [177,] -64.8027586 4.199398e+03 -2.721325e+05
#> [178,] 23.1972414 5.381120e+02 1.248271e+04
#> [179,] 11.1972414 1.253782e+02 1.403890e+03
#> [180,] 1.1972414 1.433387e+00 1.716110e+00
#> [181,] 7.1972414 5.180028e+01 3.728191e+02
#> [182,] 7.1972414 5.180028e+01 3.728191e+02
#> [183,] 18.1972414 3.311396e+02 6.025827e+03
#> [184,] -16.8027586 2.823327e+02 -4.743968e+03
#> [185,] 26.1972414 6.862955e+02 1.797905e+04
#> [186,] -30.8027586 9.488099e+02 -2.922596e+04
#> [187,] 3.1972414 1.022235e+01 3.268333e+01
#> [188,] NA NA NA
#> [189,] 2.1972414 4.827870e+00 1.060800e+01
#> [190,] -26.8027586 7.183879e+02 -1.925478e+04
#> [191,] 13.1972414 1.741672e+02 2.298526e+03
#> [192,] 16.1972414 2.623506e+02 4.249356e+03
#> [193,] -22.8027586 5.199658e+02 -1.185665e+04
#> [194,] -11.8027586 1.393051e+02 -1.644185e+03
#> [195,] 59.1972414 3.504313e+03 2.074457e+05
#> [196,] -1.8027586 3.249939e+00 -5.858855e+00
#> [197,] -27.8027586 7.729934e+02 -2.149135e+04
#> [198,] -24.8027586 6.151768e+02 -1.525808e+04
#> [199,] 65.1972414 4.250680e+03 2.771326e+05
#> [200,] -7.8027586 6.088304e+01 -4.750557e+02
#> [201,] -28.8027586 8.295989e+02 -2.389474e+04
#> [202,] -8.8027586 7.748856e+01 -6.821131e+02
#> [203,] -30.8027586 9.488099e+02 -2.922596e+04
#> [204,] 9.1972414 8.458925e+01 7.779877e+02
#> [205,] 80.1972414 6.431598e+03 5.157964e+05
#> [206,] 24.1972414 5.855065e+02 1.416764e+04
#> [207,] -3.8027586 1.446097e+01 -5.499159e+01
#> [208,] 14.1972414 2.015617e+02 2.861620e+03
#> [209,] -34.8027586 1.211232e+03 -4.215422e+04
#> [210,] -4.8027586 2.306649e+01 -1.107828e+02
#> [211,] 34.1972414 1.169451e+03 3.999201e+04
#> [212,] 36.1972414 1.310240e+03 4.742708e+04
#> [213,] 62.1972414 3.868497e+03 2.406098e+05
#> [214,] -30.8027586 9.488099e+02 -2.922596e+04
#> [215,] 38.1972414 1.459029e+03 5.573089e+04
#> [216,] 4.1972414 1.761684e+01 7.394211e+01
#> [217,] 28.1972414 7.950844e+02 2.241919e+04
#> [218,] NA NA NA
#> [219,] 10.1972414 1.039837e+02 1.060347e+03
#> [220,] -30.8027586 9.488099e+02 -2.922596e+04
#> [221,] 121.1972414 1.468877e+04 1.780239e+06
#> [222,] 18.1972414 3.311396e+02 6.025827e+03
#> [223,] -42.8027586 1.832076e+03 -7.841791e+04
#> [224,] -3.8027586 1.446097e+01 -5.499159e+01
#> [225,] 31.1972414 9.732679e+02 3.036327e+04
#> [226,] -18.8027586 3.535437e+02 -6.647597e+03
#> [227,] 5.1972414 2.701132e+01 1.403843e+02
#> [228,] 14.1972414 2.015617e+02 2.861620e+03
#> [229,] 74.1972414 5.505231e+03 4.084729e+05
#> [230,] -30.8027586 9.488099e+02 -2.922596e+04
#> [231,] 20.1972414 4.079286e+02 8.239032e+03
#> [232,] -23.8027586 5.665713e+02 -1.348596e+04
#> [233,] 11.1972414 1.253782e+02 1.403890e+03
#> [234,] 24.1972414 5.855065e+02 1.416764e+04
#> [235,] 22.1972414 4.927175e+02 1.093697e+04
#> [236,] -53.8027586 2.894737e+03 -1.557448e+05
#> [237,] 16.1972414 2.623506e+02 4.249356e+03
#> [238,] -34.8027586 1.211232e+03 -4.215422e+04
#> [239,] 27.1972414 7.396899e+02 2.011753e+04
#> [240,] 82.1972414 6.756386e+03 5.553563e+05
#> [241,] -7.8027586 6.088304e+01 -4.750557e+02
#> [242,] 24.1972414 5.855065e+02 1.416764e+04
#> [243,] 25.1972414 6.349010e+02 1.599775e+04
#> [244,] 1.1972414 1.433387e+00 1.716110e+00
#> [245,] -25.8027586 6.657824e+02 -1.717902e+04
#> [246,] -11.8027586 1.393051e+02 -1.644185e+03
#> [247,] -13.8027586 1.905161e+02 -2.629648e+03
#> [248,] 3.1972414 1.022235e+01 3.268333e+01
#> [249,] 53.1972414 2.829946e+03 1.505453e+05
#> [250,] 8.1972414 6.719477e+01 5.508117e+02
#> [251,] -10.8027586 1.166996e+02 -1.260678e+03
#> [252,] -17.8027586 3.169382e+02 -5.642375e+03
#> [253,] -26.8027586 7.183879e+02 -1.925478e+04
#> [254,] 81.1972414 6.592992e+03 5.353328e+05
#> [255,] -48.8027586 2.381709e+03 -1.162340e+05
#> [256,] 15.1972414 2.309561e+02 3.509896e+03
#> [257,] 4.1972414 1.761684e+01 7.394211e+01
#> [258,] 36.1972414 1.310240e+03 4.742708e+04
#> [259,] 1.1972414 1.433387e+00 1.716110e+00
#> [260,] -33.8027586 1.142626e+03 -3.862393e+04
#> [261,] NA NA NA
#> [262,] -25.8027586 6.657824e+02 -1.717902e+04
#> [263,] 61.1972414 3.745102e+03 2.291899e+05
#> [264,] -12.8027586 1.639106e+02 -2.098508e+03
#> [265,] 2.1972414 4.827870e+00 1.060800e+01
#> [266,] 57.1972414 3.271524e+03 1.871222e+05
#> [267,] NA NA NA
#> [268,] -15.8027586 2.497272e+02 -3.946378e+03
#> [269,] -22.8027586 5.199658e+02 -1.185665e+04
#> [270,] 30.1972414 9.118734e+02 2.753606e+04
#> [271,] -26.8027586 7.183879e+02 -1.925478e+04
#> [272,] 29.1972414 8.524789e+02 2.489003e+04
#> [273,] 55.1972414 3.046735e+03 1.681714e+05
#> [274,] -7.8027586 6.088304e+01 -4.750557e+02
#> [275,] 6.1972414 3.840580e+01 2.380100e+02
#> [276,] 22.1972414 4.927175e+02 1.093697e+04
