Important Dates/Information

Due date: Friday, March 30, 2018 11:59PM . No late submission allowed! Please submit to blackboard.

Update to submission guidelines: Submit both RMD and PDF files. R script files are not necessary, nor will they be accepted. Please submit all files in such format: _lab#_mmdd.extension ********

Learning Goals

  1. Use and inteprete a MARS model via mda
  2. Use and inerprete a BART model via bartMachine

Introduction

Multivariate Adaptive Regression Splines (MARS) models are yet another way to build predictive models. Put simply, MARS is a non-parametric regression technique which builds linear models which allows for ‘piecewise-continuous linear’ models to represent non-linearities in the data. The term MARS is trademarked so sometimes these are called “Earth” models.

MARS Overview

A MARS model introduces hinge functions which allow us to have piecewise linear representations of our data. That is, we can have a ‘kink’ in the line of best fit. These inflection points are called knots.

PUT IN MARS PLOT

These hinge functions are extremely flexible! As you can imagine we could use a sufficiently large number of hinges to represent every small intracacy of our data. And in the process of building it, that’s exactly what we do. A MARS fitting routine will search over all potential combinations of existing terms in the model (starting with the intercept), all variables, and all knot locations to each variable. This is called the forward pass. It’s usually done via a brute force method, so as you can imagine the first result is likely overfit to our data. As such, most MARS packages will also implement a backward pass to start to trim out unneded knots. This is similar to variable pruning in which we start with the least influential variable and begin discarding the least ‘important’ variables until we end up with a suitable model.

Lucky for us, there is a lovely R package mda which handles most of this for us. An example follows:

# load the package
library('mda') # note MDA stands for Mixture Disriminant Analysis
## Loading required package: class
## Loaded mda 0.4-10
# read in our old friend College.df
df <-read.csv("College.csv")

head(df)
##                              X Private Apps Accept Enroll Top10perc
## 1 Abilene Christian University     Yes 1660   1232    721        23
## 2           Adelphi University     Yes 2186   1924    512        16
## 3               Adrian College     Yes 1428   1097    336        22
## 4          Agnes Scott College     Yes  417    349    137        60
## 5    Alaska Pacific University     Yes  193    146     55        16
## 6            Albertson College     Yes  587    479    158        38
##   Top25perc F.Undergrad P.Undergrad Outstate Room.Board Books Personal PhD
## 1        52        2885         537     7440       3300   450     2200  70
## 2        29        2683        1227    12280       6450   750     1500  29
## 3        50        1036          99    11250       3750   400     1165  53
## 4        89         510          63    12960       5450   450      875  92
## 5        44         249         869     7560       4120   800     1500  76
## 6        62         678          41    13500       3335   500      675  67
##   Terminal S.F.Ratio perc.alumni Expend Grad.Rate
## 1       78      18.1          12   7041        60
## 2       30      12.2          16  10527        56
## 3       66      12.9          30   8735        54
## 4       97       7.7          37  19016        59
## 5       72      11.9           2  10922        15
## 6       73       9.4          11   9727        55
#divide covariates and response
df.response <-df$Grad.Rate
df.covariate <-df[,c("PhD","Top10perc","S.F.Ratio")]

# now let's build a model predicting species using everything else
model1 <- mars(x=df.response,y=df.covariate,trace.mars=F,prune=F)

