Defines a 'calibration' object for the calculation of concentrations
from measurement signals including estimations for the limit of detection
(LOD) and limit of quantification (LOQ) in accordance with DIN 32645 (2008).
Usage
calibration(
formula,
data = NULL,
blanks = NULL,
weights = NULL,
model = "lm",
check_assumptions = TRUE,
...
)
# S3 method for class 'calibration'
print(x, ...)
# S3 method for class 'calibration'
summary(object, ...)
# S3 method for class 'calibration'
plot(x, interval = "conf", level = 0.95, ...)
# S3 method for class 'calibration'
as.list(x, which = c("coef", "adj.r.squared", "lod", "loq", "blanks"), ...)
lod(x, ...)
# Default S3 method
lod(x, ...)
# S3 method for class 'calibration'
lod(x, blanks = NULL, alpha = 0.01, level = 0.05, ...)
loq(x, ...)
# Default S3 method
loq(x, ...)
# S3 method for class 'calibration'
loq(x, blanks = NULL, alpha = 0.01, k = 3, level = 0.05, maxiter = 10, ...)
# S3 method for class 'calibration'
predict(object, newdata = NULL, interval = "conf", ...)
inv_predict(x, ...)
# Default S3 method
inv_predict(x, ...)
# S3 method for class 'calibration'
inv_predict(x, y, below_lod = NULL, method = "analytic", ...)Arguments
- formula
model formula providing the recorded signal intensities with respect to the nominal/specified analyte concentrations in the form of
signal ~ concentrationorsignal ~ concentration - 1; model formulas are currently restricted to those forms.- data
an optional data frame containing the variables in the model.
- blanks
a vector of numeric blank values overriding those automatically retrieved from calibration data.
- weights
an optional character string containing one or more model variables, for example, in the form of "
1/concentration^0.5" or "1/signal" which is internally converted to a numeric vector and passed to the fitting process of the selected model; see alsoweight_select()- model
model class to be used for fitting; currently,
lm()andrlm()are supported.- check_assumptions
automatically check for normality and homoscedasticity of model residuals using
shapiro.test()andbptest(), respectively; only executed ifweights == NULL.- ...
further arguments passed to submethods; for instance, the respective model environment such as
lm(),print(), orplot().- x, object
an object of class '
calibration' with a model formula as shown above.- interval
type of interval plotted (can be abbreviated); see
predict()for details.- level
tolerance/confidence level; see
predict()andconfint()for details.- which
character vector indicating the parameters to export; defaults to
c("coef", "adj.r.squared", "lod", "loq", "blanks").- alpha
numeric; error tolerance for the detection limit (critical value).
- k
numeric; relative uncertainty for the limit of quantification (
1/beta).- maxiter
a positive integer specifying the maximum number of iterations to calculate the LOQ.
- newdata
a data frame in which to look for variables with which to predict. If
NULL, values are guessed;predict.lm()for details.- y
numeric; the value to inverse predict.
- below_lod
value to be assigned if inverse prediction is below LOD; defaults to
"NULL"which keeps predicted values untouched. Other options may beNAor0.- method
character indicating the method used for inverse prediction; defaults to
"analytic".
Value
calibration returns an object of class
'calibration'.
print() calls the function parameters together with the respective LOD
and LOQ.
summary() may be used to retrieve the summary of the underlying model.
plot() plots the respective calibration curve together with the
measurement values.
as.list() returns a named list.
lod() and loq() return a named vector with the LOD and LOQ
together with lower and upper confidence limits.
predict() returns a data.frame of predictions.
inv_predict() predicts/calculates analyte concentrations from signal
intensities.
Details
The LOD is defined as the lowest quantity of a substance that can be
distinguished from the absence of that substance (blank value) within a given
confidence level (alpha). The LOQ is defined as the lowest quantity of
a substance that can be quantified/distinguished from another sample given
with respect to a defined confidence level (k).
If the data supplied to calibration contain more than one blank
value, namely measurements with a nominal/specified concentration of or close
to zero, the LOD and LOQ are calculated from the deviation of the blank
samples. This method is called "blank method" according to DIN 32645 (2008)
and supposed to be more accurate than the so-called "calibration method"
which will be used for the estimation of LOD and LOQ when data does
not contain zero concentration measurements.
References
Almeida, A.M.D., Castel-Branco, M.M., & Falcao, A.C. (2002). Linear regression for calibration lines revisited: weighting schemes for bioanalytical methods. Journal of Chromatography B, 774(2), 215-222. doi:10.1016/S1570-0232(02)00244-1 .
Currie, L.A. (1999). Nomenclature in evaluation of analytical methods including detection and quantification capabilities: (IUPAC Recommendations 1995). Analytica Chimica Acta 391, 105-126.
DIN 32645 (2008). Chemical analysis - Decision limit, detection limit and determination limit under repeatability conditions - Terms, methods, evaluation. Technical standard. Deutsches Institut für Normung, Berlin.
Massart, D.L., Vandeginste, B.G., Buydens, L.M.C., Lewi, P.J., & Smeyers-Verbeke, J. (1997). Handbook of chemometrics and qualimetrics: Part A. Elsevier Science Inc.
See also
invest() for alternative inverse prediction methods;
Other calibration:
din32645,
icp,
matrix_effect(),
neitzel2003,
phenolics,
weight_select()
Examples
data(din32645)
din <- calibration(Area ~ Conc, data = din32645)
print(din)
#>
#> Call:
#> calibration(formula = Area ~ Conc, data = din32645)
#>
#> Coefficients:
#> (Intercept) Conc
#> 2481 9662
#>
#> Adjusted R-squared: 0.983
#> Sum relative error: 0.7978
#>
#> Blanks:
#> [1] 2003 1901 2212 1976 2279 1853 2165 2108 2368 1943
#>
#> Conc lwr upr
#> LOD 0.053 0.036 0.096
#> LOQ 0.212 0.146 0.387
#>
#> Check for normality of residuals:
#>
#> Shapiro-Wilk normality test
#>
#> data: residuals(calibration(formula = Area ~ Conc, data = din32645))
#> W = 0.90059, p-value = 0.2224
#>
#> Check for homoscedasticity of residuals:
#>
#> studentized Breusch-Pagan test
#>
#> data: Area ~ Conc
#> BP = 1.6198, df = 1, p-value = 0.2031
#>
summary(din)
#>
#> Call:
#> calibration(formula = Area ~ Conc, data = din32645)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -223.16 -138.94 -29.16 121.92 327.26