#> [277,] -35.8027586 1.281838e+03 -4.589332e+04
#> [278,] 5.1972414 2.701132e+01 1.403843e+02
#> [279,] 12.1972414 1.487727e+02 1.814616e+03
#> [280,] -16.8027586 2.823327e+02 -4.743968e+03
#> [281,] 10.1972414 1.039837e+02 1.060347e+03
#> [282,] 13.1972414 1.741672e+02 2.298526e+03
#> [283,] -34.8027586 1.211232e+03 -4.215422e+04
#> [284,] 50.1972414 2.519763e+03 1.264852e+05
#> [285,] 22.1972414 4.927175e+02 1.093697e+04
#> [286,] -38.8027586 1.505654e+03 -5.842353e+04
#> [287,] -12.8027586 1.639106e+02 -2.098508e+03
#> [288,] 29.1972414 8.524789e+02 2.489003e+04
#> [289,] 59.1972414 3.504313e+03 2.074457e+05
#> [290,] 11.1972414 1.253782e+02 1.403890e+03
#> [291,] 11.1972414 1.253782e+02 1.403890e+03
#> [292,] 43.1972414 1.866002e+03 8.060612e+04
#> [293,] 80.1972414 6.431598e+03 5.157964e+05
#> [294,] -37.8027586 1.429049e+03 -5.402198e+04
#> [295,] 13.1972414 1.741672e+02 2.298526e+03
#> [296,] 56.1972414 3.158130e+03 1.774782e+05
#> [297,] 11.1972414 1.253782e+02 1.403890e+03
#> [298,] 59.1972414 3.504313e+03 2.074457e+05
#> [299,] -9.8027586 9.609408e+01 -9.419870e+02
#> [300,] -11.8027586 1.393051e+02 -1.644185e+03
#> [301,] -56.8027586 3.226553e+03 -1.832771e+05
#> [302,] -6.8027586 4.627752e+01 -3.148148e+02
#> [303,] -43.8027586 1.918682e+03 -8.404355e+04
#> [304,] 4.1972414 1.761684e+01 7.394211e+01
#> [305,] -15.8027586 2.497272e+02 -3.946378e+03
#> [306,] 36.1972414 1.310240e+03 4.742708e+04
#> [307,] -12.8027586 1.639106e+02 -2.098508e+03
#> [308,] -32.8027586 1.076021e+03 -3.529646e+04
#> [309,] -7.8027586 6.088304e+01 -4.750557e+02
#> [310,] 70.1972414 4.927653e+03 3.459076e+05
#> [311,] -47.8027586 2.285104e+03 -1.092343e+05
#> [312,] -14.8027586 2.191217e+02 -3.243605e+03
#> [313,] -54.8027586 3.003342e+03 -1.645914e+05
#> [314,] 15.1972414 2.309561e+02 3.509896e+03
#> [315,] -13.8027586 1.905161e+02 -2.629648e+03
#> [316,] 69.1972414 4.788258e+03 3.313343e+05
#> [317,] -9.8027586 9.609408e+01 -9.419870e+02
#> [318,] 18.1972414 3.311396e+02 6.025827e+03
#> [319,] 47.1972414 2.227580e+03 1.051356e+05
#> [320,] 27.1972414 7.396899e+02 2.011753e+04
#> [321,] 10.1972414 1.039837e+02 1.060347e+03
#> [322,] 56.1972414 3.158130e+03 1.774782e+05
#> [323,] -35.8027586 1.281838e+03 -4.589332e+04
#> [324,] 2.1972414 4.827870e+00 1.060800e+01
#> [325,] 62.1972414 3.868497e+03 2.406098e+05
#> [326,] 58.1972414 3.386919e+03 1.971093e+05
#> [327,] -4.8027586 2.306649e+01 -1.107828e+02
#> [328,] -0.8027586 6.444214e-01 -5.173148e-01
#> [329,] -12.8027586 1.639106e+02 -2.098508e+03
#> [330,] 8.1972414 6.719477e+01 5.508117e+02
#> [331,] 14.1972414 2.015617e+02 2.861620e+03
#> [332,] -45.8027586 2.097893e+03 -9.608927e+04
#> [333,] 45.1972414 2.042791e+03 9.232850e+04
#> [334,] -44.8027586 2.007287e+03 -8.993200e+04
#> [335,] -13.8027586 1.905161e+02 -2.629648e+03
#> [336,] -9.8027586 9.609408e+01 -9.419870e+02
#> [337,] 32.1972414 1.036662e+03 3.337767e+04
#> [338,] -19.8027586 3.921492e+02 -7.765637e+03
#> [339,] 32.1972414 1.036662e+03 3.337767e+04
#> [340,] -34.8027586 1.211232e+03 -4.215422e+04
#> [341,] 6.1972414 3.840580e+01 2.380100e+02
#> [342,] -37.8027586 1.429049e+03 -5.402198e+04
#> [343,] -12.8027586 1.639106e+02 -2.098508e+03
#> [344,] 21.1972414 4.493230e+02 9.524409e+03
#> [345,] 16.1972414 2.623506e+02 4.249356e+03
#> [346,] -58.8027586 3.457764e+03 -2.033261e+05
#> [347,] 35.1972414 1.238846e+03 4.360395e+04
#> [348,] 52.1972414 2.724552e+03 1.422141e+05
#> [349,] -17.8027586 3.169382e+02 -5.642375e+03
#> [350,] -38.8027586 1.505654e+03 -5.842353e+04
#> [351,] 11.1972414 1.253782e+02 1.403890e+03
#> [352,] 34.1972414 1.169451e+03 3.999201e+04
#> [353,] 1.1972414 1.433387e+00 1.716110e+00
#> [354,] -29.8027586 8.882044e+02 -2.647094e+04
#> [355,] -15.8027586 2.497272e+02 -3.946378e+03
#> [356,] 49.1972414 2.420369e+03 1.190755e+05
#> [357,] 45.1972414 2.042791e+03 9.232850e+04
#> [358,] 5.1972414 2.701132e+01 1.403843e+02
#> [359,] -32.8027586 1.076021e+03 -3.529646e+04
#> [360,] -17.8027586 3.169382e+02 -5.642375e+03
#> [361,] -7.8027586 6.088304e+01 -4.750557e+02
#> [362,] -9.8027586 9.609408e+01 -9.419870e+02
#> [363,] -68.8027586 4.733820e+03 -3.256998e+05
#> [364,] 1.1972414 1.433387e+00 1.716110e+00
#> [365,] 55.1972414 3.046735e+03 1.681714e+05
#> [366,] -17.8027586 3.169382e+02 -5.642375e+03
#> [367,] 7.1972414 5.180028e+01 3.728191e+02
#> [368,] 16.1972414 2.623506e+02 4.249356e+03
#> [369,] 8.1972414 6.719477e+01 5.508117e+02
#> [370,] 0.1972414 3.890416e-02 7.673511e-03
#> [371,] 38.1972414 1.459029e+03 5.573089e+04
#> [372,] -48.8027586 2.381709e+03 -1.162340e+05
#> [373,] -28.8027586 8.295989e+02 -2.389474e+04