# note turning trace.mars to false gives us less output
model1
## $call
## mars(x = df.response, y = df.covariate, prune = F, trace.mars = F)
## 
## $all.terms
## [1]  1  2  3  4  6  8 10
## 
## $selected.terms
## [1]  1  2  3  4  6  8 10
## 
## $penalty
## [1] 2
## 
## $degree
## [1] 1
## 
## $nk
## [1] 21
## 
## $thresh
## [1] 0.001
## 
## $gcv
## [1] 485.3313
## 
## $factor
##       [,1]
##  [1,]    0
##  [2,]    1
##  [3,]   -1
##  [4,]    1
##  [5,]   -1
##  [6,]    1
##  [7,]   -1
##  [8,]    1
##  [9,]   -1
## [10,]    1
## [11,]   -1
## 
## $cuts
##       [,1]
##  [1,]    0
##  [2,]   94
##  [3,]   94
##  [4,]   84
##  [5,]   84
##  [6,]   59
##  [7,]   59
##  [8,]   38
##  [9,]   38
## [10,]   70
## [11,]   70
## 
## $residuals
##                [,1]          [,2]         [,3]
##   [1,]   2.43431735  -0.334435748   3.35884847
##   [2,] -38.10951982  -5.630417000  -2.86713355
##   [3,] -14.36302809   1.105809977  -2.30910055
##   [4,]  25.27074260  37.265242534  -7.15418304
##   [5,]  22.60126347   2.729238700  -1.90057374
##   [6,]  -0.23627395  16.737696489  -5.73811705
##   [7,]  19.92504159  -8.133470594  -2.90205701
##   [8,]  12.73227527   6.821438053   0.20654228
##   [9,]   1.94409964  -2.155696494  -1.91957397
##  [10,] -27.61653637   0.842036955  -3.85106756
##  [11,]   5.73227527   6.821438053  -2.19345772
##  [12,]  -3.60551428  12.974094676  -3.47607897
##  [13,] -16.38032124   7.538990261  -0.15433147
##  [14,]   4.74291533  15.868137995   1.46310052
##  [15,] -31.23627395   1.737696489  -4.03811705
##  [16,]   2.90649008 -19.731540287   0.97613203
##  [17,]  18.88076259  35.938930441  -3.68126094
##  [18,] -18.72925740  -3.734757466  -2.75418304
##  [19,]  -6.37706121  -3.949282113  -4.27696858
##  [20,]  -6.60981471   9.297123692   7.19764390
##  [21,]   0.87644707   6.314490909  -4.33500157
##  [22,]   7.07006483  -9.331218569   4.68916354
##  [23,] -16.74780891  -6.332827159  -1.47599400
##  [24,]  19.87644707   5.314490909   3.26499843
##  [25,]  11.63697191  25.105809977  -2.60910055
##  [26,] -11.12355293  -6.685509091   3.96499843
##  [27,]  11.07334857 -18.505521046   1.73523650
##  [28,]   9.90649008  -3.731540287   2.97613203
##  [29,]  -1.85601154 -10.366643977  -2.12516654
##  [30,]   1.95746831   6.386333638  -0.87171021
##  [31,]  -9.09350992  -7.731540287  -3.32386797
##  [32,]   4.95746831  12.386333638  -0.57171021
##  [33,]  -9.12355293  -2.685509091   6.76499843
##  [34,] -13.74780891  -5.332827159  -3.17599400
##  [35,] -10.61137768  -5.340496010   4.78650739
##  [36,] -19.04253169 -14.613666362  -3.87171021
##  [37,]  21.05669616  18.126751298  -2.85870022
##  [38,]  -2.24192519   5.329453917  -1.01603439
##  [39,]  -0.15512821 -11.896114154  -0.93258396
##  [40,]  -5.15512821   4.103885846   4.96741604
##  [41,]   1.73227527  -7.178561947  -1.29345772
##  [42,]  -3.50628643   5.714512336   0.03693102
##  [43,]  10.38346363  -3.157963045  -2.15106756
##  [44,]  -6.99679879   8.946377421  -4.46401807
##  [45,]  11.90649008  -2.731540287  -2.62386797
##  [46,] -11.37706121  -5.949282113   3.82303142
##  [47,]  -2.85601154  -8.366643977  -0.82516654
##  [48,] -32.23627395   3.737696489  -5.03811705
##  [49,]   9.71890661 -12.720592079   4.35867852
##  [50,]   9.92504159  11.866529406   1.89794299
##  [51,]  -6.12355293  -2.685509091  -4.03500157
##  [52,]  -6.10951982  -2.630417000  -6.26713355
##  [53,]  -4.30513461  -3.778250782  -4.31297622
##  [54,] -18.85601154 -10.366643977  -1.12516654
##  [55,]  -2.15512821  37.103885846   0.46741604
##  [56,]   8.25670949   5.210150443  -1.12205106
##  [57,] -10.49291776 -15.743457532   4.58479478
##  [58,]  -6.48978223  -5.526076534   2.51991594
##  [59,]   9.14398846  -2.366643977  -1.62516654
##  [60,]   3.84487179  15.103885846  -1.63258396
##  [61,]   9.25545490  24.422596067   0.12804284
##  [62,]   7.57934059 -13.532183723   7.15006902
##  [63,] -11.37706121 -12.949282113  -5.57696858
##  [64,]  -3.61137768  -5.340496010   1.58650739
##  [65,]  12.49371357  14.714512336  -3.26306898
##  [66,]   3.00320121  -7.053622579  -1.86401807
##  [67,]   6.51530375  -3.496884722  -1.53243411
##  [68,] -27.85601154  -6.366643977  -1.82516654
##  [69,]  -9.28109339 -10.720592079   0.05867852
##  [70,]  10.08550519  33.372498166   4.70826402
##  [71,]  17.66178183  36.551679661  -3.72428311
##  [72,]  16.96825732  27.439470608   0.48481287
##  [73,]   7.54789231  -2.780562774   3.38311835
##  [74,] -14.83070732   0.409199091  -4.49782647
##  [75,]  -0.39368991   6.996960128  -2.20219523
##  [76,] -17.04253169 -21.613666362   2.92828979
##  [77,]  19.76372605  -4.262303511  -1.23811705
##  [78,]   4.43431735  -0.334435748  -2.34115153
##  [79,]   5.27074260  24.265242534   4.94581696
##  [80,]  21.59789210 -18.934114030   6.57187997
##  [81,]  -2.16849687  -3.438144287   1.61955228
##  [82,]   6.92504159  -5.133470594   7.39794299
##  [83,]  -5.99679879   5.946377421   2.13598193
##  [84,]  19.08861634  -9.733148876   0.31097449
##  [85,] -13.39368991   0.996960128  -1.00219523
##  [86,] -57.61653637 -10.157963045  -3.25106756
##  [87,]  -4.24192519  27.329453917  -0.91603439
##  [88,]   9.61967876  29.538990261  -4.25433147
##  [89,]  -2.94330384 -12.873248702   4.54129978
##  [90,] -12.42065941  -0.532183723  -0.34993098
##  [91,]   4.76146685  -4.533792312   1.38491148
##  [92,]  21.57934059  43.467816277 -11.04993098
##  [93,]  12.05669616 -22.873248702   1.44129978
##  [94,]   7.76372605  -8.262303511  -1.63811705
##  [95,]  13.50708224  -6.743457532  -4.11520522
##  [96,]  -8.80535282 -17.737564878  -2.32312793
##  [97,] -18.38032124  -5.461009739  -1.75433147
##  [98,] -20.91138366  -0.733148876   1.01097449
##  [99,] -18.65661567  -1.949131567  -5.29615486
## [100,]  13.41576584   8.067494559  -2.76296249
## [101,] -60.25030707 -17.317395602  -8.90598507
## [102,]   2.57934059   3.467816277  -0.44993098
## [103,]   1.00320121 -13.053622579   1.13598193
## [104,]   1.12995535  -9.421736068   4.20696544
## [105,]  -0.74329051 -11.789849557   2.67794894
## [106,]  -4.85601154 -14.366643977   0.27483346
## [107,]  18.61967876  24.538990261  -2.05433147
## [108,]   