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 2480.9 131.4 18.89 6.39e-08 ***
#> Conc 9661.9 423.4 22.82 1.44e-08 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 192.3 on 8 degrees of freedom
#> Multiple R-squared: 0.9849, Adjusted R-squared: 0.983
#> F-statistic: 520.7 on 1 and 8 DF, p-value: 1.442e-08
#>
plot(din)
as.list(din)
#> $`(Intercept)`
#> [1] 2480.867
#>
#> $Conc
#> [1] 9661.939
#>
#> $adj.r.squared
#> [1] 0.9829773
#>
#> $lod
#> [1] 0.053
#>
#> $loq
#> [1] 0.212
#>
#> $blank_mean
#> [1] 2080.8
#>
#> $blank_sd
#> [1] 172.2581
#>
lod(din)
#> Conc lwr upr
#> LOD 0.053 0.036 0.096
loq(din)
#> Conc lwr upr
#> LOQ 0.212 0.146 0.387
predict(din)
#> Conc fit lwr upr
#> 1 0.05000000 2963.964 2703.336 3224.592
#> 2 0.05045045 2968.316 2708.058 3228.573
#> 3 0.05090090 2972.668 2712.781 3232.555
#> 4 0.05135135 2977.020 2717.504 3236.537
#> 5 0.05180180 2981.373 2722.226 3240.519
#> 6 0.05225225 2985.725 2726.948 3244.502
#> 7 0.05270270 2990.077 2731.669 3248.484
#> 8 0.05315315 2994.429 2736.391 3252.467
#> 9 0.05360360 2998.781 2741.112 3256.451
#> 10 0.05405405 3003.134 2745.833 3260.434
#> 11 0.05450450 3007.486 2750.554 3264.417
#> 12 0.05495495 3011.838 2755.275 3268.401
#> 13 0.05540541 3016.190 2759.995 3272.385
#> 14 0.05585586 3020.543 2764.716 3276.369
#> 15 0.05630631 3024.895 2769.436 3280.354
#> 16 0.05675676 3029.247 2774.155 3284.339
#> 17 0.05720721 3033.599 2778.875 3288.324
#> 18 0.05765766 3037.951 2783.594 3292.309
#> 19 0.05810811 3042.304 2788.313 3296.294
#> 20 0.05855856 3046.656 2793.032 3300.280
#> 21 0.05900901 3051.008 2797.751 3304.266
#> 22 0.05945946 3055.360 2802.469 3308.252
#> 23 0.05990991 3059.713 2807.187 3312.238
#> 24 0.06036036 3064.065 2811.905 3316.225
#> 25 0.06081081 3068.417 2816.623 3320.211
#> 26 0.06126126 3072.769 2821.340 3324.198
#> 27 0.06171171 3077.121 2826.057 3328.186
#> 28 0.06216216 3081.474 2830.774 3332.173
#> 29 0.06261261 3085.826 2835.491 3336.161
#> 30 0.06306306 3090.178 2840.207 3340.149
#> 31 0.06351351 3094.530 2844.924 3344.137
#> 32 0.06396396 3098.883 2849.639 3348.126
#> 33 0.06441441 3103.235 2854.355 3352.114
#> 34 0.06486486 3107.587 2859.071 3356.103
#> 35 0.06531532 3111.939 2863.786 3360.093
#> 36 0.06576577 3116.292 2868.501 3364.082
#> 37 0.06621622 3120.644 2873.216 3368.072
#> 38 0.06666667 3124.996 2877.930 3372.062
#> 39 0.06711712 3129.348 2882.644 3376.052
#> 40 0.06756757 3133.700 2887.358 3380.043
#> 41 0.06801802 3138.053 2892.072 3384.033
#> 42 0.06846847 3142.405 2896.785 3388.024
#> 43 0.06891892 3146.757 2901.499 3392.016
#> 44 0.06936937 3151.109 2906.211 3396.007
#> 45 0.06981982 3155.462 2910.924 3399.999
#> 46 0.07027027 3159.814 2915.637 3403.991
#> 47 0.07072072 3164.166 2920.349 3407.983
#> 48 0.07117117 3168.518 2925.061 3411.976
#> 49 0.07162162 3172.870 2929.772 3415.969
#> 50 0.07207207 3177.223 2934.484 3419.962
#> 51 0.07252252 3181.575 2939.195 3423.955
#> 52 0.07297297 3185.927 2943.906 3427.949
#> 53 0.07342342 3190.279 2948.616 3431.943
#> 54 0.07387387 3194.632 2953.326 3435.937
#> 55 0.07432432 3198.984 2958.036 3439.931
#> 56 0.07477477 3203.336 2962.746 3443.926
#> 57 0.07522523 3207.688 2967.456 3447.921
#> 58 0.07567568 3212.040 2972.165 3451.916
#> 59 0.07612613 3216.393 2976.874 3455.912
#> 60 0.07657658 3220.745 2981.583 3459.907
#> 61 0.07702703 3225.097 2986.291 3463.903
#> 62 0.07747748 3229.449 2990.999 3467.900
#> 63 0.07792793 3233.802 2995.707 3471.896
#> 64 0.07837838 3238.154 3000.414 3475.893
#> 65 0.07882883 3242.506 3005.122 3479.890
#> 66 0.07927928 3246.858 3009.829 3483.888
#> 67 0.07972973 3251.210 3014.535 3487.886
#> 68 0.08018018 3255.563 3019.242 3491.884
#> 69 0.08063063 3259.915 3023.948 3495.882
#> 70 0.08108108 3264.267 3028.654 3499.881
#> 71 0.08153153 3268.619 3033.359 3503.880
#> 72 0.08198198 3272.972 3038.064 3507.879
#> 73 0.08243243 3277.324 3042.769 3511.878
#> 74 0.08288288 3281.676 3047.474 3515.878
#> 75 0.08333333 3286.028 3052.178 3519.878
#> 76 0.08378378 3290.381 3056.882 3523.879
#> 77 0.08423423 3294.733 3061.586 3527.879
#> 78 0.08468468 3299.085 3066.290 3531.880
#> 79 0.08513514 3303.437 3070.993 3535.882
#> 80 0.08558559 3307.789 3075.696 3539.883
#> 81 0.08603604 3312.142 3080.398 3543.885
#> 82 0.08648649 3316.494 3085.100 3547.887
#> 83 0.08693694 3320.846 3089.802 3551.890
#> 84 0.08738739 3325.198 3094.504 3555.893
#> 85 0.08783784 3329.551 3099.205 3559.896
#> 86 0.08828829 3333.903 3103.906 3563.899
#> 87 0.08873874 3338.255 3108.607 3567.903
#> 88 0.08918919 3342.607 3113.307 3571.907
#> 89 0.08963964 3346.959 3118.007 3575.912
#> 90 0.09009009 3351.312 3122.707 3579.916
#> 91 0.09054054 3355.664 3127.406 3583.921
#> 92 0.09099099 3360.016 3132.106 3587.927
#> 93 0.09144144 3364.368 3136.804 3591.932
#> 94 0.09189189 3368.721 3141.503 3595.938
#> 95 0.09234234 3373.073 3146.201 3599.945
#> 96 0.09279279 3377.425 3150.899 3603.951
#> 97 0.09324324 3381.777 3155.596 3607.958
#> 98 0.09369369 3386.129 3160.293 3611.966
#> 99 0.09414414 3390.482 3164.990 3615.973
#> 100 0.09459459 3394.834 3169.687 3619.981
#> 101 0.09504505 3399.186 3174.383 3623.989
#> 102 0.09549550 3403.538 3179.079 3627.998
#> 103 0.09594595 3407.891 3183.774 3632.007
#> 104 0.09639640 3412.243 3188.469 3636.016
#> 105 0.09684685 3416.595 3193.164 3640.026
#> 106 0.09729730 3420.947 3197.859 3644.036
#> 107 0.09774775 3425.299 3202.553 3648.046
#> 108 0.09819820 3429.652 3207.247 3652.057
#> 109 0.09864865 3434.004 3211.940 3656.068
#> 110 0.09909910 3438.356 3216.633 3660.079
#> 111 0.09954955 3442.708 3221.326 3664.091
#> 112 0.10000000 3447.061 3226.018 3668.103
#> 113 0.10045045 3451.413 3230.710 3672.115
#> 114 0.10090090 3455.765 3235.402 3676.128
#> 115 0.10135135 3460.117 3240.093 3680.141
#> 116 0.10180180 3464.470 3244.784 3684.155
#> 117 0.10225225 3468.822 3249.475 3688.169
#> 118 0.10270270 3473.174 3254.165 3692.183
#> 119 0.10315315 3477.526 3258.855 3696.197
#> 120 0.10360360 3481.878 3263.545 3700.212
#> 121 0.10405405 3486.231 3268.234 3704.228
#> 122 0.10450450 3490.583 3272.922 3708.243
#> 123 0.10495495 3494.935 3277.611 3712.259
#> 124 0.10540541 3499.287 3282.299 3716.276
#> 125 0.10585586 3503.640 3286.987 3720.292
#> 126 0.10630631 3507.992 3291.674 3724.310
#> 127 0.10675676 3512.344 3296.361 3728.327
#> 128 0.10720721 3516.696 3301.047 3732.345
#> 129 0.10765766 3521.048 3305.734 3736.363
#> 130 0.10810811 3525.401 3310.419 3740.382
#> 131 0.10855856 3529.753 3315.105 3744.401