#> [374,] -70.8027586 5.013031e+03 -3.549364e+05
#> [375,] -32.8027586 1.076021e+03 -3.529646e+04
#> [376,] -57.8027586 3.341159e+03 -1.931282e+05
#> [377,] 10.1972414 1.039837e+02 1.060347e+03
#> [378,] -1.8027586 3.249939e+00 -5.858855e+00
#> [379,] 7.1972414 5.180028e+01 3.728191e+02
#> [380,] -4.8027586 2.306649e+01 -1.107828e+02
#> [381,] -45.8027586 2.097893e+03 -9.608927e+04
#> [382,] 17.1972414 2.957451e+02 5.086000e+03
#> [383,] 16.1972414 2.623506e+02 4.249356e+03
#> [384,] -48.8027586 2.381709e+03 -1.162340e+05
#> [385,] -53.8027586 2.894737e+03 -1.557448e+05
#> [386,] -36.8027586 1.354443e+03 -4.984724e+04
#> [387,] -48.8027586 2.381709e+03 -1.162340e+05
#> [388,] -32.8027586 1.076021e+03 -3.529646e+04
#> [389,] 75.1972414 5.654625e+03 4.252122e+05
#> [390,] 55.1972414 3.046735e+03 1.681714e+05
#> [391,] -55.8027586 3.113948e+03 -1.737669e+05
#> [392,] -52.8027586 2.788131e+03 -1.472210e+05
#> [393,] -20.8027586 4.327548e+02 -9.002493e+03
#> [394,] 8.1972414 6.719477e+01 5.508117e+02
#> [395,] -18.8027586 3.535437e+02 -6.647597e+03
#> [396,] 94.1972414 8.873120e+03 8.358235e+05
#> [397,] 40.1972414 1.615818e+03 6.495143e+04
#> [398,] 7.1972414 5.180028e+01 3.728191e+02
#> [399,] 99.1972414 9.840093e+03 9.761101e+05
#> [400,] 6.1972414 3.840580e+01 2.380100e+02
#> [401,] 17.1972414 2.957451e+02 5.086000e+03
#> [402,] -41.8027586 1.747471e+03 -7.304909e+04
#> [403,] 33.1972414 1.102057e+03 3.658525e+04
#> [404,] -11.8027586 1.393051e+02 -1.644185e+03
#> [405,] -50.8027586 2.580920e+03 -1.311179e+05
#> [406,] -14.8027586 2.191217e+02 -3.243605e+03
#> [407,] -11.8027586 1.393051e+02 -1.644185e+03
#> [408,] 44.1972414 1.953396e+03 8.633472e+04
#> [409,] -16.8027586 2.823327e+02 -4.743968e+03
#> [410,] 32.1972414 1.036662e+03 3.337767e+04
#> [411,] 47.1972414 2.227580e+03 1.051356e+05
#> [412,] -31.8027586 1.011415e+03 -3.216580e+04
#> [413,] 27.1972414 7.396899e+02 2.011753e+04
#> [414,] 0.1972414 3.890416e-02 7.673511e-03
#> [415,] 6.1972414 3.840580e+01 2.380100e+02
#> [416,] -10.8027586 1.166996e+02 -1.260678e+03
#> [417,] -35.8027586 1.281838e+03 -4.589332e+04
#> [418,] 2.1972414 4.827870e+00 1.060800e+01
#> [419,] 19.1972414 3.685341e+02 7.074838e+03
#> [420,] 18.1972414 3.311396e+02 6.025827e+03
#> [421,] 13.1972414 1.741672e+02 2.298526e+03
#> [422,] 21.1972414 4.493230e+02 9.524409e+03
#> [423,] -44.8027586 2.007287e+03 -8.993200e+04
#> [424,] 69.1972414 4.788258e+03 3.313343e+05
#> [425,] 35.1972414 1.238846e+03 4.360395e+04
#> [426,] -28.8027586 8.295989e+02 -2.389474e+04
#> [427,] -19.8027586 3.921492e+02 -7.765637e+03
#> [428,] -73.8027586 5.446847e+03 -4.019923e+05
#> [429,] 20.1972414 4.079286e+02 8.239032e+03
#> [430,] 2.1972414 4.827870e+00 1.060800e+01
#> [431,] -3.8027586 1.446097e+01 -5.499159e+01
#> [432,] 7.1972414 5.180028e+01 3.728191e+02
#> [433,] -14.8027586 2.191217e+02 -3.243605e+03
#> [434,] 30.1972414 9.118734e+02 2.753606e+04
#> [435,] -16.8027586 2.823327e+02 -4.743968e+03
#> [436,] 13.1972414 1.741672e+02 2.298526e+03
#> [437,] -11.8027586 1.393051e+02 -1.644185e+03
#> [438,] -114.8027586 1.317967e+04 -1.513063e+06
#> [439,] 0.1972414 3.890416e-02 7.673511e-03
#> [440,] -4.8027586 2.306649e+01 -1.107828e+02
#> [441,] 7.1972414 5.180028e+01 3.728191e+02
#> [442,] -86.8027586 7.534719e+03 -6.540344e+05
#> [443,] -19.8027586 3.921492e+02 -7.765637e+03
#> [444,] 11.1972414 1.253782e+02 1.403890e+03
#> [445,] 30.1972414 9.118734e+02 2.753606e+04
#> [446,] 36.1972414 1.310240e+03 4.742708e+04
#> [447,] -15.8027586 2.497272e+02 -3.946378e+03
#> [448,] -3.8027586 1.446097e+01 -5.499159e+01
#> [449,] 21.1972414 4.493230e+02 9.524409e+03
#> [450,] 43.1972414 1.866002e+03 8.060612e+04
#> [451,] 40.1972414 1.615818e+03 6.495143e+04
#> [452,] -31.8027586 1.011415e+03 -3.216580e+04
#> [453,] -33.8027586 1.142626e+03 -3.862393e+04
#> [454,] -9.8027586 9.609408e+01 -9.419870e+02
#> [455,] -29.8027586 8.882044e+02 -2.647094e+04
#> [456,] -36.8027586 1.354443e+03 -4.984724e+04
#> [457,] 13.1972414 1.741672e+02 2.298526e+03
#> [458,] 61.1972414 3.745102e+03 2.291899e+05
#> [459,] 47.1972414 2.227580e+03 1.051356e+05
#> [460,] -35.8027586 1.281838e+03 -4.589332e+04
#> [461,] -23.8027586 5.665713e+02 -1.348596e+04
#> [462,] 18.1972414 3.311396e+02 6.025827e+03
#> [463,] -35.8027586 1.281838e+03 -4.589332e+04
#> [464,] 42.1972414 1.780607e+03 7.513671e+04
#> [465,] -14.8027586 2.191217e+02 -3.243605e+03
#> [466,] -24.8027586 6.151768e+02 -1.525808e+04
#> [467,] -23.8027586 5.665713e+02 -1.348596e+04
#> [468,] -55.8027586 3.113948e+03 -1.737669e+05
#> [469,] 63.1972414 3.993891e+03 2.524029e+05
#> [470,] -21.8027586 4.753603e+02 -1.036417e+04