3.74969293   4.682604398  -2.90598507
## [109,]  27.38346363   7.842036955  -6.05106756
## [110,]  -5.26772473  -5.178561947  -5.19345772
## [111,]  25.14398846  10.633356023  -5.62516654
## [112,]  10.92504159  -9.133470594  -3.30205701
## [113,]  11.87644707 -15.685509091   5.56499843
## [114,]  11.42934404   7.276991856   2.43570552
## [115,]  18.17843982  31.549487299  -2.71433987
## [116,]  17.05669616  -1.873248702  -2.75870022
## [117,]  -9.38032124 -16.461009739  -2.45433147
## [118,]  18.28188920   3.691646883   2.46304728
## [119,]   5.73227527   6.821438053   4.50654228
## [120,]  -1.37706121  -2.949282113   2.32303142
## [121,]  -0.42065941   1.467816277  -1.24993098
## [122,] -12.49291776 -15.743457532  -1.31520522
## [123,]  -2.24192519  10.329453917  -1.11603439
## [124,]   7.54789231  -5.780562774  -0.31688165
## [125,] -27.74454510 -22.577403933   1.82804284
## [126,]   5.25670949   2.210150443   1.77794894
## [127,] -28.11923741 -33.061069559  -0.98126094
## [128,]  -2.39368991 -10.003039872  -1.20219523
## [129,]   8.24267637  -5.844941648  -5.58991908
## [130,] -12.49291776   4.256542468  -1.91520522
## [131,]  -6.15512821  -0.896114154  -0.43258396
## [132,] -13.71811080  -8.308353117  -1.83695272
## [133,]  -8.83070732   2.409199091  -1.89782647
## [134,]  -4.91138366  -2.733148876   0.01097449
## [135,] -37.05590036 -16.155696494   0.78042603
## [136,] -23.60551428 -19.025905324  -3.87607897
## [137,] -22.15512821  -0.896114154  -1.93258396
## [138,]   5.84912798  17.293512474   0.48036878
## [139,]   1.54789231  16.219437226   1.28311835
## [140,]   8.90649008   0.268459713  -2.62386797
## [141,]   7.49371357  22.714512336  -1.76306898
## [142,]  20.27074260   6.265242534   4.34581696
## [143,]  18.30422558  -4.928999730  -0.93421647
## [144,] -15.60551428 -10.025905324   1.32392103
## [145,]  20.47443567  29.809846847  -5.92893500
## [146,]   0.49618465  -4.581168625  -3.04795208
## [147,]  -1.88407777  -0.476828159  -3.96090259
## [148,] -12.23627395   8.737696489  -2.03811705
## [149,] -20.49291776  -8.743457532  -1.31520522
## [150,]   0.75807481  -5.670546083  -0.61603439
## [151,] -13.49291776   4.256542468  -3.21520522
## [152,]   0.08861634   7.266851124  -2.08902551
## [153,]   6.38862232  -5.340496010  -6.31349261
## [154,] -16.74329051   4.210150443  -1.32205106
## [155,] -28.07495841   0.866529406  -1.40205701
## [156,]  -0.37706121   0.050717887  -1.17696858
## [157,] -21.36302809 -10.894190023  -2.60910055
## [158,] -15.15512821 -17.896114154   8.66741604
## [159,]  16.06810875  37.680763254  -6.87660905
## [160,]   6.44280106  23.164428881   1.43269472
## [161,]  -9.10951982 -11.630417000  -2.26713355
## [162,] -17.85601154  -7.366643977   2.17483346
## [163,]  10.83150313  -0.438144287  -1.58044772
## [164,]   0.71890661  17.279407921  -2.04132148
## [165,]   6.17843982  -8.450512701  -1.11433987
## [166,] -18.37706121  -7.949282113   0.72303142
## [167,] -16.40210790  17.065885970  -0.52812003
## [168,]  -0.56568265  -3.334435748   0.35884847
## [169,] -24.36302809 -16.894190023  -2.50910055
## [170,] -19.82156018 -14.450512701   0.18566013
## [171,]   8.11592223  -7.476828159  -3.66090259
## [172,]  11.28188920   2.691646883   1.66304728
## [173,]  15.60631009  22.996960128  -2.90219523
## [174,]   8.57934059   5.467816277  -0.74993098
## [175,]  13.66178183  39.551679661  -6.32428311
## [176,]  13.16929268   3.409199091  -2.69782647
## [177,]   7.14398846  -8.366643977  -1.72516654
## [178,]   4.11592223  -1.476828159  -2.06090259
## [179,]  -7.39109433  -5.004374204  -0.64483660
## [180,]  -7.36302809  -4.894190023  -1.60910055
## [181,]   3.12995535  -5.421736068   1.40696544
## [182,] -14.60551428 -19.025905324   2.82392103
## [183,] -31.28109339 -13.720592079  -1.74132148
## [184,] -17.92993517 -12.331218569   3.68916354
## [185,]  15.27074260  10.265242534  -2.05418304
## [186,] -12.16849687   3.561855713  -0.38044772
## [187,]   6.08861634   1.266851124   7.21097449
## [188,]  -8.71646893 -14.395504355  -1.26391624
## [189,]  -0.07495841 -14.133470594   4.49794299
## [190,] -31.63056949  -3.213055136   0.58106442
## [191,]   1.71890661  -2.720592079   0.75867852
## [192,]  13.25545490  24.422596067  -6.07195716
## [193,]   4.12995535  23.578263932   3.80696544
## [194,]   2.57934059  19.467816277  -0.44993098
## [195,]  -5.48978223  15.473923466  -4.68008406
## [196,]   0.74291533 -14.131862005   4.26310052
## [197,]  -2.55719894 -23.835571119   4.53269472
## [198,]  15.34338433 -12.949131567   0.30384514
## [199,]  -5.26597586  -1.798382618  -2.07491461
## [200,] -23.09350992 -10.731540287   4.37613203
## [201,]  23.01723432  17.001469511  -4.39615005
## [202,]   8.41576584  15.067494559  -0.16296249
## [203,]  -9.25708467  -8.131862005   3.56310052
## [204,]  13.14398846  27.633356023   8.17483346
## [205,] -24.23853315  -8.533792312   6.98491148
## [206,]   8.94409964  -2.155696494   1.18042603
## [207,]  20.62293879  -1.949282113   3.32303142
## [208,]   7.24267637  -3.844941648   3.11008092
## [209,] -20.39368991 -11.003039872   1.79780477
## [210,] -13.56568265   5.665564252  -2.24115153
## [211,] -17.74329051 -16.789849557   2.17794894
## [212,]  -1.23853315  -4.533792312   1.58491148
## [213,]  -8.36302809  30.105809977  -4.70910055
## [214,]  14.71890661  23.279407921   0.35867852
## [215,] -24.74780891  -2.332827159  -0.87599400
## [216,]   1.86678481   3.673996063  -0.14925548
## [217,]  -9.38032124 -11.461009739   6.64566853
## [218,] -14.61653637   6.842036955  -1.85106756
## [219,]  24.62293879  -0.949282113   3.52303142
## [220,]  15.84487179   8.103885846  -5.93258396
## [221,]   5.76372605   8.737696489  -1.83811705
## [222,]   4.84912798  18.293512474  -3.61963122
## [223,]  16.07006483  59.668781431   5.68916354
## [224,]  20.39018529  -5.702876308   3.09764390
## [225,] -20.60551428 -19.025905324  -1.17607897
## [226,]  16.60631009   8.996960128  -1.00219523
## [227,] -43.00045452  -4.853625256  11.47640365
## [228,]   2.90649008   2.268459713   0.97613203
## [229,]   0.41576584  -1.932505441   0.13703751
## [230,] -25.15512821  -3.896114154  -3.63258396
## [231,]   1.28188920   8.691646883  -4.13695272
## [232,] -17.91138366  -7.733148876   1.01097449
## [233,] -17.25030707  -4.317395602   7.89401493
## [234,]  -2.98276568  -1.998530489   5.60384995
## [235,]   0.39448572 -24.025905324   0.62392103
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## [239,]  -9.11923741   9.938930441   6.31873906