#> 132 0.10900901 3534.105 3319.790 3748.420
#> 133 0.10945946 3538.457 3324.474 3752.440
#> 134 0.10990991 3542.810 3329.159 3756.460
#> 135 0.11036036 3547.162 3333.843 3760.481
#> 136 0.11081081 3551.514 3338.526 3764.502
#> 137 0.11126126 3555.866 3343.209 3768.523
#> 138 0.11171171 3560.218 3347.892 3772.545
#> 139 0.11216216 3564.571 3352.574 3776.567
#> 140 0.11261261 3568.923 3357.256 3780.590
#> 141 0.11306306 3573.275 3361.937 3784.613
#> 142 0.11351351 3577.627 3366.619 3788.636
#> 143 0.11396396 3581.980 3371.299 3792.660
#> 144 0.11441441 3586.332 3375.980 3796.684
#> 145 0.11486486 3590.684 3380.659 3800.709
#> 146 0.11531532 3595.036 3385.339 3804.734
#> 147 0.11576577 3599.388 3390.018 3808.759
#> 148 0.11621622 3603.741 3394.697 3812.785
#> 149 0.11666667 3608.093 3399.375 3816.811
#> 150 0.11711712 3612.445 3404.052 3820.838
#> 151 0.11756757 3616.797 3408.730 3824.865
#> 152 0.11801802 3621.150 3413.407 3828.892
#> 153 0.11846847 3625.502 3418.083 3832.920
#> 154 0.11891892 3629.854 3422.759 3836.949
#> 155 0.11936937 3634.206 3427.435 3840.977
#> 156 0.11981982 3638.559 3432.110 3845.007
#> 157 0.12027027 3642.911 3436.785 3849.036
#> 158 0.12072072 3647.263 3441.460 3853.066
#> 159 0.12117117 3651.615 3446.133 3857.097
#> 160 0.12162162 3655.967 3450.807 3861.128
#> 161 0.12207207 3660.320 3455.480 3865.159
#> 162 0.12252252 3664.672 3460.153 3869.191
#> 163 0.12297297 3669.024 3464.825 3873.223
#> 164 0.12342342 3673.376 3469.497 3877.256
#> 165 0.12387387 3677.729 3474.168 3881.289
#> 166 0.12432432 3682.081 3478.839 3885.323
#> 167 0.12477477 3686.433 3483.509 3889.357
#> 168 0.12522523 3690.785 3488.179 3893.392
#> 169 0.12567568 3695.137 3492.848 3897.427
#> 170 0.12612613 3699.490 3497.517 3901.462
#> 171 0.12657658 3703.842 3502.186 3905.498
#> 172 0.12702703 3708.194 3506.854 3909.534
#> 173 0.12747748 3712.546 3511.522 3913.571
#> 174 0.12792793 3716.899 3516.189 3917.608
#> 175 0.12837838 3721.251 3520.855 3921.646
#> 176 0.12882883 3725.603 3525.522 3925.684
#> 177 0.12927928 3729.955 3530.187 3929.723
#> 178 0.12972973 3734.307 3534.853 3933.762
#> 179 0.13018018 3738.660 3539.517 3937.802
#> 180 0.13063063 3743.012 3544.182 3941.842
#> 181 0.13108108 3747.364 3548.845 3945.883
#> 182 0.13153153 3751.716 3553.509 3949.924
#> 183 0.13198198 3756.069 3558.171 3953.966
#> 184 0.13243243 3760.421 3562.834 3958.008
#> 185 0.13288288 3764.773 3567.496 3962.050
#> 186 0.13333333 3769.125 3572.157 3966.094
#> 187 0.13378378 3773.477 3576.818 3970.137
#> 188 0.13423423 3777.830 3581.478 3974.181
#> 189 0.13468468 3782.182 3586.138 3978.226
#> 190 0.13513514 3786.534 3590.797 3982.271
#> 191 0.13558559 3790.886 3595.456 3986.317
#> 192 0.13603604 3795.239 3600.115 3990.363
#> 193 0.13648649 3799.591 3604.772 3994.409
#> 194 0.13693694 3803.943 3609.430 3998.456
#> 195 0.13738739 3808.295 3614.086 4002.504
#> 196 0.13783784 3812.648 3618.743 4006.552
#> 197 0.13828829 3817.000 3623.398 4010.601
#> 198 0.13873874 3821.352 3628.054 4014.650
#> 199 0.13918919 3825.704 3632.708 4018.700
#> 200 0.13963964 3830.056 3637.362 4022.750
#> 201 0.14009009 3834.409 3642.016 4026.801
#> 202 0.14054054 3838.761 3646.669 4030.853
#> 203 0.14099099 3843.113 3651.322 4034.904
#> 204 0.14144144 3847.465 3655.974 4038.957
#> 205 0.14189189 3851.818 3660.625 4043.010
#> 206 0.14234234 3856.170 3665.276 4047.063
#> 207 0.14279279 3860.522 3669.927 4051.117
#> 208 0.14324324 3864.874 3674.576 4055.172
#> 209 0.14369369 3869.226 3679.226 4059.227
#> 210 0.14414414 3873.579 3683.874 4063.283
#> 211 0.14459459 3877.931 3688.523 4067.339
#> 212 0.14504505 3882.283 3693.170 4071.396
#> 213 0.14549550 3886.635 3697.817 4075.453
#> 214 0.14594595 3890.988 3702.464 4079.511
#> 215 0.14639640 3895.340 3707.110 4083.570
#> 216 0.14684685 3899.692 3711.755 4087.629
#> 217 0.14729730 3904.044 3716.400 4091.689
#> 218 0.14774775 3908.396 3721.044 4095.749
#> 219 0.14819820 3912.749 3725.688 4099.810
#> 220 0.14864865 3917.101 3730.331 4103.871
#> 221 0.14909910 3921.453 3734.973 4107.933
#> 222 0.14954955 3925.805 3739.615 4111.996
#> 223 0.15000000 3930.158 3744.256 4116.059
#> 224 0.15045045 3934.510 3748.897 4120.123
#> 225 0.15090090 3938.862 3753.537 4124.187
#> 226 0.15135135 3943.214 3758.176 4128.252
#> 227 0.15180180 3947.566 3762.815 4132.318
#> 228 0.15225225 3951.919 3767.454 4136.384
#> 229 0.15270270 3956.271 3772.091 4140.451
#> 230 0.15315315 3960.623 3776.728 4144.518
#> 231 0.15360360 3964.975 3781.365 4148.586
#> 232 0.15405405 3969.328 3786.001 4152.655
#> 233 0.15450450 3973.680 3790.636 4156.724
#> 234 0.15495495 3978.032 3795.271 4160.794
#> 235 0.15540541 3982.384 3799.905 4164.864
#> 236 0.15585586 3986.737 3804.538 4168.935
#> 237 0.15630631 3991.089 3809.171 4173.007
#> 238 0.15675676 3995.441 3813.803 4177.079
#> 239 0.15720721 3999.793 3818.434 4181.152
#> 240 0.15765766 4004.145 3823.065 4185.226
#> 241 0.15810811 4008.498 3827.695 4189.300
#> 242 0.15855856 4012.850 3832.325 4193.375
#> 243 0.15900901 4017.202 3836.954 4197.451
#> 244 0.15945946 4021.554 3841.582 4201.527
#> 245 0.15990991 4025.907 3846.209 4205.604
#> 246 0.16036036 4030.259 3850.836 4209.681
#> 247 0.16081081 4034.611 3855.463 4213.759
#> 248 0.16126126 4038.963 3860.088 4217.838
#> 249 0.16171171 4043.315 3864.713 4221.918
#> 250 0.16216216 4047.668 3869.338 4225.998
#> 251 0.16261261 4052.020 3873.961 4230.079
#> 252 0.16306306 4056.372 3878.584 4234.160
#> 253 0.16351351 4060.724 3883.206 4238.242
#> 254 0.16396396 4065.077 3887.828 4242.325
#> 255 0.16441441 4069.429 3892.449 4246.409
#> 256 0.16486486 4073.781 3897.069 4250.493
#> 257 0.16531532 4078.133 3901.689 4254.578
#> 258 0.16576577 4082.485 3906.307 4258.663
#> 259 0.16621622 4086.838 3910.926 4262.750
#> 260 0.16666667 4091.190 3915.543 4266.837
#> 261 0.16711712 4095.542 3920.160 4270.924
#> 262 0.16756757 4099.894 3924.776 4275.013
#> 263 0.16801802 4104.247 3929.391 4279.102
#> 264 0.16846847 4108.599 3934.006 4283.192
#> 265 0.16891892 4112.951 3938.620 4287.282
#> 266 0.16936937 4117.303 3943.233 4291.374
#> 267 0.16981982 4121.655 3947.845 4295.466
#> 268 0.17027027 4126.008 3952.457 4299.558
#> 269 0.17072072 4130.360 3957.068 4303.652
#> 270 0.17117117 4134.712 3961.678 4307.746
#> 271 0.17162162 4139.064 3966.288 4311.841
#> 272 0.17207207 4143.417 3970.897 4315.937
#> 273 0.17252252 4147.769 3975.505 4320.033
#> 274 0.17297297 4152.121 3980.112 4324.130
#> 275 0.17342342 4156.473 3984.719 4328.228
#> 276 0.17387387 4160.825 3989.324 4332.327