#> [471,] -65.8027586 4.330003e+03 -2.849261e+05
#> [472,] -42.8027586 1.832076e+03 -7.841791e+04
#> [473,] 0.1972414 3.890416e-02 7.673511e-03
#> [474,] -63.8027586 4.070792e+03 -2.597278e+05
#> [475,] -4.8027586 2.306649e+01 -1.107828e+02
#> [476,] -12.8027586 1.639106e+02 -2.098508e+03
#> [477,] -23.8027586 5.665713e+02 -1.348596e+04
#> [478,] 12.1972414 1.487727e+02 1.814616e+03
#> [479,] -1.8027586 3.249939e+00 -5.858855e+00
#> [480,] 78.1972414 6.114809e+03 4.781612e+05
#> [481,] -5.8027586 3.367201e+01 -1.953905e+02
#> [482,] -11.8027586 1.393051e+02 -1.644185e+03
#> [483,] 25.1972414 6.349010e+02 1.599775e+04
#> [484,] -43.8027586 1.918682e+03 -8.404355e+04
#> [485,] -31.8027586 1.011415e+03 -3.216580e+04
#> [486,] 7.1972414 5.180028e+01 3.728191e+02
#> [487,] -88.8027586 7.885930e+03 -7.002923e+05
#> [488,] 30.1972414 9.118734e+02 2.753606e+04
#> [489,] 45.1972414 2.042791e+03 9.232850e+04
#> [490,] -23.8027586 5.665713e+02 -1.348596e+04
#> [491,] -57.8027586 3.341159e+03 -1.931282e+05
#> [492,] -9.8027586 9.609408e+01 -9.419870e+02
#> [493,] 39.1972414 1.536424e+03 6.022357e+04
#> [494,] 22.1972414 4.927175e+02 1.093697e+04
#> [495,] 15.1972414 2.309561e+02 3.509896e+03
#> [496,] -17.8027586 3.169382e+02 -5.642375e+03
#> [497,] 48.1972414 2.322974e+03 1.119609e+05
#> [498,] -5.8027586 3.367201e+01 -1.953905e+02
#> [499,] -38.8027586 1.505654e+03 -5.842353e+04
#> [500,] 3.1972414 1.022235e+01 3.268333e+01
#> [501,] 23.1972414 5.381120e+02 1.248271e+04
#> [502,] 24.1972414 5.855065e+02 1.416764e+04
#> [503,] -13.8027586 1.905161e+02 -2.629648e+03
#> [504,] 32.1972414 1.036662e+03 3.337767e+04
#> [505,] -2.8027586 7.855456e+00 -2.201695e+01
#> [506,] NA NA NA
#> [507,] 90.1972414 8.135542e+03 7.338035e+05
#> [508,] 14.1972414 2.015617e+02 2.861620e+03
#> [509,] 35.1972414 1.238846e+03 4.360395e+04
#> [510,] 25.1972414 6.349010e+02 1.599775e+04
#> [511,] 6.1972414 3.840580e+01 2.380100e+02
#> [512,] 6.1972414 3.840580e+01 2.380100e+02
#> [513,] 0.1972414 3.890416e-02 7.673511e-03
#> [514,] 26.1972414 6.862955e+02 1.797905e+04
#> [515,] -35.8027586 1.281838e+03 -4.589332e+04
#> [516,] -30.8027586 9.488099e+02 -2.922596e+04
#> [517,] 10.1972414 1.039837e+02 1.060347e+03
#> [518,] 17.1972414 2.957451e+02 5.086000e+03
#> [519,] -12.8027586 1.639106e+02 -2.098508e+03
#> [520,] -21.8027586 4.753603e+02 -1.036417e+04
#> [521,] -48.8027586 2.381709e+03 -1.162340e+05
#> [522,] -26.8027586 7.183879e+02 -1.925478e+04
#> [523,] -20.8027586 4.327548e+02 -9.002493e+03
#> [524,] 1.1972414 1.433387e+00 1.716110e+00
#> [525,] 15.1972414 2.309561e+02 3.509896e+03
#> [526,] -57.8027586 3.341159e+03 -1.931282e+05
#> [527,] -4.8027586 2.306649e+01 -1.107828e+02
#> [528,] 36.1972414 1.310240e+03 4.742708e+04
#> [529,] -17.8027586 3.169382e+02 -5.642375e+03
#> [530,] -12.8027586 1.639106e+02 -2.098508e+03
#> [531,] -16.8027586 2.823327e+02 -4.743968e+03
#> [532,] -27.8027586 7.729934e+02 -2.149135e+04
#> [533,] 60.1972414 3.623708e+03 2.181372e+05
#> [534,] -4.8027586 2.306649e+01 -1.107828e+02
#> [535,] 41.1972414 1.697213e+03 6.992048e+04
#> [536,] -64.8027586 4.199398e+03 -2.721325e+05
#> [537,] 7.1972414 5.180028e+01 3.728191e+02
#> [538,] 22.1972414 4.927175e+02 1.093697e+04
#> [539,] 18.1972414 3.311396e+02 6.025827e+03
#> [540,] 21.1972414 4.493230e+02 9.524409e+03
#> [541,] -15.8027586 2.497272e+02 -3.946378e+03
#> [542,] -21.8027586 4.753603e+02 -1.036417e+04
#> [543,] 31.1972414 9.732679e+02 3.036327e+04
#> [544,] 4.1972414 1.761684e+01 7.394211e+01
#> [545,] NA NA NA
#> [546,] 7.1972414 5.180028e+01 3.728191e+02
#> [547,] -22.8027586 5.199658e+02 -1.185665e+04
#> [548,] 16.1972414 2.623506e+02 4.249356e+03
#> [549,] 4.1972414 1.761684e+01 7.394211e+01
#> [550,] 26.1972414 6.862955e+02 1.797905e+04
#> [551,] -30.8027586 9.488099e+02 -2.922596e+04
#> [552,] 5.1972414 2.701132e+01 1.403843e+02
#> [553,] 23.1972414 5.381120e+02 1.248271e+04
#> [554,] -38.8027586 1.505654e+03 -5.842353e+04
#> [555,] 29.1972414 8.524789e+02 2.489003e+04
#> [556,] -33.8027586 1.142626e+03 -3.862393e+04
#> [557,] 28.1972414 7.950844e+02 2.241919e+04
#> [558,] NA NA NA
#> [559,] -0.8027586 6.444214e-01 -5.173148e-01
#> [560,] 12.1972414 1.487727e+02 1.814616e+03
#> [561,] -4.8027586 2.306649e+01 -1.107828e+02
#> [562,] 17.1972414 2.957451e+02 5.086000e+03
#> [563,] -13.8027586 1.905161e+02 -2.629648e+03
#> [564,] -7.8027586 6.088304e+01 -4.750557e+02
#> [565,] -37.8027586 1.429049e+03 -5.402198e+04
#> [566,] -2.8027586 7.855456e+00 -2.201695e+01
#> [567,] 29.1972414 8.524789e+02 2.489003e+04
#> [568,] -79.8027586 6.368480e+03 -5.082223e+05
#> [569,] 14.1972414 2.015617e+02 2.861620e+03
#> [570,] -13.8027586 1.905161e+02 -2.629648e+03