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## [268,]   7.38346363   7.842036955   0.24893244
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## [270,]   9.63697191 -10.894190023   5.79089945
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## [276,] -17.60981471   5.297123692  23.89764390
## [277,]  -6.58423416 -13.932505441   1.93703751
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## [280,]  -1.93189125 -17.319236746   6.32339095
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## [287,] -33.10951982 -11.630417000  -4.46713355
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## [291,]   4.59789210 -18.934114030   1.47187997
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## [295,] -14.82156018 -19.450512701   3.28566013
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## [304,] -13.04725548  -4.099880515   3.38260489
## [305,]  -6.56568265  -8.334435748   1.35884847
## [306,]  -0.74329051 -10.789849557   1.57794894
## [307,]  -0.71811080  18.691646883  -3.23695272
## [308,]   0.44280106 -32.835571119   2.73269472
## [309,]   5.38862232  -7.340496010  -0.51349261
## [310,]  10.75807481  -7.670546083   1.18396561
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## [312,]   4.14398846 -10.366643977  12.87483346
## [313,]  -9.10951982   7.369583000   5.73286645
## [314,]  21.90649008   6.268459713  -1.42386797
## [315,] -32.40210790 -11.934114030  -0.32812003
## [316,]  -0.48978223   0.473923466  -0.68008406
## [317,]   2.49618465  -2.581168625  -3.24795208
## [318,]  -9.11923741 -41.061069559  12.01873906
## [319,]  11.83150313  15.561855713   4.61955228
## [320,] -33.34701644 -27.725554428  -0.66645802
## [321,] -23.07495841  -8.133470594   1.69794299
## [322,]   4.76146685 -12.533792312   3.88491148
## [323,] -14.92993517  -9.331218569   0.58916354
## [324,]  -2.72925740  10.265242534  -4.35418304
## [325,]  14.30422558  14.071000270  -0.33421647
## [326,]  -2.50381535   4.418831375   4.15204792
## [327,]   8.94409964  -7.155696494   1.48042603
## [328,]   6.49371357   8.714512336   1.13693102
## [329,]   9.51021777   3.473923466  -3.58008406
## [330,]  22.25219109  -1.332827159  -7.97599400
## [331,]  -3.71811080   6.691646883   0.46304728
## [332,]  -1.15512821 -13.896114154   0.46741604
## [333,] -13.92993517 -26.331218569  -1.21083646
## [334,] -19.74329051 -13.789849557  -2.82205106
## [335,]   8.28188920  24.691646883  -1.43695272
## [336,] -17.72925740 -10.734757466  -4.05418304
## [337,] -25.23627395  -0.262303511   2.46188295
## [338,]  -7.91138366  -2.733148876  -2.48902551
## [339,]  15.05669616 -11.873248702   0.34129978
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## [341,] -17.25708467 -19.131862005   5.16310052
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## [343,]  -3.74454510 -24.577403933   2.12804284
## [344,]  -1.09350992 -16.731540287   3.87613203
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## [347,] -18.13683394 -19.615537737  -4.76561076
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## [353,] -16.40210790   2.065885970  -1.52812003
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## [357,]   2.38346363  -4.157963045   2.34893244
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## [360,]   7.75807481 -10.670546083  -2.11603439
## [361,] -31.83070732 -16.590800909   3.40217353
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## [363,]  -4.05590036 -14.155696494   3.58042603
## [364,] -18.72925740 -16.734757466  13.94581696
## [365,] -15.03174268 -13.560529392   2.28481287
## [366,]   2.38862232  -0.340496010   4.78650739
## [367,]  16.95746831  -6.613666362   0.42828979
## [368,]  10.25219109  15.667172841   2.82400600
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## [370,]  -4.04253169  -7.613666362   3.22828979
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## [374,] -38.42065941   8.467816277   2.75006902
## [375,]   8.59789210  12.065885970   1.87187997
## [376,]   9.51021777  -2.526076534   0.61991594
## [377,] -21.07495841  -6.133470594   1.39794299
## [378,] -22.11923741 -34.061069559   8.21873906
## [379,] -26.74257538  -9.175254989   2.27198477
## [380,]  23.89048018   6.369583000  -3.46713355
## [381,]   2.63697191  -6.894190023  -1.00910055
## [382,]  -5.38032124  14.538990261   2.94566853
## [383,]   6.30422558   0.071000270   1.36578353
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## [385,] -11.39873653  -3.270761300  -2.70057374
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## [390,] -14.56568265 -21.334435748   3.85884847
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## [405,]   8.59789210  12.065885970  -1.02812003
## [406,]  15.84487179  -2.896114154  -0.03258396
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## [412,]   3.36943051  -5.213055136   0.78106442
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## [414,]   9.38346363 -13.157963045  -2.65106756
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## [417,]  -0.38032124 -11.461009739  -0.35433147
## [418,]  -7.60551428   4.974094676   2.32392103
## [419,]   4.62293879  -1.949282113  -2.87696858
## [420,]   8.98916809   6.891285330   5.56811391
## [421,]   5.89048018  -9.630417000   2.23286645
## [422,]  -5.36302809 -12.894190023   6.49089945
## [423,]  -7.85601154   6.633356023  -0.12516654
## [424,]  -6.25708467  -6.131862005   1.06310052
## [425,]   9.65298356  35.274445572  -4.26645802
## [426,]   0.92504159 -17.133470594  -1.30205701
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## [428,]  20.51021777  -4.526076534   4.41991594
## [429,]  -0.39368991  16.996960128  -3.00219523
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## [432,]  -4.39368991   1.996960128   1.39780477
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## [435,]  -4.87004465  15.578263932  -0.39303456