#> 277 0.17432432 4165.178 3993.930 4336.426
#> 278 0.17477477 4169.530 3998.534 4340.526
#> 279 0.17522523 4173.882 4003.137 4344.627
#> 280 0.17567568 4178.234 4007.740 4348.729
#> 281 0.17612613 4182.587 4012.342 4352.831
#> 282 0.17657658 4186.939 4016.943 4356.934
#> 283 0.17702703 4191.291 4021.544 4361.038
#> 284 0.17747748 4195.643 4026.144 4365.143
#> 285 0.17792793 4199.996 4030.743 4369.249
#> 286 0.17837838 4204.348 4035.341 4373.355
#> 287 0.17882883 4208.700 4039.938 4377.462
#> 288 0.17927928 4213.052 4044.535 4381.570
#> 289 0.17972973 4217.404 4049.130 4385.679
#> 290 0.18018018 4221.757 4053.725 4389.788
#> 291 0.18063063 4226.109 4058.319 4393.898
#> 292 0.18108108 4230.461 4062.913 4398.009
#> 293 0.18153153 4234.813 4067.505 4402.121
#> 294 0.18198198 4239.166 4072.097 4406.234
#> 295 0.18243243 4243.518 4076.688 4410.348
#> 296 0.18288288 4247.870 4081.278 4414.462
#> 297 0.18333333 4252.222 4085.867 4418.577
#> 298 0.18378378 4256.574 4090.456 4422.693
#> 299 0.18423423 4260.927 4095.043 4426.810
#> 300 0.18468468 4265.279 4099.630 4430.928
#> 301 0.18513514 4269.631 4104.216 4435.046
#> 302 0.18558559 4273.983 4108.801 4439.165
#> 303 0.18603604 4278.336 4113.386 4443.286
#> 304 0.18648649 4282.688 4117.969 4447.407
#> 305 0.18693694 4287.040 4122.551 4451.529
#> 306 0.18738739 4291.392 4127.133 4455.651
#> 307 0.18783784 4295.744 4131.714 4459.775
#> 308 0.18828829 4300.097 4136.294 4463.899
#> 309 0.18873874 4304.449 4140.873 4468.025
#> 310 0.18918919 4308.801 4145.451 4472.151
#> 311 0.18963964 4313.153 4150.029 4476.278
#> 312 0.19009009 4317.506 4154.605 4480.406
#> 313 0.19054054 4321.858 4159.181 4484.535
#> 314 0.19099099 4326.210 4163.756 4488.664
#> 315 0.19144144 4330.562 4168.330 4492.795
#> 316 0.19189189 4334.914 4172.902 4496.927
#> 317 0.19234234 4339.267 4177.475 4501.059
#> 318 0.19279279 4343.619 4182.046 4505.192
#> 319 0.19324324 4347.971 4186.616 4509.326
#> 320 0.19369369 4352.323 4191.185 4513.461
#> 321 0.19414414 4356.676 4195.754 4517.597
#> 322 0.19459459 4361.028 4200.321 4521.734
#> 323 0.19504505 4365.380 4204.888 4525.872
#> 324 0.19549550 4369.732 4209.454 4530.011
#> 325 0.19594595 4374.085 4214.018 4534.151
#> 326 0.19639640 4378.437 4218.582 4538.291
#> 327 0.19684685 4382.789 4223.145 4542.433
#> 328 0.19729730 4387.141 4227.707 4546.575
#> 329 0.19774775 4391.493 4232.268 4550.719
#> 330 0.19819820 4395.846 4236.828 4554.863
#> 331 0.19864865 4400.198 4241.388 4559.008
#> 332 0.19909910 4404.550 4245.946 4563.154
#> 333 0.19954955 4408.902 4250.503 4567.302
#> 334 0.20000000 4413.255 4255.059 4571.450
#> 335 0.20045045 4417.607 4259.615 4575.599
#> 336 0.20090090 4421.959 4264.169 4579.749
#> 337 0.20135135 4426.311 4268.722 4583.900
#> 338 0.20180180 4430.663 4273.275 4588.052
#> 339 0.20225225 4435.016 4277.826 4592.205
#> 340 0.20270270 4439.368 4282.377 4596.359
#> 341 0.20315315 4443.720 4286.926 4600.514
#> 342 0.20360360 4448.072 4291.475 4604.670
#> 343 0.20405405 4452.425 4296.022 4608.827
#> 344 0.20450450 4456.777 4300.569 4612.985
#> 345 0.20495495 4461.129 4305.114 4617.144
#> 346 0.20540541 4465.481 4309.659 4621.304
#> 347 0.20585586 4469.833 4314.202 4625.464
#> 348 0.20630631 4474.186 4318.745 4629.626
#> 349 0.20675676 4478.538 4323.286 4633.789
#> 350 0.20720721 4482.890 4327.827 4637.953
#> 351 0.20765766 4487.242 4332.366 4642.118
#> 352 0.20810811 4491.595 4336.905 4646.284
#> 353 0.20855856 4495.947 4341.442 4650.451
#> 354 0.20900901 4500.299 4345.979 4654.619
#> 355 0.20945946 4504.651 4350.514 4658.789
#> 356 0.20990991 4509.003 4355.048 4662.959
#> 357 0.21036036 4513.356 4359.582 4667.130
#> 358 0.21081081 4517.708 4364.114 4671.302
#> 359 0.21126126 4522.060 4368.645 4675.475
#> 360 0.21171171 4526.412 4373.175 4679.650
#> 361 0.21216216 4530.765 4377.704 4683.825
#> 362 0.21261261 4535.117 4382.232 4688.002
#> 363 0.21306306 4539.469 4386.759 4692.179
#> 364 0.21351351 4543.821 4391.285 4696.358
#> 365 0.21396396 4548.174 4395.810 4700.537
#> 366 0.21441441 4552.526 4400.333 4704.718
#> 367 0.21486486 4556.878 4404.856 4708.900
#> 368 0.21531532 4561.230 4409.378 4713.083
#> 369 0.21576577 4565.582 4413.898 4717.267
#> 370 0.21621622 4569.935 4418.418 4721.452
#> 371 0.21666667 4574.287 4422.936 4725.638
#> 372 0.21711712 4578.639 4427.453 4729.825
#> 373 0.21756757 4582.991 4431.969 4734.014
#> 374 0.21801802 4587.344 4436.484 4738.203
#> 375 0.21846847 4591.696 4440.998 4742.394
#> 376 0.21891892 4596.048 4445.511 4746.585
#> 377 0.21936937 4600.400 4450.022 4750.778
#> 378 0.21981982 4604.752 4454.533 4754.972
#> 379 0.22027027 4609.105 4459.042 4759.167
#> 380 0.22072072 4613.457 4463.551 4763.363
#> 381 0.22117117 4617.809 4468.058 4767.560
#> 382 0.22162162 4622.161 4472.564 4771.759
#> 383 0.22207207 4626.514 4477.069 4775.958
#> 384 0.22252252 4630.866 4481.572 4780.159
#> 385 0.22297297 4635.218 4486.075 4784.361
#> 386 0.22342342 4639.570 4490.576 4788.564
#> 387 0.22387387 4643.922 4495.077 4792.768
#> 388 0.22432432 4648.275 4499.576 4796.973
#> 389 0.22477477 4652.627 4504.074 4801.180
#> 390 0.22522523 4656.979 4508.571 4805.388
#> 391 0.22567568 4661.331 4513.066 4809.596
#> 392 0.22612613 4665.684 4517.561 4813.806
#> 393 0.22657658 4670.036 4522.054 4818.017
#> 394 0.22702703 4674.388 4526.546 4822.230
#> 395 0.22747748 4678.740 4531.037 4826.443
#> 396 0.22792793 4683.092 4535.527 4830.658
#> 397 0.22837838 4687.445 4540.016 4834.874
#> 398 0.22882883 4691.797 4544.503 4839.091
#> 399 0.22927928 4696.149 4548.990 4843.309
#> 400 0.22972973 4700.501 4553.475 4847.528
#> 401 0.23018018 4704.854 4557.958 4851.749
#> 402 0.23063063 4709.206 4562.441 4855.971
#> 403 0.23108108 4713.558 4566.923 4860.194
#> 404 0.23153153 4717.910 4571.403 4864.418
#> 405 0.23198198 4722.263 4575.882 4868.643
#> 406 0.23243243 4726.615 4580.360 4872.870
#> 407 0.23288288 4730.967 4584.836 4877.098
#> 408 0.23333333 4735.319 4589.312 4881.327
#> 409 0.23378378 4739.671 4593.786 4885.557
#> 410 0.23423423 4744.024 4598.259 4889.789
#> 411 0.23468468 4748.376 4602.730 4894.021
#> 412 0.23513514 4752.728 4607.201 4898.255
#> 413 0.23558559 4757.080 4611.670 4902.490
#> 414 0.23603604 4761.433 4616.138 4906.727
#> 415 0.23648649 4765.785 4620.605 4910.965
#> 416 0.23693694 4770.137 4625.070 4915.204
#> 417 0.23738739 4774.489 4629.535 4919.444
#> 418 0.23783784 4778.841 4633.998 4923.685
#> 419 0.23828829 4783.194 4638.460 4927.928
#> 420 0.23873874 4787.546 4642.920 4932.172
#> 421 0.23918919 4791.898 4647.379 4936.417