#> [571,] 6.1972414 3.840580e+01 2.380100e+02
#> [572,] -1.8027586 3.249939e+00 -5.858855e+00
#> [573,] 25.1972414 6.349010e+02 1.599775e+04
#> [574,] -48.8027586 2.381709e+03 -1.162340e+05
#> [575,] 33.1972414 1.102057e+03 3.658525e+04
#> [576,] -14.8027586 2.191217e+02 -3.243605e+03
#> [577,] 5.1972414 2.701132e+01 1.403843e+02
#> [578,] -14.8027586 2.191217e+02 -3.243605e+03
#> [579,] -2.8027586 7.855456e+00 -2.201695e+01
#> [580,] 18.1972414 3.311396e+02 6.025827e+03
#> [581,] -50.8027586 2.580920e+03 -1.311179e+05
#> [582,] -39.8027586 1.584260e+03 -6.305790e+04
#> [583,] -16.8027586 2.823327e+02 -4.743968e+03
#> [584,] 90.1972414 8.135542e+03 7.338035e+05
#> [585,] -4.8027586 2.306649e+01 -1.107828e+02
#> [586,] -42.8027586 1.832076e+03 -7.841791e+04
#> [587,] 16.1972414 2.623506e+02 4.249356e+03
#> [588,] 2.1972414 4.827870e+00 1.060800e+01
#> [589,] -3.8027586 1.446097e+01 -5.499159e+01
#> [590,] 30.1972414 9.118734e+02 2.753606e+04
#> [591,] -4.8027586 2.306649e+01 -1.107828e+02
#> [592,] 42.1972414 1.780607e+03 7.513671e+04
#> [593,] -61.8027586 3.819581e+03 -2.360606e+05
#> [594,] -16.8027586 2.823327e+02 -4.743968e+03
#> [595,] -15.8027586 2.497272e+02 -3.946378e+03
#> [596,] -47.8027586 2.285104e+03 -1.092343e+05
#> [597,] 39.1972414 1.536424e+03 6.022357e+04
#> [598,] 33.1972414 1.102057e+03 3.658525e+04
#> [599,] -3.8027586 1.446097e+01 -5.499159e+01
#> [600,] 27.1972414 7.396899e+02 2.011753e+04
#> [601,] -36.8027586 1.354443e+03 -4.984724e+04
#> [602,] 38.1972414 1.459029e+03 5.573089e+04
#> [603,] -25.8027586 6.657824e+02 -1.717902e+04
#> [604,] -31.8027586 1.011415e+03 -3.216580e+04
#> [605,] -47.8027586 2.285104e+03 -1.092343e+05
#> [606,] -4.8027586 2.306649e+01 -1.107828e+02
#> [607,] 41.1972414 1.697213e+03 6.992048e+04
#> [608,] -20.8027586 4.327548e+02 -9.002493e+03
#> [609,] 9.1972414 8.458925e+01 7.779877e+02
#> [610,] -3.8027586 1.446097e+01 -5.499159e+01
#> [611,] -42.8027586 1.832076e+03 -7.841791e+04
#> [612,] -10.8027586 1.166996e+02 -1.260678e+03
#> [613,] -23.8027586 5.665713e+02 -1.348596e+04
#> [614,] 43.1972414 1.866002e+03 8.060612e+04
#> [615,] -19.8027586 3.921492e+02 -7.765637e+03
#> [616,] -33.8027586 1.142626e+03 -3.862393e+04
#> [617,] 35.1972414 1.238846e+03 4.360395e+04
#> [618,] 21.1972414 4.493230e+02 9.524409e+03
#> [619,] 30.1972414 9.118734e+02 2.753606e+04
#> [620,] 22.1972414 4.927175e+02 1.093697e+04
#> [621,] -10.8027586 1.166996e+02 -1.260678e+03
#> [622,] -25.8027586 6.657824e+02 -1.717902e+04
#> [623,] 56.1972414 3.158130e+03 1.774782e+05
#> [624,] -31.8027586 1.011415e+03 -3.216580e+04
#> [625,] 20.1972414 4.079286e+02 8.239032e+03
#> [626,] 71.1972414 5.069047e+03 3.609022e+05
#> [627,] -4.8027586 2.306649e+01 -1.107828e+02
#> [628,] 5.1972414 2.701132e+01 1.403843e+02
#> [629,] 7.1972414 5.180028e+01 3.728191e+02
#> [630,] -1.8027586 3.249939e+00 -5.858855e+00
#> [631,] -33.8027586 1.142626e+03 -3.862393e+04
#> [632,] 30.1972414 9.118734e+02 2.753606e+04
#> [633,] -26.8027586 7.183879e+02 -1.925478e+04
#> [634,] -25.8027586 6.657824e+02 -1.717902e+04
#> [635,] -39.8027586 1.584260e+03 -6.305790e+04
#> [636,] 4.1972414 1.761684e+01 7.394211e+01
#> [637,] 46.1972414 2.134185e+03 9.859346e+04
#> [638,] -9.8027586 9.609408e+01 -9.419870e+02
#> [639,] 24.1972414 5.855065e+02 1.416764e+04
#> [640,] 8.1972414 6.719477e+01 5.508117e+02
#> [641,] -25.8027586 6.657824e+02 -1.717902e+04
#> [642,] 92.1972414 8.500331e+03 7.837071e+05
#> [643,] 30.1972414 9.118734e+02 2.753606e+04
#> [644,] -1.8027586 3.249939e+00 -5.858855e+00
#> [645,] -13.8027586 1.905161e+02 -2.629648e+03
#> [646,] 35.1972414 1.238846e+03 4.360395e+04
#> [647,] -17.8027586 3.169382e+02 -5.642375e+03
#> [648,] -22.8027586 5.199658e+02 -1.185665e+04
#> [649,] -50.8027586 2.580920e+03 -1.311179e+05
#> [650,] -9.8027586 9.609408e+01 -9.419870e+02
#> [651,] 12.1972414 1.487727e+02 1.814616e+03
#> [652,] 43.1972414 1.866002e+03 8.060612e+04
#> [653,] 26.1972414 6.862955e+02 1.797905e+04
#> [654,] -1.8027586 3.249939e+00 -5.858855e+00
#> [655,] -26.8027586 7.183879e+02 -1.925478e+04
#> [656,] -42.8027586 1.832076e+03 -7.841791e+04
#> [657,] -32.8027586 1.076021e+03 -3.529646e+04
#> [658,] 42.1972414 1.780607e+03 7.513671e+04
#> [659,] 15.1972414 2.309561e+02 3.509896e+03
#> [660,] -11.8027586 1.393051e+02 -1.644185e+03
#> [661,] -34.8027586 1.211232e+03 -4.215422e+04
#> [662,] -2.8027586 7.855456e+00 -2.201695e+01
#> [663,] -48.8027586 2.381709e+03 -1.162340e+05
#> [664,] 26.1972414 6.862955e+02 1.797905e+04
#> [665,] 6.1972414 3.840580e+01 2.380100e+02
#> [666,] -20.8027586 4.327548e+02 -9.002493e+03
#> [667,] -29.8027586 8.882044e+02 -2.647094e+04