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## [445,]   8.87644707  -4.685509091  -0.63500157
## [446,]   6.92504159  22.866529406   3.69794299
## [447,]  22.41576584  59.067494559  -2.46296249
## [448,] -20.63056949  -7.213055136   4.18106442
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## [450,] -26.25708467  -9.131862005  -0.93689948
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## [453,] -20.40210790   4.065885970  -1.22812003
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## [455,]   3.63697191  -0.894190023   0.89089945
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## [457,]  20.76146685  33.466207688  -4.11508852
## [458,] -12.30513461  -4.778250782   3.38702378
## [459,]   1.38862232  -1.340496010   0.58650739
## [460,]  14.47443567  41.809846847  -3.42893500
## [461,] -17.74454510 -31.577403933   7.32804284
## [462,]  12.57934059   1.467816277   4.25006902
## [463,]   6.14398846   9.633356023  -0.92516654
## [464,]  -8.05590036 -10.155696494   3.08042603
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## [466,]   3.76146685  -9.533792312   5.08491148
## [467,]   5.74969293 -12.317395602   2.09401493
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## [469,]  13.74291533   6.868137995  -4.63689948
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## [471,]   3.49371357 -15.285487664  -2.76306898
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## [475,]  16.08861634   2.266851124  -4.88902551
## [476,] -18.16849687 -26.438144287  -0.98044772
## [477,]   8.84487179  -2.896114154  -0.53258396
## [478,] -16.94330384  -9.873248702  -2.55870022
## [479,] -18.25708467 -17.131862005  -2.53689948
## [480,] -24.40210790 -13.934114030   1.77187997
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## [482,]   1.83150313  -4.438144287  -0.28044772
## [483,]   8.25670949   1.210150443   6.67794894
## [484,]  13.28188920   4.691646883   6.16304728
## [485,]  23.01723432   5.001469511   3.60384995
## [486,]  23.14398846   3.633356023   2.47483346
## [487,]  -6.28109339 -13.720592079   1.65867852
## [488,] -19.92993517 -17.331218569   0.48916354
## [489,] -11.33821817 -35.448320339   3.17571689
## [490,]   3.14398846 -12.366643977   3.97483346
## [491,] -25.12355293  -5.685509091  -3.13500157
## [492,] -11.09350992  -7.731540287   5.57613203
## [493,]   0.07006483 -11.331218569  -1.61083646
## [494,] -18.42065941  -3.532183723   0.85006902
## [495,] -25.61137768 -23.340496010  14.38650739
## [496,]   6.60631009   5.996960128   4.29780477
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## [498,]  10.57934059  16.467816277  -9.34993098
## [499,]  -4.93189125 -23.319236746  -1.67660905
## [500,]  -8.83070732 -17.590800909   5.50217353
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## [502,]   1.49371357 -17.285487664   1.43693102
## [503,]   4.60631009   4.996960128  -3.10219523
## [504,]  10.51021777   2.473923466  -3.18008406
## [505,] -19.92665143 -22.505521046   0.23523650
## [506,]  19.76372605  -6.262303511  -1.43811705
## [507,] -32.93189125 -26.319236746   1.42339095
## [508,]   0.43431735   4.665564252  -3.54115153
## [509,]   5.89048018  -1.630417000   2.83286645
## [510,]   5.59789210  10.065885970   0.07187997
## [511,]  17.98916809   3.891285330   3.36811391
## [512,]  13.88076259  -7.061069559   1.81873906
## [513,]  11.60631009  23.996960128  -7.00219523
## [514,] -53.23627395  -1.262303511   0.96188295
## [515,] -16.61653637  -1.157963045  -3.55106756
## [516,]  18.73227527  29.821438053  -5.29345772
## [517,]  10.41576584  15.067494559   2.73703751
## [518,]   1.96825732 -15.560529392   0.38481287
## [519,]  10.08861634  -9.733148876   0.11097449
## [520,]  -5.04253169  -5.613666362  -2.37171021
## [521,]   3.84487179 -15.896114154   5.26741604
## [522,]  -4.85601154   0.633356023  -1.72516654
## [523,]  -3.11923741 -23.061069559   2.01873906
## [524,] -39.25030707  -8.317395602  -8.50598507
## [525,]  -2.94330384  -8.873248702  -4.35870022
## [526,]  -9.92993517  -2.331218569   2.18916354
## [527,]   4.87644707  -5.685509091  -0.83500157
## [528,]   9.83150313  -7.438144287  -0.48044772
## [529,]   0.86316606   5.384462263  -1.26561076
## [530,] -11.42065941 -14.532183723   1.05006902
## [531,]   6.49618465   0.418831375   1.25204792
## [532,] -12.48978223  -0.526076534   4.31991594
## [533,]  -5.75732363   1.155058352   2.61008092
## [534,]   7.24267637  -3.844941648   0.51008092
## [535,]  -2.15512821  11.103885846  -0.03258396
## [536,] -24.04253169 -17.613666362   2.32828979
## [537,]   2.89048018  -6.630417000   4.83286645
## [538,]  -9.74329051  -6.789849557   1.07794894
## [539,] -24.00045452  -3.853625256  -3.12359635
## [540,] -11.61653637   7.842036955  -3.55106756
## [541,]   9.57934059  16.467816277  -2.64993098
## [542,] -33.03174268 -33.560529392  -1.21518713
## [543,]   1.25219109  20.667172841  -1.67599400
## [544,] -19.99679879  -4.053622579  -0.16401807
## [545,]  14.16929268 -18.590800909   4.40217353
## [546,]  -7.91138366   5.266851124  -7.08902551
## [547,]  13.41576584  -7.932505441   0.43703751
## [548,]  11.38862232  -4.340496010  -1.31349261
## [549,] -26.13758605 -10.740601182  -1.70286959
## [550,]  11.16929268   4.409199091   2.80217353
## [551,]  13.92504159  16.866529406  -2.80205701
## [552,]   5.84487179   3.103885846   2.66741604
## [553,]  -7.92665143 -11.505521046   3.03523650
## [554,] -23.50381535  -9.581168625  -1.84795208
## [555,]  -4.42065941 -17.532183723   2.15006902
## [556,] -20.72925740  -5.734757466  -3.95418304
## [557,]   8.73227527   6.821438053  -0.99345772
## [558,]  12.05669616  19.126751298   5.74129978
## [559,]   7.08861634  -2.733148876   5.21097449
## [560,]  -2.33821817 -25.448320339   1.67571689
## [561,]  16.61967876 -14.461009739   3.94566853
## [562,]   5.94409964  27.844303506   4.78042603
## [563,]  22.89048018  14.369583000  -1.46713355
## [564,]  24.01723432   5.001469511  -4.49615005
## [565,]  11.00320121 -12.053622579   3.43598193
## [566,]  -1.07495841  -8.133470594   7.59794299
## [567,]   2.11592223  -8.476828159   2.63909741
## [568,]  14.51021777 -14.526076534   2.51991594