#> 422 0.23963964 4796.250 4651.837 4940.663
#> 423 0.24009009 4800.603 4656.294 4944.911
#> 424 0.24054054 4804.955 4660.750 4949.160
#> 425 0.24099099 4809.307 4665.204 4953.410
#> 426 0.24144144 4813.659 4669.657 4957.662
#> 427 0.24189189 4818.011 4674.108 4961.915
#> 428 0.24234234 4822.364 4678.559 4966.169
#> 429 0.24279279 4826.716 4683.008 4970.424
#> 430 0.24324324 4831.068 4687.456 4974.681
#> 431 0.24369369 4835.420 4691.902 4978.938
#> 432 0.24414414 4839.773 4696.348 4983.198
#> 433 0.24459459 4844.125 4700.791 4987.458
#> 434 0.24504505 4848.477 4705.234 4991.720
#> 435 0.24549550 4852.829 4709.676 4995.983
#> 436 0.24594595 4857.181 4714.116 5000.247
#> 437 0.24639640 4861.534 4718.554 5004.513
#> 438 0.24684685 4865.886 4722.992 5008.780
#> 439 0.24729730 4870.238 4727.428 5013.048
#> 440 0.24774775 4874.590 4731.863 5017.318
#> 441 0.24819820 4878.943 4736.297 5021.589
#> 442 0.24864865 4883.295 4740.729 5025.861
#> 443 0.24909910 4887.647 4745.160 5030.134
#> 444 0.24954955 4891.999 4749.589 5034.409
#> 445 0.25000000 4896.352 4754.018 5038.685
#> 446 0.25045045 4900.704 4758.445 5042.963
#> 447 0.25090090 4905.056 4762.870 5047.242
#> 448 0.25135135 4909.408 4767.295 5051.522
#> 449 0.25180180 4913.760 4771.718 5055.803
#> 450 0.25225225 4918.113 4776.139 5060.086
#> 451 0.25270270 4922.465 4780.560 5064.370
#> 452 0.25315315 4926.817 4784.979 5068.655
#> 453 0.25360360 4931.169 4789.397 5072.942
#> 454 0.25405405 4935.522 4793.813 5077.230
#> 455 0.25450450 4939.874 4798.228 5081.520
#> 456 0.25495495 4944.226 4802.642 5085.810
#> 457 0.25540541 4948.578 4807.054 5090.102
#> 458 0.25585586 4952.930 4811.465 5094.396
#> 459 0.25630631 4957.283 4815.875 5098.691
#> 460 0.25675676 4961.635 4820.283 5102.987
#> 461 0.25720721 4965.987 4824.690 5107.284
#> 462 0.25765766 4970.339 4829.096 5111.583
#> 463 0.25810811 4974.692 4833.500 5115.883
#> 464 0.25855856 4979.044 4837.903 5120.185
#> 465 0.25900901 4983.396 4842.304 5124.488
#> 466 0.25945946 4987.748 4846.705 5128.792
#> 467 0.25990991 4992.100 4851.103 5133.097
#> 468 0.26036036 4996.453 4855.501 5137.404
#> 469 0.26081081 5000.805 4859.897 5141.713
#> 470 0.26126126 5005.157 4864.292 5146.022
#> 471 0.26171171 5009.509 4868.685 5150.333
#> 472 0.26216216 5013.862 4873.077 5154.646
#> 473 0.26261261 5018.214 4877.468 5158.960
#> 474 0.26306306 5022.566 4881.857 5163.275
#> 475 0.26351351 5026.918 4886.245 5167.591
#> 476 0.26396396 5031.270 4890.632 5171.909
#> 477 0.26441441 5035.623 4895.017 5176.228
#> 478 0.26486486 5039.975 4899.401 5180.549
#> 479 0.26531532 5044.327 4903.784 5184.871
#> 480 0.26576577 5048.679 4908.165 5189.194
#> 481 0.26621622 5053.032 4912.545 5193.519
#> 482 0.26666667 5057.384 4916.923 5197.845
#> 483 0.26711712 5061.736 4921.300 5202.172
#> 484 0.26756757 5066.088 4925.676 5206.501
#> 485 0.26801802 5070.441 4930.050 5210.831
#> 486 0.26846847 5074.793 4934.423 5215.163
#> 487 0.26891892 5079.145 4938.794 5219.496
#> 488 0.26936937 5083.497 4943.164 5223.830
#> 489 0.26981982 5087.849 4947.533 5228.166
#> 490 0.27027027 5092.202 4951.901 5232.503
#> 491 0.27072072 5096.554 4956.267 5236.841
#> 492 0.27117117 5100.906 4960.631 5241.181
#> 493 0.27162162 5105.258 4964.994 5245.522
#> 494 0.27207207 5109.611 4969.356 5249.865
#> 495 0.27252252 5113.963 4973.717 5254.209
#> 496 0.27297297 5118.315 4978.076 5258.554
#> 497 0.27342342 5122.667 4982.434 5262.901
#> 498 0.27387387 5127.019 4986.790 5267.249
#> 499 0.27432432 5131.372 4991.145 5271.598
#> 500 0.27477477 5135.724 4995.499 5275.949
#> 501 0.27522523 5140.076 4999.851 5280.301
#> 502 0.27567568 5144.428 5004.202 5284.655
#> 503 0.27612613 5148.781 5008.551 5289.010
#> 504 0.27657658 5153.133 5012.899 5293.366
#> 505 0.27702703 5157.485 5017.246 5297.724
#> 506 0.27747748 5161.837 5021.591 5302.083
#> 507 0.27792793 5166.189 5025.935 5306.444
#> 508 0.27837838 5170.542 5030.278 5310.806
#> 509 0.27882883 5174.894 5034.619 5315.169
#> 510 0.27927928 5179.246 5038.959 5319.533
#> 511 0.27972973 5183.598 5043.297 5323.899
#> 512 0.28018018 5187.951 5047.634 5328.267
#> 513 0.28063063 5192.303 5051.970 5332.636
#> 514 0.28108108 5196.655 5056.304 5337.006
#> 515 0.28153153 5201.007 5060.637 5341.377
#> 516 0.28198198 5205.359 5064.969 5345.750
#> 517 0.28243243 5209.712 5069.299 5350.124
#> 518 0.28288288 5214.064 5073.628 5354.500
#> 519 0.28333333 5218.416 5077.955 5358.877
#> 520 0.28378378 5222.768 5082.281 5363.255
#> 521 0.28423423 5227.121 5086.606 5367.635
#> 522 0.28468468 5231.473 5090.929 5372.016
#> 523 0.28513514 5235.825 5095.251 5376.399
#> 524 0.28558559 5240.177 5099.572 5380.783
#> 525 0.28603604 5244.530 5103.891 5385.168
#> 526 0.28648649 5248.882 5108.209 5389.555
#> 527 0.28693694 5253.234 5112.525 5393.943
#> 528 0.28738739 5257.586 5116.840 5398.332
#> 529 0.28783784 5261.938 5121.154 5402.723
#> 530 0.28828829 5266.291 5125.467 5407.115
#> 531 0.28873874 5270.643 5129.778 5411.508
#> 532 0.28918919 5274.995 5134.087 5415.903
#> 533 0.28963964 5279.347 5138.396 5420.299
#> 534 0.29009009 5283.700 5142.703 5424.697
#> 535 0.29054054 5288.052 5147.008 5429.095
#> 536 0.29099099 5292.404 5151.312 5433.496
#> 537 0.29144144 5296.756 5155.615 5437.897
#> 538 0.29189189 5301.108 5159.917 5442.300
#> 539 0.29234234 5305.461 5164.217 5446.704
#> 540 0.29279279 5309.813 5168.516 5451.110
#> 541 0.29324324 5314.165 5172.813 5455.517
#> 542 0.29369369 5318.517 5177.109 5459.925
#> 543 0.29414414 5322.870 5181.404 5464.335
#> 544 0.29459459 5327.222 5185.698 5468.746
#> 545 0.29504505 5331.574 5189.990 5473.158
#> 546 0.29549550 5335.926 5194.280 5477.572
#> 547 0.29594595 5340.278 5198.570 5481.987
#> 548 0.29639640 5344.631 5202.858 5486.403
#> 549 0.29684685 5348.983 5207.145 5490.821
#> 550 0.29729730 5353.335 5211.430 5495.240
#> 551 0.29774775 5357.687 5215.714 5499.661
#> 552 0.29819820 5362.040 5219.997 5504.082
#> 553 0.29864865 5366.392 5224.278 5508.505
#> 554 0.29909910 5370.744 5228.558 5512.930
#> 555 0.29954955 5375.096 5232.837 5517.355
#> 556 0.30000000 5379.448 5237.115 5521.782
#> 557 0.30045045 5383.801 5241.391 5526.211
#> 558 0.30090090 5388.153 5245.666 5530.640
#> 559 0.30135135 5392.505 5249.939 5535.071
#> 560 0.30180180 5396.857 5254.211 5539.503
#> 561 0.30225225 5401.210 5258.482 5543.937
#> 562 0.30270270 5405.562 5262.752 5548.372
#> 563 0.30315315 5409.914 5267.020 5552.808
#> 564 0.30360360 5414.266 5271.287 5557.246
#> 565 0.30405405 5418.619 5275.553 5561.684
#> 566 0.30450450 5422.971 5279.817 5566.124