#> [668,] 7.1972414 5.180028e+01 3.728191e+02
#> [669,] 45.1972414 2.042791e+03 9.232850e+04
#> [670,] 13.1972414 1.741672e+02 2.298526e+03
#> [671,] -39.8027586 1.584260e+03 -6.305790e+04
#> [672,] 2.1972414 4.827870e+00 1.060800e+01
#> [673,] -23.8027586 5.665713e+02 -1.348596e+04
#> [674,] 10.1972414 1.039837e+02 1.060347e+03
#> [675,] 62.1972414 3.868497e+03 2.406098e+05
#> [676,] 2.1972414 4.827870e+00 1.060800e+01
#> [677,] 57.1972414 3.271524e+03 1.871222e+05
#> [678,] -36.8027586 1.354443e+03 -4.984724e+04
#> [679,] -46.8027586 2.190498e+03 -1.025214e+05
#> [680,] -19.8027586 3.921492e+02 -7.765637e+03
#> [681,] 45.1972414 2.042791e+03 9.232850e+04
#> [682,] -13.8027586 1.905161e+02 -2.629648e+03
#> [683,] 10.1972414 1.039837e+02 1.060347e+03
#> [684,] -29.8027586 8.882044e+02 -2.647094e+04
#> [685,] -13.8027586 1.905161e+02 -2.629648e+03
#> [686,] -48.8027586 2.381709e+03 -1.162340e+05
#> [687,] -16.8027586 2.823327e+02 -4.743968e+03
#> [688,] 5.1972414 2.701132e+01 1.403843e+02
#> [689,] -34.8027586 1.211232e+03 -4.215422e+04
#> [690,] -9.8027586 9.609408e+01 -9.419870e+02
#> [691,] -41.8027586 1.747471e+03 -7.304909e+04
#> [692,] 6.1972414 3.840580e+01 2.380100e+02
#> [693,] 52.1972414 2.724552e+03 1.422141e+05
#> [694,] 42.1972414 1.780607e+03 7.513671e+04
#> [695,] -56.8027586 3.226553e+03 -1.832771e+05
#> [696,] 20.1972414 4.079286e+02 8.239032e+03
#> [697,] -33.8027586 1.142626e+03 -3.862393e+04
#> [698,] 12.1972414 1.487727e+02 1.814616e+03
#> [699,] -5.8027586 3.367201e+01 -1.953905e+02
#> [700,] -15.8027586 2.497272e+02 -3.946378e+03
#> [701,] -8.8027586 7.748856e+01 -6.821131e+02
#> [702,] -36.8027586 1.354443e+03 -4.984724e+04
#> [703,] 13.1972414 1.741672e+02 2.298526e+03
#> [704,] -22.8027586 5.199658e+02 -1.185665e+04
#> [705,] 25.1972414 6.349010e+02 1.599775e+04
#> [706,] -40.8027586 1.664865e+03 -6.793109e+04
#> [707,] -2.8027586 7.855456e+00 -2.201695e+01
#> [708,] 34.1972414 1.169451e+03 3.999201e+04
#> [709,] -13.8027586 1.905161e+02 -2.629648e+03
#> [710,] -4.8027586 2.306649e+01 -1.107828e+02
#> [711,] 35.1972414 1.238846e+03 4.360395e+04
#> [712,] -32.8027586 1.076021e+03 -3.529646e+04
#> [713,] 27.1972414 7.396899e+02 2.011753e+04
#> [714,] 30.1972414 9.118734e+02 2.753606e+04
#> [715,] -5.8027586 3.367201e+01 -1.953905e+02
#> [716,] -54.8027586 3.003342e+03 -1.645914e+05
#> [717,] 2.1972414 4.827870e+00 1.060800e+01
#> [718,] 19.1972414 3.685341e+02 7.074838e+03
#> [719,] 15.1972414 2.309561e+02 3.509896e+03
#> [720,] -25.8027586 6.657824e+02 -1.717902e+04
#> [721,] 55.1972414 3.046735e+03 1.681714e+05
#> [722,] -68.8027586 4.733820e+03 -3.256998e+05
#> [723,] 56.1972414 3.158130e+03 1.774782e+05
#> [724,] 7.1972414 5.180028e+01 3.728191e+02
#> [725,] -32.8027586 1.076021e+03 -3.529646e+04
#> [726,] 12.1972414 1.487727e+02 1.814616e+03
#> [727,] -15.8027586 2.497272e+02 -3.946378e+03
#> [728,] -39.8027586 1.584260e+03 -6.305790e+04
#> [729,] 22.1972414 4.927175e+02 1.093697e+04
#> [730,] 1.1972414 1.433387e+00 1.716110e+00
#> [731,] -1.8027586 3.249939e+00 -5.858855e+00
#> [732,] 18.1972414 3.311396e+02 6.025827e+03
#> [733,] -3.8027586 1.446097e+01 -5.499159e+01
#> [734,] 29.1972414 8.524789e+02 2.489003e+04
#> [735,] 21.1972414 4.493230e+02 9.524409e+03
#> attr(,"transformation")
#> [1] "polynomial"
#> attr(,"name")
#> [1] "polynomial(mri$ldl)"
#> attr(,"prnm")
#> [1] "mri$ldl"
#> attr(,"degree")
#> [1] 1 2 3
#> attr(,"center")
#> [1] 125.8028
#> attr(,"original")
#> [1] 9.1972414 -41.8027586 -10.8027586 -64.8027586 22.1972414
#> [6] 37.1972414 -24.8027586 -9.8027586 -1.8027586 -15.8027586
#> [11] 10.1972414 -17.8027586 80.1972414 4.1972414 -4.8027586
#> [16] -30.8027586 -47.8027586 -15.8027586 10.1972414 34.1972414
#> [21] 4.1972414 -42.8027586 28.1972414 -55.8027586 -50.8027586
#> [26] -11.8027586 13.1972414 -44.8027586 -4.8027586 -20.8027586
#> [31] -3.8027586 9.1972414 10.1972414 62.1972414 19.1972414
#> [36] -26.8027586 45.1972414 -42.8027586 29.1972414 17.1972414
#> [41] 22.1972414 36.1972414 56.1972414 -43.8027586 25.1972414
#> [46] -13.8027586 33.1972414 -50.8027586 -27.8027586 63.1972414
#> [51] -2.8027586 101.1972414 -52.8027586 -26.8027586 90.1972414
#> [56] -21.8027586 -45.8027586 -36.8027586 -17.8027586 21.1972414
#> [61] 17.1972414 25.1972414 25.1972414 12.1972414 -12.8027586
#> [66] 20.1972414 23.1972414 -53.8027586 6.1972414 -31.8027586
#> [71] -40.8027586 -46.8027586 9.1972414 13.1972414 -40.8027586
#> [76] -22.8027586 1.1972414 14.1972414 -24.8027586 -4.8027586
#> [81] 20.1972414 -38.8027586 24.1972414 8.1972414 -45.8027586
#> [86] 3.1972414 28.1972414 -26.8027586 -8.8027586 47.1972414