## [569,]   9.41576584 -13.932505441   2.23703751
## [570,]   2.39448572  24.974094676   5.72392103
## [571,]  17.51021777  -1.526076534   0.01991594
## [572,]   8.25219109 -17.332827159   3.72400600
## [573,]   4.27074260  -6.734757466   0.24581696
## [574,]  11.62293879 -12.949282113  -0.87696858
## [575,]  -1.13683394 -18.615537737   2.33438924
## [576,]  22.59789210  12.065885970  -8.12812003
## [577,]  -0.42065941   0.467816277  -2.64993098
## [578,] -12.48978223  -1.526076534  -5.28008406
## [579,] -12.37706121  12.050717887  -0.27696858
## [580,] -18.93189125  -8.319236746   2.62339095
## [581,]  -9.00045452  -7.853625256  -7.22359635
## [582,]  13.90649008  20.268459713   9.37613203
## [583,]  34.24267637   5.155058352   1.41008092
## [584,]  10.08861634   7.266851124   0.51097449
## [585,] -13.87004465   7.578263932  -1.69303456
## [586,]  15.07786298   2.106111071   4.95252688
## [587,]  11.24267637   2.155058352  -1.48991908
## [588,]  17.49371357 -21.285487664   4.03693102
## [589,]   0.43431735  -8.334435748  -3.14115153
## [590,] -10.26434019 -10.372487693   2.72614691
## [591,]   5.07006483  27.668781431  -1.51083646
## [592,]   3.83150313  22.561855713   1.21955228
## [593,] -18.74780891 -12.332827159  -1.37599400
## [594,]   5.75807481  -1.670546083  -0.91603439
## [595,]   5.25545490 -32.577403933  -2.77195716
## [596,] -18.83070732 -15.590800909  -2.89782647
## [597,]   6.54789231  10.219437226  -1.21688165
## [598,]  21.61967876  16.538990261  -4.35433147
## [599,]   2.38346363  -8.157963045   6.54893244
## [600,]  -1.74780891  -6.332827159  -1.97599400
## [601,] -10.91138366 -16.733148876  -0.18902551
## [602,]  12.07334857   7.494478954  -0.56476350
## [603,]   5.89048018  -7.630417000   4.13286645
## [604,]  30.08550519   9.372498166  -9.09173598
## [605,]   3.73565981   9.627512307  -1.47385309
## [606,]  16.16929268  63.409199091   2.50217353
## [607,]  23.41576584  58.067494559   2.03703751
## [608,]  11.62293879   7.050717887   6.42303142
## [609,] -40.98276568   0.001469511 -12.49615005
## [610,]  14.86316606  22.384462263  -6.26561076
## [611,]  21.63697191   5.105809977  -4.40910055
## [612,]  12.95746831  -6.613666362   2.42828979
## [613,]  14.92504159  18.866529406  -1.00205701
## [614,]  -6.45210769 -25.780562774   3.98311835
## [615,]   5.50708224  -8.743457532   4.88479478
## [616,]  10.57934059   1.467816277   1.95006902
## [617,]   4.25670949   4.210150443  -1.92205106
## [618,]  16.49618465  -6.581168625   0.65204792
## [619,] -16.71811080   3.691646883   2.46304728
## [620,]  15.41576584  27.067494559  -0.66296249
## [621,]  17.92504159  17.866529406   0.29794299
## [622,] -11.58423416 -15.932505441  -3.36296249
## [623,]  17.63697191  15.105809977  -3.40910055
## [624,]   9.83150313  19.561855713   4.21955228
## [625,]  15.39018529   7.297123692  -5.90235610
## [626,] -20.09350992  -2.731540287  -2.62386797
## [627,]  21.01723432   3.001469511  -1.29615005
## [628,]  -2.25030707  -2.317395602  -1.60598507
## [629,]  19.47614500   1.523247115  -4.47049573
## [630,]   0.27074260  -2.734757466   1.04581696
## [631,] -24.91138366  -8.733148876   0.81097449
## [632,]  -0.30513461  -4.778250782  -0.81297622
## [633,]  14.76372605   5.737696489   3.26188295
## [634,]  18.92504159  -3.133470594   3.69794299
## [635,]  13.74291533 -16.131862005   2.86310052
## [636,]   6.89048018 -11.630417000  -0.06713355
## [637,]  15.27074260  19.265242534  -8.95418304
## [638,]   9.17843982  26.549487299  -0.81433987
## [639,]  11.51021777  -5.526076534   3.71991594
## [640,]   6.25670949  36.210150443  -0.82205106
## [641,]  19.49618465   8.418831375  -3.64795208
## [642,]  13.51021777   5.473923466   5.01991594
## [643,]  20.14398846   9.633356023  -2.22516654
## [644,]  20.00320121  29.946377421  -1.16401807
## [645,]   2.87644707  -0.685509091  -2.23500157
## [646,]  -8.61653637  -3.157963045   1.24893244
## [647,]   4.25670949  -1.789849557   3.47794894
## [648,]  18.51021777  12.473923466  -0.18008406
## [649,]   1.08861634  -6.733148876  -2.88902551
## [650,]  12.50708224  -6.743457532   4.08479478
## [651,]   8.30422558  17.071000270  -3.23421647
## [652,]  10.60631009  41.996960128  -4.20219523
## [653,]   9.76146685  -5.533792312   2.28491148
## [654,]   7.51021777  -5.526076534   0.21991594
## [655,]  14.76372605  -6.262303511   3.96188295
## [656,]  29.00320121   0.946377421   0.33598193
## [657,]  13.74969293  25.682604398   2.09401493
## [658,]  18.69486539   8.221749218   6.58702378
## [659,]   5.86241395  -3.740601182   5.29713041
## [660,]   1.28188920 -13.308353117   2.96304728
## [661,]  14.66178183  28.551679661   1.77571689
## [662,]  17.36943051  14.786944864  -4.41893558
## [663,]  11.63697191   4.105809977   4.49089945
## [664,]   7.54789231  33.219437226  -4.51688165
## [665,]  20.41576584  -1.932505441  -6.26296249
## [666,]  15.84487179  -2.896114154  -0.33258396
## [667,]   8.92504159  25.866529406   0.59794299
## [668,]  13.92504159 -13.133470594   2.19794299
## [669,]   0.88076259  -1.061069559  -0.38126094
## [670,]  15.94409964  23.844303506  -7.31957397
## [671,]  20.41576584  13.067494559   1.53703751
## [672,]  16.76146685  -1.533792312  -0.91508852
## [673,]  -1.75732363   4.155058352   7.61008092
## [674,]  -3.34701644 -20.725554428   3.03354198
## [675,]  -6.12355293  -4.685509091  -0.83500157
## [676,]  13.92504159   4.866529406   2.49794299
## [677,]  15.74969293  10.682604398   1.29401493
## [678,]  15.74291533  16.868137995  -2.43689948
## [679,]  -5.00045452  -4.853625256   3.27640365
## [680,] -13.39109433  -7.004374204   5.65516340
## [681,]   9.49618465   2.418831375   2.85204792
## [682,]  -3.03174268 -17.560529392   1.98481287
## [683,]   5.76146685  20.466207688  -1.91508852
## [684,]  18.51021777   6.473923466   1.21991594
## [685,]   9.86678481   4.673996063   5.65074452
## [686,]  19.25219109  21.667172841   5.52400600
## [687,]  26.12995535  -2.421736068   9.80696544
## [688,] -50.98276568 -16.998530489  -7.49615005
## [689,]  15.25219109   9.667172841  -2.97599400
## [690,]  11.71890661  13.279407921  -2.84132148
## [691,]  25.74969293  22.682604398  -4.20598507