#> 567 0.30495495 5427.323 5284.080 5570.566
#> 568 0.30540541 5431.675 5288.342 5575.009
#> 569 0.30585586 5436.027 5292.602 5579.452
#> 570 0.30630631 5440.380 5296.862 5583.898
#> 571 0.30675676 5444.732 5301.119 5588.344
#> 572 0.30720721 5449.084 5305.376 5592.792
#> 573 0.30765766 5453.436 5309.631 5597.241
#> 574 0.30810811 5457.789 5313.885 5601.692
#> 575 0.30855856 5462.141 5318.138 5606.143
#> 576 0.30900901 5466.493 5322.390 5610.596
#> 577 0.30945946 5470.845 5326.640 5615.050
#> 578 0.30990991 5475.197 5330.889 5619.506
#> 579 0.31036036 5479.550 5335.137 5623.963
#> 580 0.31081081 5483.902 5339.383 5628.421
#> 581 0.31126126 5488.254 5343.628 5632.880
#> 582 0.31171171 5492.606 5347.872 5637.340
#> 583 0.31216216 5496.959 5352.115 5641.802
#> 584 0.31261261 5501.311 5356.356 5646.265
#> 585 0.31306306 5505.663 5360.596 5650.730
#> 586 0.31351351 5510.015 5364.835 5655.195
#> 587 0.31396396 5514.367 5369.073 5659.662
#> 588 0.31441441 5518.720 5373.310 5664.130
#> 589 0.31486486 5523.072 5377.545 5668.599
#> 590 0.31531532 5527.424 5381.779 5673.070
#> 591 0.31576577 5531.776 5386.011 5677.541
#> 592 0.31621622 5536.129 5390.243 5682.014
#> 593 0.31666667 5540.481 5394.473 5686.488
#> 594 0.31711712 5544.833 5398.702 5690.964
#> 595 0.31756757 5549.185 5402.930 5695.440
#> 596 0.31801802 5553.537 5407.157 5699.918
#> 597 0.31846847 5557.890 5411.382 5704.397
#> 598 0.31891892 5562.242 5415.606 5708.877
#> 599 0.31936937 5566.594 5419.829 5713.359
#> 600 0.31981982 5570.946 5424.051 5717.842
#> 601 0.32027027 5575.299 5428.272 5722.325
#> 602 0.32072072 5579.651 5432.491 5726.810
#> 603 0.32117117 5584.003 5436.709 5731.297
#> 604 0.32162162 5588.355 5440.926 5735.784
#> 605 0.32207207 5592.708 5445.142 5740.273
#> 606 0.32252252 5597.060 5449.357 5744.763
#> 607 0.32297297 5601.412 5453.570 5749.254
#> 608 0.32342342 5605.764 5457.783 5753.746
#> 609 0.32387387 5610.116 5461.994 5758.239
#> 610 0.32432432 5614.469 5466.204 5762.734
#> 611 0.32477477 5618.821 5470.412 5767.229
#> 612 0.32522523 5623.173 5474.620 5771.726
#> 613 0.32567568 5627.525 5478.827 5776.224
#> 614 0.32612613 5631.878 5483.032 5780.723
#> 615 0.32657658 5636.230 5487.236 5785.224
#> 616 0.32702703 5640.582 5491.439 5789.725
#> 617 0.32747748 5644.934 5495.641 5794.228
#> 618 0.32792793 5649.286 5499.842 5798.731
#> 619 0.32837838 5653.639 5504.041 5803.236
#> 620 0.32882883 5657.991 5508.240 5807.742
#> 621 0.32927928 5662.343 5512.437 5812.249
#> 622 0.32972973 5666.695 5516.633 5816.758
#> 623 0.33018018 5671.048 5520.828 5821.267
#> 624 0.33063063 5675.400 5525.022 5825.778
#> 625 0.33108108 5679.752 5529.215 5830.289
#> 626 0.33153153 5684.104 5533.406 5834.802
#> 627 0.33198198 5688.456 5537.597 5839.316
#> 628 0.33243243 5692.809 5541.786 5843.831
#> 629 0.33288288 5697.161 5545.975 5848.347
#> 630 0.33333333 5701.513 5550.162 5852.864
#> 631 0.33378378 5705.865 5554.348 5857.382
#> 632 0.33423423 5710.218 5558.533 5861.902
#> 633 0.33468468 5714.570 5562.717 5866.422
#> 634 0.33513514 5718.922 5566.900 5870.944
#> 635 0.33558559 5723.274 5571.082 5875.467
#> 636 0.33603604 5727.626 5575.263 5879.990
#> 637 0.33648649 5731.979 5579.442 5884.515
#> 638 0.33693694 5736.331 5583.621 5889.041
#> 639 0.33738739 5740.683 5587.798 5893.568
#> 640 0.33783784 5745.035 5591.975 5898.096
#> 641 0.33828829 5749.388 5596.150 5902.625
#> 642 0.33873874 5753.740 5600.325 5907.155
#> 643 0.33918919 5758.092 5604.498 5911.686
#> 644 0.33963964 5762.444 5608.670 5916.218
#> 645 0.34009009 5766.797 5612.841 5920.752
#> 646 0.34054054 5771.149 5617.011 5925.286
#> 647 0.34099099 5775.501 5621.181 5929.821
#> 648 0.34144144 5779.853 5625.349 5934.358
#> 649 0.34189189 5784.205 5629.516 5938.895
#> 650 0.34234234 5788.558 5633.682 5943.434
#> 651 0.34279279 5792.910 5637.847 5947.973
#> 652 0.34324324 5797.262 5642.011 5952.514
#> 653 0.34369369 5801.614 5646.174 5957.055
#> 654 0.34414414 5805.967 5650.336 5961.598
#> 655 0.34459459 5810.319 5654.496 5966.141
#> 656 0.34504505 5814.671 5658.656 5970.686
#> 657 0.34549550 5819.023 5662.815 5975.231
#> 658 0.34594595 5823.375 5666.973 5979.778
#> 659 0.34639640 5827.728 5671.130 5984.325
#> 660 0.34684685 5832.080 5675.286 5988.874
#> 661 0.34729730 5836.432 5679.441 5993.423
#> 662 0.34774775 5840.784 5683.595 5997.974
#> 663 0.34819820 5845.137 5687.748 6002.525
#> 664 0.34864865 5849.489 5691.900 6007.078
#> 665 0.34909910 5853.841 5696.051 6011.631
#> 666 0.34954955 5858.193 5700.201 6016.185
#> 667 0.35000000 5862.545 5704.350 6020.741
#> 668 0.35045045 5866.898 5708.498 6025.297
#> 669 0.35090090 5871.250 5712.646 6029.854
#> 670 0.35135135 5875.602 5716.792 6034.412
#> 671 0.35180180 5879.954 5720.937 6038.972
#> 672 0.35225225 5884.307 5725.081 6043.532
#> 673 0.35270270 5888.659 5729.225 6048.093
#> 674 0.35315315 5893.011 5733.367 6052.655
#> 675 0.35360360 5897.363 5737.509 6057.218
#> 676 0.35405405 5901.715 5741.649 6061.782
#> 677 0.35450450 5906.068 5745.789 6066.346
#> 678 0.35495495 5910.420 5749.928 6070.912
#> 679 0.35540541 5914.772 5754.066 6075.479
#> 680 0.35585586 5919.124 5758.203 6080.046
#> 681 0.35630631 5923.477 5762.339 6084.615
#> 682 0.35675676 5927.829 5766.474 6089.184
#> 683 0.35720721 5932.181 5770.608 6093.754
#> 684 0.35765766 5936.533 5774.741 6098.325
#> 685 0.35810811 5940.886 5778.873 6102.898
#> 686 0.35855856 5945.238 5783.005 6107.470
#> 687 0.35900901 5949.590 5787.136 6112.044
#> 688 0.35945946 5953.942 5791.265 6116.619
#> 689 0.35990991 5958.294 5795.394 6121.195
#> 690 0.36036036 5962.647 5799.522 6125.771
#> 691 0.36081081 5966.999 5803.649 6130.349
#> 692 0.36126126 5971.351 5807.775 6134.927
#> 693 0.36171171 5975.703 5811.901 6139.506
#> 694 0.36216216 5980.056 5816.025 6144.086
#> 695 0.36261261 5984.408 5820.149 6148.667
#> 696 0.36306306 5988.760 5824.271 6153.249
#> 697 0.36351351 5993.112 5828.393 6157.831
#> 698 0.36396396 5997.464 5832.514 6162.414
#> 699 0.36441441 6001.817 5836.635 6166.999
#> 700 0.36486486 6006.169 5840.754 6171.584
#> 701 0.36531532 6010.521 5844.872 6176.170
#> 702 0.36576577 6014.873 5848.990 6180.757
#> 703 0.36621622 6019.226 5853.107 6185.344
#> 704 0.36666667 6023.578 5857.223 6189.933
#> 705 0.36711712 6027.930 5861.338 6194.522
#> 706 0.36756757 6032.282 5865.452 6199.112
#> 707 0.36801802 6036.634 5869.566 6203.703
#> 708 0.36846847 6040.987 5873.679 6208.295
#> 709 0.36891892 6045.339 5877.791 6212.887
#> 710 0.36936937 6049.691 5881.902 6217.481
#> 711 0.36981982 6054.043 5886.012 6222.075