#> [91] -5.8027586 -0.8027586 -15.8027586 -40.8027586 -55.8027586
#> [96] 41.1972414 -3.8027586 37.1972414 -25.8027586 32.1972414
#> [101] -10.8027586 -28.8027586 -41.8027586 -44.8027586 25.1972414
#> [106] 65.1972414 41.1972414 -8.8027586 -21.8027586 -12.8027586
#> [111] -7.8027586 -5.8027586 -27.8027586 0.1972414 16.1972414
#> [116] 20.1972414 -42.8027586 7.1972414 2.1972414 4.1972414
#> [121] -35.8027586 10.1972414 -18.8027586 -2.8027586 -21.8027586
#> [126] -23.8027586 -25.8027586 51.1972414 -39.8027586 NA
#> [131] 38.1972414 30.1972414 -17.8027586 -72.8027586 24.1972414
#> [136] 69.1972414 8.1972414 16.1972414 -37.8027586 4.1972414
#> [141] 48.1972414 25.1972414 22.1972414 -6.8027586 35.1972414
#> [146] 10.1972414 30.1972414 -26.8027586 -11.8027586 12.1972414
#> [151] -21.8027586 -12.8027586 7.1972414 -44.8027586 -47.8027586
#> [156] -10.8027586 15.1972414 NA -47.8027586 -24.8027586
#> [161] 29.1972414 10.1972414 5.1972414 12.1972414 14.1972414
#> [166] -10.8027586 18.1972414 0.1972414 91.1972414 19.1972414
#> [171] 1.1972414 -49.8027586 NA -74.8027586 6.1972414
#> [176] -11.8027586 -64.8027586 23.1972414 11.1972414 1.1972414
#> [181] 7.1972414 7.1972414 18.1972414 -16.8027586 26.1972414
#> [186] -30.8027586 3.1972414 NA 2.1972414 -26.8027586
#> [191] 13.1972414 16.1972414 -22.8027586 -11.8027586 59.1972414
#> [196] -1.8027586 -27.8027586 -24.8027586 65.1972414 -7.8027586
#> [201] -28.8027586 -8.8027586 -30.8027586 9.1972414 80.1972414
#> [206] 24.1972414 -3.8027586 14.1972414 -34.8027586 -4.8027586
#> [211] 34.1972414 36.1972414 62.1972414 -30.8027586 38.1972414
#> [216] 4.1972414 28.1972414 NA 10.1972414 -30.8027586
#> [221] 121.1972414 18.1972414 -42.8027586 -3.8027586 31.1972414
#> [226] -18.8027586 5.1972414 14.1972414 74.1972414 -30.8027586
#> [231] 20.1972414 -23.8027586 11.1972414 24.1972414 22.1972414
#> [236] -53.8027586 16.1972414 -34.8027586 27.1972414 82.1972414
#> [241] -7.8027586 24.1972414 25.1972414 1.1972414 -25.8027586
#> [246] -11.8027586 -13.8027586 3.1972414 53.1972414 8.1972414
#> [251] -10.8027586 -17.8027586 -26.8027586 81.1972414 -48.8027586
#> [256] 15.1972414 4.1972414 36.1972414 1.1972414 -33.8027586
#> [261] NA -25.8027586 61.1972414 -12.8027586 2.1972414
#> [266] 57.1972414 NA -15.8027586 -22.8027586 30.1972414
#> [271] -26.8027586 29.1972414 55.1972414 -7.8027586 6.1972414
#> [276] 22.1972414 -35.8027586 5.1972414 12.1972414 -16.8027586
#> [281] 10.1972414 13.1972414 -34.8027586 50.1972414 22.1972414
#> [286] -38.8027586 -12.8027586 29.1972414 59.1972414 11.1972414
#> [291] 11.1972414 43.1972414 80.1972414 -37.8027586 13.1972414
#> [296] 56.1972414 11.1972414 59.1972414 -9.8027586 -11.8027586
#> [301] -56.8027586 -6.8027586 -43.8027586 4.1972414 -15.8027586
#> [306] 36.1972414 -12.8027586 -32.8027586 -7.8027586 70.1972414
#> [311] -47.8027586 -14.8027586 -54.8027586 15.1972414 -13.8027586
#> [316] 69.1972414 -9.8027586 18.1972414 47.1972414 27.1972414
#> [321] 10.1972414 56.1972414 -35.8027586 2.1972414 62.1972414
#> [326] 58.1972414 -4.8027586 -0.8027586 -12.8027586 8.1972414
#> [331] 14.1972414 -45.8027586 45.1972414 -44.8027586 -13.8027586
#> [336] -9.8027586 32.1972414 -19.8027586 32.1972414 -34.8027586
#> [341] 6.1972414 -37.8027586 -12.8027586 21.1972414 16.1972414
#> [346] -58.8027586 35.1972414 52.1972414 -17.8027586 -38.8027586
#> [351] 11.1972414 34.1972414 1.1972414 -29.8027586 -15.8027586
#> [356] 49.1972414 45.1972414 5.1972414 -32.8027586 -17.8027586
#> [361] -7.8027586 -9.8027586 -68.8027586 1.1972414 55.1972414
#> [366] -17.8027586 7.1972414 16.1972414 8.1972414 0.1972414
#> [371] 38.1972414 -48.8027586 -28.8027586 -70.8027586 -32.8027586
#> [376] -57.8027586 10.1972414 -1.8027586 7.1972414 -4.8027586
#> [381] -45.8027586 17.1972414 16.1972414 -48.8027586 -53.8027586
#> [386] -36.8027586 -48.8027586 -32.8027586 75.1972414 55.1972414
#> [391] -55.8027586 -52.8027586 -20.8027586 8.1972414 -18.8027586
#> [396] 94.1972414 40.1972414 7.1972414 99.1972414 6.1972414
#> [401] 17.1972414 -41.8027586 33.1972414 -11.8027586 -50.8027586
#> [406] -14.8027586 -11.8027586 44.1972414 -16.8027586 32.1972414
#> [411] 47.1972414 -31.8027586 27.1972414 0.1972414 6.1972414
#> [416] -10.8027586 -35.8027586 2.1972414 19.1972414 18.1972414
#> [421] 13.1972414 21.1972414 -44.8027586 69.1972414 35.1972414
#> [426] -28.8027586 -19.8027586 -73.8027586 20.1972414 2.1972414
#> [431] -3.8027586 7.1972414 -14.8027586 30.1972414 -16.8027586
#> [436] 13.1972414 -11.8027586 -114.8027586 0.1972414 -4.8027586
#> [441] 7.1972414 -86.8027586 -19.8027586 11.1972414 30.1972414
#> [446] 36.1972414 -15.8027586 -3.8027586 21.1972414 43.1972414
#> [451] 40.1972414 -31.8027586 -33.8027586 -9.8027586 -29.8027586
#> [456] -36.8027586 13.1972414 61.1972414 47.1972414 -35.8027586
#> [461] -23.8027586 18.1972414 -35.8027586 42.1972414 -14.8027586
#> [466] -24.8027586 -23.8027586 -55.8027586 63.1972414 -21.8027586
#> [471] -65.8027586 -42.8027586 0.1972414 -63.8027586 -4.8027586
#> [476] -12.8027586 -23.8027586 12.1972414 -1.8027586 78.1972414
#> [481] -5.8027586 -11.8027586 25.1972414 -43.8027586 -31.8027586
#> [486] 7.1972414 -88.8027586 30.1972414 45.1972414 -23.8027586
#> [491] -57.8027586 -9.8027586 39.1972414 22.1972414 15.1972414
#> [496] -17.8027586 48.1972414 -5.8027586 -38.8027586 3.1972414
#> [501] 23.1972414 24.1972414 -13.8027586 32.1972414 -2.8027586
#> [506] NA 90.1972414 14.1972414 35.1972414 25.1972414
#> [511] 6.1972414 6.1972414 0.1972414 26.1972414 -35.8027586
#> [516] -30.8027586 10.1972414 17.1972414 -12.8027586 -21.8027586
#> [521] -48.8027586 -26.8027586 -20.8027586 1.1972414 15.1972414
#> [526] -57.8027586 -4.8027586 36.1972414 -17.8027586 -12.8027586
#> [531] -16.8027586 -27.8027586 60.1972414 -4.8027586 41.1972414
#> [536] -64.8027586 7.1972414 22.1972414 18.1972414 21.1972414
#> [541] -15.8027586 -21.8027586 31.1972414 4.1972414 NA
#> [546] 7.1972414 -22.8027586 16.1972414 4.1972414 26.1972414
#> [551] -30.8027586 5.1972414 23.1972414 -38.8027586 29.1972414
#> [556] -33.8027586 28.1972414 NA -0.8027586 12.1972414
#> [561] -4.8027586 17.1972414 -13.8027586 -7.8027586 -37.8027586
#> [566] -2.8027586 29.1972414 -79.8027586 14.1972414 -13.8027586
#> [571] 6.1972414 -1.8027586 25.1972414 -48.8027586 33.1972414
#> [576] -14.8027586 5.1972414 -14.8027586 -2.8027586 18.1972414
#> [581] -50.8027586 -39.8027586 -16.8027586 90.1972414 -4.8027586
#> [586] -42.8027586 16.1972414 2.1972414 -3.8027586 30.1972414
#> [591] -4.8027586 42.1972414 -61.8027586 -16.8027586 -15.8027586
#> [596] -47.8027586 39.1972414 33.1972414 -3.8027586 27.1972414
#> [601] -36.8027586 38.1972414 -25.8027586 -31.8027586 -47.8027586
#> [606] -4.8027586 41.1972414 -20.8027586 9.1972414 -3.8027586
#> [611] -42.8027586 -10.8027586 -23.8027586 43.1972414 -19.8027586
#> [616] -33.8027586 35.1972414 21.1972414 30.1972414 22.1972414
#> [621] -10.8027586 -25.8027586 56.1972414 -31.8027586 20.1972414
#> [626] 71.1972414 -4.8027586 5.1972414 7.1972414 -1.8027586
#> [631] -33.8027586 30.1972414 -26.8027586 -25.8027586 -39.8027586
#> [636] 4.1972414 46.1972414 -9.8027586 24.1972414 8.1972414
#> [641] -25.8027586 92.1972414 30.1972414 -1.8027586 -13.8027586
#> [646] 35.1972414 -17.8027586 -22.8027586 -50.8027586 -9.8027586
#> [651] 12.1972414 43.1972414 26.1972414 -1.8027586 -26.8027586
#> [656] -42.8027586 -32.8027586 42.1972414 15.1972414 -11.8027586
#> [661] -34.8027586 -2.8027586 -48.8027586 26.1972414 6.1972414
#> [666] -20.8027586 -29.8027586 7.1972414 45.1972414 13.1972414
#> [671] -39.8027586 2.1972414 -23.8027586 10.1972414 62.1972414
#> [676] 2.1972414 57.1972414 -36.8027586 -46.8027586 -19.8027586
#> [681] 45.1972414 -13.8027586 10.1972414 -29.8027586 -13.8027586
#> [686] -48.8027586 -16.8027586 5.1972414 -34.8027586 -9.8027586
#> [691] -41.8027586 6.1972414 52.1972414 42.1972414 -56.8027586
#> [696] 20.1972414 -33.8027586 12.1972414 -5.8027586 -15.8027586
#> [701] -8.8027586 -36.8027586 13.1972414 -22.8027586 25.1972414
#> [706] -40.8027586 -2.8027586 34.1972414 -13.8027586 -4.8027586
#> [711] 35.1972414 -32.8027586 27.1972414 30.1972414 -5.8027586
#> [716] -54.8027586 2.1972414 19.1972414 15.1972414 -25.8027586
#> [721] 55.1972414 -68.8027586 56.1972414 7.1972414 -32.8027586
#> [726] 12.1972414 -15.8027586 -39.8027586 22.1972414 1.1972414
#> [731] -1.8027586 18.1972414 -3.8027586 29.1972414 21.1972414
# Use a polynomial in regress
regress("mean", atrophy ~ polynomial(age, degree = 2), data = mri)
#>
#> Call:
#> regress(fnctl = "mean", formula = atrophy ~ polynomial(age, degree = 2),
#> data = mri)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -36.828 -9.063 -1.018 7.816 50.887
#>
#> Coefficients:
#> Estimate Naive SE Robust SE 95%L
#> [1] Intercept 35.34 0.5598 0.5622 34.24
#> polynomial(age, degree = 2)
#> [2] age^1 0.5869 0.1009 0.09808 0.3943
#> [3] age^2 0.02159 0.01099 0.01150 -9.897e-04
#> 95%H F stat df Pr(>F)
#> [1] Intercept 36.45 3952.13 1 < 0.00005
#> polynomial(age, degree = 2) 32.91 2 < 0.00005
#> [2] age^1 0.7794 35.80 1 < 0.00005
#> [3] age^2 0.04417 3.52 1 0.0609
#>
#> Polynomial terms calculated from age, centered at 74.566
#>
#> Residual standard error: 12.33 on 732 degrees of freedom
#> Multiple R-squared: 0.09148, Adjusted R-squared: 0.089
#> F-statistic: 32.91 on 2 and 732 DF, p-value: 2.06e-14
#>