#> 712 0.37027027 6058.396 5890.121 6226.670
#> 713 0.37072072 6062.748 5894.230 6231.265
#> 714 0.37117117 6067.100 5898.338 6235.862
#> 715 0.37162162 6071.452 5902.445 6240.459
#> 716 0.37207207 6075.804 5906.551 6245.057
#> 717 0.37252252 6080.157 5910.657 6249.656
#> 718 0.37297297 6084.509 5914.762 6254.256
#> 719 0.37342342 6088.861 5918.866 6258.857
#> 720 0.37387387 6093.213 5922.969 6263.458
#> 721 0.37432432 6097.566 5927.071 6268.060
#> 722 0.37477477 6101.918 5931.173 6272.663
#> 723 0.37522523 6106.270 5935.274 6277.266
#> 724 0.37567568 6110.622 5939.374 6281.870
#> 725 0.37612613 6114.975 5943.473 6286.476
#> 726 0.37657658 6119.327 5947.572 6291.081
#> 727 0.37702703 6123.679 5951.670 6295.688
#> 728 0.37747748 6128.031 5955.767 6300.295
#> 729 0.37792793 6132.383 5959.863 6304.903
#> 730 0.37837838 6136.736 5963.959 6309.512
#> 731 0.37882883 6141.088 5968.054 6314.122
#> 732 0.37927928 6145.440 5972.148 6318.732
#> 733 0.37972973 6149.792 5976.242 6323.343
#> 734 0.38018018 6154.145 5980.334 6327.955
#> 735 0.38063063 6158.497 5984.426 6332.567
#> 736 0.38108108 6162.849 5988.518 6337.180
#> 737 0.38153153 6167.201 5992.608 6341.794
#> 738 0.38198198 6171.553 5996.698 6346.409
#> 739 0.38243243 6175.906 6000.787 6351.024
#> 740 0.38288288 6180.258 6004.876 6355.640
#> 741 0.38333333 6184.610 6008.963 6360.257
#> 742 0.38378378 6188.962 6013.050 6364.874
#> 743 0.38423423 6193.315 6017.137 6369.493
#> 744 0.38468468 6197.667 6021.222 6374.111
#> 745 0.38513514 6202.019 6025.307 6378.731
#> 746 0.38558559 6206.371 6029.391 6383.351
#> 747 0.38603604 6210.723 6033.475 6387.972
#> 748 0.38648649 6215.076 6037.558 6392.594
#> 749 0.38693694 6219.428 6041.640 6397.216
#> 750 0.38738739 6223.780 6045.721 6401.839
#> 751 0.38783784 6228.132 6049.802 6406.462
#> 752 0.38828829 6232.485 6053.882 6411.087
#> 753 0.38873874 6236.837 6057.962 6415.712
#> 754 0.38918919 6241.189 6062.041 6420.337
#> 755 0.38963964 6245.541 6066.119 6424.964
#> 756 0.39009009 6249.893 6070.196 6429.591
#> 757 0.39054054 6254.246 6074.273 6434.218
#> 758 0.39099099 6258.598 6078.349 6438.846
#> 759 0.39144144 6262.950 6082.425 6443.475
#> 760 0.39189189 6267.302 6086.500 6448.105
#> 761 0.39234234 6271.655 6090.574 6452.735
#> 762 0.39279279 6276.007 6094.648 6457.366
#> 763 0.39324324 6280.359 6098.721 6461.997
#> 764 0.39369369 6284.711 6102.793 6466.629
#> 765 0.39414414 6289.063 6106.865 6471.262
#> 766 0.39459459 6293.416 6110.936 6475.895
#> 767 0.39504505 6297.768 6115.006 6480.529
#> 768 0.39549550 6302.120 6119.076 6485.164
#> 769 0.39594595 6306.472 6123.145 6489.799
#> 770 0.39639640 6310.825 6127.214 6494.435
#> 771 0.39684685 6315.177 6131.282 6499.072
#> 772 0.39729730 6319.529 6135.349 6503.709
#> 773 0.39774775 6323.881 6139.416 6508.346
#> 774 0.39819820 6328.234 6143.482 6512.985
#> 775 0.39864865 6332.586 6147.548 6517.624
#> 776 0.39909910 6336.938 6151.613 6522.263
#> 777 0.39954955 6341.290 6155.677 6526.903
#> 778 0.40000000 6345.642 6159.741 6531.544
#> 779 0.40045045 6349.995 6163.804 6536.185
#> 780 0.40090090 6354.347 6167.867 6540.827
#> 781 0.40135135 6358.699 6171.929 6545.469
#> 782 0.40180180 6363.051 6175.990 6550.112
#> 783 0.40225225 6367.404 6180.051 6554.756
#> 784 0.40270270 6371.756 6184.111 6559.400
#> 785 0.40315315 6376.108 6188.171 6564.045
#> 786 0.40360360 6380.460 6192.230 6568.690
#> 787 0.40405405 6384.812 6196.289 6573.336
#> 788 0.40450450 6389.165 6200.347 6577.983
#> 789 0.40495495 6393.517 6204.404 6582.630
#> 790 0.40540541 6397.869 6208.461 6587.277
#> 791 0.40585586 6402.221 6212.517 6591.926
#> 792 0.40630631 6406.574 6216.573 6596.574
#> 793 0.40675676 6410.926 6220.628 6601.224
#> 794 0.40720721 6415.278 6224.683 6605.873
#> 795 0.40765766 6419.630 6228.737 6610.524
#> 796 0.40810811 6423.982 6232.790 6615.175
#> 797 0.40855856 6428.335 6236.843 6619.826
#> 798 0.40900901 6432.687 6240.896 6624.478
#> 799 0.40945946 6437.039 6244.947 6629.131
#> 800 0.40990991 6441.391 6248.999 6633.784
#> 801 0.41036036 6445.744 6253.050 6638.438
#> 802 0.41081081 6450.096 6257.100 6643.092
#> 803 0.41126126 6454.448 6261.150 6647.746
#> 804 0.41171171 6458.800 6265.199 6652.402
#> 805 0.41216216 6463.152 6269.248 6657.057
#> 806 0.41261261 6467.505 6273.296 6661.714
#> 807 0.41306306 6471.857 6277.344 6666.370
#> 808 0.41351351 6476.209 6281.391 6671.028
#> 809 0.41396396 6480.561 6285.437 6675.685
#> 810 0.41441441 6484.914 6289.483 6680.344
#> 811 0.41486486 6489.266 6293.529 6685.003
#> 812 0.41531532 6493.618 6297.574 6689.662
#> 813 0.41576577 6497.970 6301.619 6694.322
#> 814 0.41621622 6502.323 6305.663 6698.982
#> 815 0.41666667 6506.675 6309.706 6703.643
#> 816 0.41711712 6511.027 6313.750 6708.304
#> 817 0.41756757 6515.379 6317.792 6712.966
#> 818 0.41801802 6519.731 6321.834 6717.629
#> 819 0.41846847 6524.084 6325.876 6722.291
#> 820 0.41891892 6528.436 6329.917 6726.955
#> 821 0.41936937 6532.788 6333.958 6731.618
#> 822 0.41981982 6537.140 6337.998 6736.283
#> 823 0.42027027 6541.493 6342.038 6740.947
#> 824 0.42072072 6545.845 6346.077 6745.613
#> 825 0.42117117 6550.197 6350.116 6750.278
#> 826 0.42162162 6554.549 6354.154 6754.945
#> 827 0.42207207 6558.901 6358.192 6759.611
#> 828 0.42252252 6563.254 6362.229 6764.278
#> 829 0.42297297 6567.606 6366.266 6768.946
#> 830 0.42342342 6571.958 6370.302 6773.614
#> 831 0.42387387 6576.310 6374.338 6778.283
#> 832 0.42432432 6580.663 6378.373 6782.952
#> 833 0.42477477 6585.015 6382.408 6787.621
#> 834 0.42522523 6589.367 6386.443 6792.291
#> 835 0.42567568 6593.719 6390.477 6796.961
#> 836 0.42612613 6598.071 6394.511 6801.632
#> 837 0.42657658 6602.424 6398.544 6806.303
#> 838 0.42702703 6606.776 6402.577 6810.975
#> 839 0.42747748 6611.128 6406.609 6815.647
#> 840 0.42792793 6615.480 6410.641 6820.320
#> 841 0.42837838 6619.833 6414.672 6824.993
#> 842 0.42882883 6624.185 6418.703 6829.667
#> 843 0.42927928 6628.537 6422.734 6834.340
#> 844 0.42972973 6632.889 6426.764 6839.015
#> 845 0.43018018 6637.241 6430.793 6843.690
#> 846 0.43063063 6641.594 6434.823 6848.365
#> 847 0.43108108 6645.946 6438.851 6853.041
#> 848 0.43153153 6650.298 6442.880 6857.717
#> 849 0.43198198 6654.650 6446.908 6862.393
#> 850 0.43243243 6659.003 6450.935 6867.070
#> 851 0.43288288 6663.355 6454.962 6871.748
#> 852 0.43333333 6667.707 6458.989 6876.425
#> 853 0.43378378 6672.059 6463.015 6881.103
#> 854 0.43423423 6676.412 6467.041 6885.782
#> 855 0.43468468 6680.764 6471.066 6890.461
#> 856 0.43513514 6685.116 6475.091 6895.141
#> 857 0.43558559 6689.468 6479.116 6899.820
#> 858 0.43603604 6693.820 6483.140 6904.501
#> 859 0.43648649 6698.173 6487.164 6909.181
#> 860 0.43693694 6702.525 6491.187 6913.863
#> 861 0.43738739 6706.877 6495.210 6918.544
#> 862 0.43783784 6711.229 6499.233 6923.226
#> 863 0.43828829 6715.582 6503.255 6927.908
#> 864 0.43873874 6719.934 6507.277 6932.591
#> 865 0.43918919 6724.286 6511.298 6937.274
#> 866 0.43963964 6728.638 6515.319 6941.957
#> 867 0.44009009 6732.990 6519.340 6946.641
#> 868 0.44054054 6737.343 6523.360 6951.326
#> 869 0.44099099 6741.695 6527.380 6956.010
#> 870 0.44144144 6746.047 6531.399 6960.695
#> 871 0.44189189 6750.399 6535.418 6965.381
#> 872 0.44234234 6754.752 6539.437 6970.066
#> 873 0.44279279 6759.104 6543.455 6974.753
#> 874 0.44324324 6763.456 6547.473 6979.439
#> 875 0.44369369 6767.808 6551.490 6984.126
#> 876 0.44414414 6772.160 6555.508 6988.813
#> 877 0.44459459 6776.513 6559.524 6993.501
#> 878 0.44504505 6780.865 6563.541 6998.189
#> 879 0.44549550 6785.217 6567.557 7002.878
#> 880 0.44594595 6789.569 6571.572 7007.566
#> 881 0.44639640 6793.922 6575.588 7012.255
#> 882 0.44684685 6798.274 6579.603 7016.945
#> 883 0.44729730 6802.626 6583.617 7021.635
#> 884 0.44774775 6806.978 6587.631 7026.325
#> 885 0.44819820 6811.330 6591.645 7031.016
#> 886 0.44864865 6815.683 6595.659 7035.707
#> 887 0.44909910 6820.035 6599.672 7040.398
#> 888 0.44954955 6824.387 6603.685 7045.090
#> 889 0.45000000 6828.739 6607.697 7049.782
#> 890 0.45045045 6833.092 6611.709 7054.474
#> 891 0.45090090 6837.444 6615.721 7059.167
#> 892 0.45135135 6841.796 6619.732 7063.860
#> 893 0.45180180 6846.148 6623.743 7068.553
#> 894 0.45225225 6850.501 6627.754 7073.247
#> 895 0.45270270 6854.853 6631.764 7077.941
#> 896 0.45315315 6859.205 6635.774 7082.636
#> 897 0.45360360 6863.557 6639.784 7087.331
#> 898 0.45405405 6867.909 6643.793 7092.026
#> 899 0.45450450 6872.262 6647.802 7096.721
#> 900 0.45495495 6876.614 6651.811 7101.417
#> 901 0.45540541 6880.966 6655.819 7106.113
#> 902 0.45585586 6885.318 6659.827 7110.810
#> 903 0.45630631 6889.671 6663.834 7115.507
#> 904 0.45675676 6894.023 6667.842 7120.204
#> 905 0.45720721 6898.375 6671.849 7124.901
#> 906 0.45765766 6902.727 6675.855 7129.599
#> 907 0.45810811 6907.079 6679.862 7134.297
#> 908 0.45855856 6911.432 6683.868 7138.996
#> 909 0.45900901 6915.784 6687.873 7143.694
#> 910 0.45945946 6920.136 6691.879 7148.394
#> 911 0.45990991 6924.488 6695.884 7153.093
#> 912 0.46036036 6928.841 6699.888 7157.793
#> 913 0.46081081 6933.193 6703.893 7162.493
#> 914 0.46126126 6937.545 6707.897 7167.193
#> 915 0.46171171 6941.897 6711.901 7171.894
#> 916 0.46216216 6946.249 6715.904 7176.595
#> 917 0.46261261 6950.602 6719.907 7181.296
#> 918 0.46306306 6954.954 6723.910 7185.998
#> 919 0.46351351 6959.306 6727.913 7190.700
#> 920 0.46396396 6963.658 6731.915 7195.402
#> 921 0.46441441 6968.011 6735.917 7200.104
#> 922 0.46486486 6972.363 6739.918 7204.807
#> 923 0.46531532 6976.715 6743.920 7209.510
#> 924 0.46576577 6981.067 6747.921 7214.214
#> 925 0.46621622 6985.419 6751.921 7218.918
#> 926 0.46666667 6989.772 6755.922 7223.622
#> 927 0.46711712 6994.124 6759.922 7228.326
#> 928 0.46756757 6998.476 6763.922 7233.031
#> 929 0.46801802 7002.828 6767.921 7237.736
#> 930 0.46846847 7007.181 6771.920 7242.441
#> 931 0.46891892 7011.533 6775.919 7247.146
#> 932 0.46936937 7015.885 6779.918 7251.852
#> 933 0.46981982 7020.237 6783.916 7256.558
#> 934 0.47027027 7024.590 6787.914 7261.265
#> 935 0.47072072 7028.942 6791.912 7265.971
#> 936 0.47117117 7033.294 6795.910 7270.678
#> 937 0.47162162 7037.646 6799.907 7275.386
#> 938 0.47207207 7041.998 6803.904 7280.093
#> 939 0.47252252 7046.351 6807.900 7284.801
#> 940 0.47297297 7050.703 6811.897 7289.509
#> 941 0.47342342 7055.055 6815.893 7294.217
#> 942 0.47387387 7059.407 6819.888 7298.926
#> 943 0.47432432 7063.760 6823.884 7303.635
#> 944 0.47477477 7068.112 6827.879 7308.344
#> 945 0.47522523 7072.464 6831.874 7313.054
#> 946 0.47567568 7076.816 6835.869 7317.764
#> 947 0.47612613 7081.168 6839.863 7322.474
#> 948 0.47657658 7085.521 6843.857 7327.184
#> 949 0.47702703 7089.873 6847.851 7331.894
#> 950 0.47747748 7094.225 6851.845 7336.605
#> 951 0.47792793 7098.577 6855.838 7341.316
#> 952 0.47837838 7102.930 6859.831 7346.028
#> 953 0.47882883 7107.282 6863.824 7350.739
#> 954 0.47927928 7111.634 6867.817 7355.451
#> 955 0.47972973 7115.986 6871.809 7360.163
#> 956 0.48018018 7120.338 6875.801 7364.876
#> 957 0.48063063 7124.691 6879.793 7369.589
#> 958 0.48108108 7129.043 6883.784 7374.301
#> 959 0.48153153 7133.395 6887.776 7379.015
#> 960 0.48198198 7137.747 6891.767 7383.728
#> 961 0.48243243 7142.100 6895.757 7388.442
#> 962 0.48288288 7146.452 6899.748 7393.156
#> 963 0.48333333 7150.804 6903.738 7397.870
#> 964 0.48378378 7155.156 6907.728 7402.584
#> 965 0.48423423 7159.508 6911.718 7407.299
#> 966 0.48468468 7163.861 6915.707 7412.014
#> 967 0.48513514 7168.213 6919.697 7416.729
#> 968 0.48558559 7172.565 6923.686 7421.445
#> 969 0.48603604 7176.917 6927.674 7426.161
#> 970 0.48648649 7181.270 6931.663 7430.876
#> 971 0.48693694 7185.622 6935.651 7435.593
#> 972 0.48738739 7189.974 6939.639 7440.309
#> 973 0.48783784 7194.326 6943.627 7445.026
#> 974 0.48828829 7198.679 6947.614 7449.743
#> 975 0.48873874 7203.031 6951.602 7454.460
#> 976 0.48918919 7207.383 6955.589 7459.177
#> 977 0.48963964 7211.735 6959.575 7463.895
#> 978 0.49009009 7216.087 6963.562 7468.613
#> 979 0.49054054 7220.440 6967.548 7473.331
#> 980 0.49099099 7224.792 6971.534 7478.049
#> 981 0.49144144 7229.144 6975.520 7482.768
#> 982 0.49189189 7233.496 6979.506 7487.487
#> 983 0.49234234 7237.849 6983.491 7492.206
#> 984 0.49279279 7242.201 6987.476 7496.925
#> 985 0.49324324 7246.553 6991.461 7501.645
#> 986 0.49369369 7250.905 6995.446 7506.364
#> 987 0.49414414 7255.257 6999.431 7511.084
#> 988 0.49459459 7259.610 7003.415 7515.805
#> 989 0.49504505 7263.962 7007.399 7520.525
#> 990 0.49549550 7268.314 7011.383 7525.246
#> 991 0.49594595 7272.666 7015.366 7529.967
#> 992 0.49639640 7277.019 7019.349 7534.688
#> 993 0.49684685 7281.371 7023.333 7539.409
#> 994 0.49729730 7285.723 7027.316 7544.131
#> 995 0.49774775 7290.075 7031.298 7548.852
#> 996 0.49819820 7294.427 7035.281 7553.574
#> 997 0.49864865 7298.780 7039.263 7558.296
#> 998 0.49909910 7303.132 7043.245 7563.019
#> 999 0.49954955 7307.484 7047.227 7567.742
#> 1000 0.50000000 7311.836 7051.208 7572.464
inv_predict(din, 5000)
#> [1] 0.2607275