## [692,]  20.30422558  12.071000270  -3.43421647
## [693,]  10.05669616 -13.873248702  -3.35870022
## [694,]   3.84912798  21.293512474  -1.31963122
## [695,]  24.25219109  13.667172841  -5.17599400
## [696,]  15.51021777  -0.526076534   8.11991594
## [697,]   6.25219109 -17.332827159   6.82400600
## [698,]   6.99954548  -0.853625256  -0.92359635
## [699,]  16.57934059 -15.532183723   9.15006902
## [700,]  12.62293879  -0.949282113   6.42303142
## [701,]  16.84487179   6.103885846  -2.03258396
## [702,]   9.60890567  -3.004374204  -0.44483660
## [703,]  22.49618465   5.418831375  -0.74795208
## [704,]  -7.83070732 -21.590800909   4.10217353
## [705,]   5.05669616  12.126751298  -1.65870022
## [706,] -35.25708467  -7.131862005  -3.33689948
## [707,] -30.13758605 -10.740601182  -1.30286959
## [708,]   0.84912798  -3.706487526   3.38036878
## [709,]  15.60631009  37.996960128  -7.30219523
## [710,]   5.86316606   7.384462263  -1.86561076
## [711,]   5.25545490 -21.577403933   2.32804284
## [712,]  12.49618465   0.418831375  -7.14795208
## [713,]  -3.52385500 -12.476752885   0.42950427
## [714,]   8.73227527  -1.178561947   0.30654228
## [715,] -12.82853509   4.598621589  -1.75987560
## [716,]  -4.25708467  -8.131862005   1.86310052
## [717,] -25.26772473 -13.178561947  -2.79345772
## [718,] -23.85601154 -12.366643977   7.97483346
## [719,]   1.84487179  11.103885846  -3.63258396
## [720,]  -9.49291776 -20.743457532  -0.21520522
## [721,]  11.96825732  31.439470608  -7.51518713
## [722,] -32.25708467  -1.131862005  -2.53689948
## [723,]  -5.07495841  -0.133470594  -3.00205701
## [724,]  -7.42065941   6.467816277  -1.54993098
## [725,]  11.28353107   4.604495645  -0.46391624
## [726,]  -3.13683394  22.384462263  -1.96561076
## [727,]   7.25219109   4.667172841  -2.97599400
## [728,]  16.89048018   9.369583000   1.83286645
## [729,]   6.86316606  16.384462263  -7.66561076
## [730,]  -7.61653637 -14.157963045   4.94893244
## [731,] -13.07495841 -13.133470594   1.79794299
## [732,] -31.13683394 -40.615537737   3.53438924
## [733,]  -0.12355293  -1.685509091   4.96499843
## [734,]   8.75807481  32.329453917  -0.71603439
## [735,]  17.90649008  11.268459713  -5.42386797
## [736,] -60.91138366 -19.733148876   1.11097449
## [737,] -25.50628643 -23.285487664   1.33693102
## [738,]   3.65298356  10.274445572   1.03354198
## [739,]   8.38346363  -9.157963045  -0.05106756
## [740,] -34.56568265 -11.334435748   1.55884847
## [741,] -15.42065941   0.467816277   2.45006902
## [742,]  -0.23627395 -10.262303511  -0.53811705
## [743,]  16.43431735   7.665564252  -2.24115153
## [744,]  12.76372605   2.737696489   9.56188295
## [745,]   7.27074260 -15.734757466   0.54581696
## [746,]   8.38346363 -13.157963045   4.04893244
## [747,]  14.59789210   6.065885970   8.07187997
## [748,]   3.25219109 -23.332827159   1.52400600
## [749,]  -3.23853315  -4.533792312  -2.01508852
## [750,] -15.05590036  -3.155696494  -0.71957397
## [751,]   0.12995535   1.578263932  -4.99303456
## [752,]  -3.82156018   2.549487299   2.58566013
## [753,]   2.38862232  20.659503990  -0.11349261
## [754,]  15.95746831  -8.613666362  -0.37171021
## [755,] -10.15512821 -14.896114154   0.56741604
## [756,]   3.84487179  15.103885846  -3.03258396
## [757,]  16.38346363  14.842036955  -1.75106756
## [758,]   2.94409964  10.844303506   3.68042603
## [759,]  17.92504159  -1.133470594  -1.80205701
## [760,]   4.57934059 -12.532183723  -0.64993098
## [761,]  16.74291533  20.868137995  -0.53689948
## [762,]   7.27074260   9.265242534  -3.65418304
## [763,] -28.61653637  -3.157963045  -2.45106756
## [764,]  17.47443567  32.809846847  -2.82893500
## [765,]  -6.42065941 -11.532183723  -5.64993098
## [766,] -16.24192519 -37.670546083   2.58396561
## [767,] -13.85601154  -2.366643977   5.27483346
## [768,]   4.27074260   1.265242534  -2.05418304
## [769,] -19.87004465  -2.421736068  -6.99303456
## [770,]   5.16929268  10.409199091  -0.49782647
## [771,]  14.50708224  20.256542468   1.88479478
## [772,]  14.71890661  16.279407921   2.05867852
## [773,]  -9.13758605 -11.740601182   4.79713041
## [774,]  -4.39368991  -9.003039872   0.19780477
## [775,]  -0.99679879  14.946377421  -1.16401807
## [776,]  19.47443567  46.809846847  -6.02893500
## [777,]  -1.52556433 -20.190153153   6.27106500
## 
## $fitted.values
##             PhD Top10perc S.F.Ratio
##   [1,] 67.56568  23.33444  14.74115
##   [2,] 67.10952  21.63042  15.06713
##   [3,] 67.36303  20.89419  15.20910
##   [4,] 66.72926  22.73476  14.85418
##   [5,] 53.39874  13.27076  13.80057
##   [6,] 67.23627  21.26230  15.13812
##   [7,] 70.07496  25.13347  14.40206
##   [8,] 76.26772  30.17856  13.49346
##   [9,] 77.05590  32.15570  13.21957
##  [10,] 67.61654  20.15796  15.35107
##  [11,] 76.26772  30.17856  13.49346
##  [12,] 76.60551  31.02591  13.37608
##  [13,] 76.38032  30.46101  13.45433
##  [14,] 74.25708  28.13186  13.83690
##  [15,] 67.23627  21.26230  15.13812
##  [16,] 75.09351  28.73154  13.72387
##  [17,] 74.11924  47.06107  12.08126
##  [18,] 66.72926  22.73476  14.85418
##  [19,] 68.37706  17.94928  15.77697
##  [20,] 66.60981  14.70288  15.90236
##  [21,] 68.12355  18.68551  15.63500
##  [22,] 75.92994  29.33122  13.61084
##  [23,] 71.74781  26.33283  14.17599
##  [24,] 68.12355  18.68551  15.63500
##  [25,] 67.36303  20.89419  15.20910
##  [26,] 68.12355  18.68551  15.63500
##  [27,] 81.92665  41.50552  12.06476
##  [28,] 75.09351  28.73154  13.72387
##  [29,] 66.85601  22.36664  14.92517
##  [30,] 76.04253  29.61367  13.57171
##  [31,] 75.09351  28.73154  13.72387
##  [32,] 76.04253  29.61367  13.57171
##  [33,] 68.12355  18.68551  15.63500
##  [34,] 71.74781  26.33283  14.17599
##  [35,] 78.61138  35.34050  12.81349
##  [36,] 76.04253  29.61367  13.57171
##  [37,] 76.94330  31.87325  13.25870
##  [38,] 85.24193  47.67055  11.31603
##  [39,] 76.15513  29.89611  13.53258
##  [40,] 76.15513  29.89611  13.53258
##  [41,] 76.26772  30.17856  13.49346
##  [42,] 77.50629  33.28549  13.06307
##  [43,] 67.61654  20.15796  15.35107
##  [44,] 67.99680  19.05362  15.56402
##  [45,] 75.09351  28.73154  13.72387
##  [46,] 68.37706  17.94928  15.77697
##  [47,] 66.85601  22.36664  14.92517
##  [48,] 67.23627  21.26230  15.13812
##  [49,] 77.28109  32.72059  13.14132
##  [50,] 70.07496  25.13347  14.40206
##  [51,] 68.12355  18.68551  15.63500
##  [52,] 67.10952  21.63042  15.06713
##  [53,] 67.30513  14.77825  16.01298
##  [54,] 66.85601  22.36664  14.92517
##  [55,] 76.15513  29.89611  13.53258
##  [56,] 67.74329  19.78985  15.42205
##  [57,] 76.49292  30.74346  13.41521
##  [58,] 67.48978  20.52608  15.28008
##  [59,] 66.85601  22.36664  14.92517
##  [60,] 76.15513  29.89611  13.53258
##  [61,] 83.74455  51.57740  11.07196
##  [62,] 73.42066  27.53218  13.94993
##  [63,] 68.37706  17.94928  15.77697
##  [64,] 78.61138  35.34050  12.81349
##  [65,] 77.50629  33.28549  13.06307
##  [66,] 67.99680  19.05362  15.56402
##  [67,] 55.48470  13.49688  14.13243
##  [68,] 66.85601  22.36664  14.92517
##  [69,] 77.28109  32.72059  13.14132
##  [70,] 65.91449  14.62750  15.79174
##  [71,] 81.33822  50.44832  11.32428
##  [72,] 83.03174  43.56053  11.81519
##  [73,] 87.45211  51.78056  10.81688
##  [74,] 76.83071  31.59080  13.29783
##  [75,] 77.39369  33.00304  13.10220
##  [76,] 76.04253  29.61367  13.57171
##  [77,] 67.23627  21.26230  15.13812
##  [78,] 67.56568  23.33444  14.74115
##  [79,] 66.72926  22.73476  14.85418
##  [80,] 68.40211  23.93411  14.62812
##  [81,] 77.16850  32.43814  13.18045
##  [82,] 70.07496  25.13347  14.40206
##  [83,] 67.99680  19.05362  15.56402
##  [84,] 70.91138  25.73315  14.28903
##  [85,] 77.39369  33.00304  13.10220
##  [86,] 67.61654  20.15796  15.35107
##  [87,] 85.24193  47.67055  11.31603
##  [88,] 76.38032  30.46101  13.45433
##  [89,] 76.94330  31.87325  13.25870
##  [90,] 73.42066  27.53218  13.94993
##  [91,] 69.23853  24.53379  14.51509
##  [92,] 73.42066  27.53218  13.94993
##  [93,] 76.94330  31.87325  13.25870
##  [94,] 67.23627  21.26230  15.13812
##  [95,] 76.49292  30.74346  13.41521
##  [96,] 30.80535  26.73756  16.62313
##  [97,] 76.38032  30.46101  13.45433
##  [98,] 70.91138  25.73315  14.28903
##  [99,] 59.65662  13.94913  14.79615
## [100,] 72.58423  26.93251  14.06296
## [101,] 68.25031  18.31740  15.70599
## [102,] 73.42066  27.53218  13.94993
## [103,] 67.99680  19.05362  15.56402
## [104,] 67.87004  19.42174  15.49303
## [105,] 67.74329  19.78985  15.42205
## [106,] 66.85601  22.36664  14.92517
## [107,] 76.38032  30.46101  13.45433
## [108,] 68.25031  18.31740  15.70599
## [109,] 67.61654  20.15796  15.35107
## [110,] 76.26772  30.17856  13.49346
## [111,] 66.85601  22.36664  14.92517
## [112,] 70.07496  25.13347  14.40206
## [113,] 68.12355  18.68551  15.63500
## [114,] 57.57066  13.72301  14.46429
## [115,] 80.82156  39.45051  12.31434
## [116,] 76.94330  31.87325  13.25870
## [117,] 76.38032  30.46101  13.45433
## [118,] 76.71811  31.30835  13.33695
## [119,] 76.26772  30.17856  13.49346
## [120,] 68.37706  17.94928  15.77697
## [121,] 73.42066  27.53218  13.94993
## [122,] 76.49292  30.74346  13.41521
## [123,] 85.24193  47.67055  11.31603
## [124,] 87.45211  51.78056  10.81688
## [125,] 83.74455  51.57740  11.07196
## [126,] 67.74329  19.78985  15.42205
## [127,] 74.11924  47.06107  12.08126
## [128,] 77.39369  33.00304  13.10220
## [129,] 68.75732  16.84494  15.98992
## [130,] 76.49292  30.74346  13.41521
## [131,] 76.15513  29.89611  13.53258
## [132,] 76.71811  31.30835  13.33695
## [133,] 76.83071  31.59080  13.29783
## [134,] 70.91138  25.73315  14.28903
## [135,] 77.05590  32.15570  13.21957
## [136,] 76.60551  31.02591  13.37608
## [137,] 76.15513  29.89611  13.53258
## [138,] 86.15087  52.70649  10.81963
## [139,] 87.45211  51.78056  10.81688
## [140,] 75.09351  28.73154  13.72387
## [141,] 77.50629  33.28549  13.06307
## [142,] 66.72926  22.73476  14.85418
## [143,] 68.69577  14.92900  16.23422
## [144,] 76.60551  31.02591  13.37608
## [145,] 76.52556  48.19015  11.82893
## [146,] 68.50382  17.58117  15.84795
## [147,] 68.88408  16.47683  16.06090
## [148,] 67.23627  21.26230  15.13812
## [149,] 76.49292  30.74346  13.41521
## [150,] 85.24193  47.67055  11.31603
## [151,] 76.49292  30.74346  13.41521
## [152,] 70.91138  25.73315  14.28903
## [153,] 78.61138  35.34050  12.81349
## [154,] 67.74329  19.78985  15.42205
## [155,] 70.07496  25.13347  14.40206
## [156,] 68.37706  17.94928  15.77697
## [157,] 67.36303  20.89419  15.20910
## [158,] 76.15513  29.89611  13.53258
## [159,] 78.93189  49.31924  11.57661
## [160,] 88.55720  53.83557  10.56731
## [161,] 67.10952  21.63042  15.06713
## [162,] 66.85601  22.36664  14.92517
## [163,] 77.16850  32.43814  13.18045
## [164,] 77.28109  32.72059  13.14132
## [165,] 80.82156  39.45051  12.31434
## [166,] 68.37706  17.94928  15.77697
## [167,] 68.40211  23.93411  14.62812
## [168,] 67.56568  23.33444  14.74115
## [169,] 67.36303  20.89419  15.20910
## [170,] 80.82156  39.45051  12.31434
## [171,] 68.88408  16.47683  16.06090
## [172,] 76.71811  31.30835  13.33695
## [173,] 77.39369  33.00304  13.10220
## [174,] 73.42066  27.53218  13.94993
## [175,] 81.33822  50.44832  11.32428
## [176,] 76.83071  31.59080  13.29783
## [177,] 66.85601  22.36664  14.92517
## [178,] 68.88408  16.47683  16.06090
## [179,] 69.39109  15.00437  16.34484
## [180,] 67.36303  20.89419  15.20910
## [181,] 67.87004  19.42174  15.49303
## [182,] 76.60551  31.02591  13.37608
## [183,] 77.28109  32.72059  13.14132
## [184,] 75.92994  29.33122  13.61084
## [185,] 66.72926  22.73476  14.85418
## [186,] 77.16850  32.43814  13.18045
## [187,] 70.91138  25.73315  14.28903
## [188,] 79.71647  37.39550  12.56392
## [189,] 70.07496  25.13347  14.40206
## [190,] 68.63057  17.21306  15.91894
## [191,] 77.28109  32.72059  13.14132
## [192,] 83.74455  51.57740  11.07196
## [193,] 67.87004  19.42174  15.49303
## [194,] 73.42066  27.53218  13.94993
## [195,] 67.48978  20.52608  15.28008
## [196,] 74.25708  28.13186  13.83690
## [197,] 88.55720  53.83557  10.56731
## [198,] 59.65662  13.94913  14.79615
## [199,] 58.26598  13.79838  14.57491
## [200,] 75.09351  28.73154  13.72387
## [201,] 66.98277  21.99853  14.99615
## [202,] 72.58423  26.93251  14.06296
## [203,] 74.25708  28.13186  13.83690
## [204,] 66.85601  22.36664  14.92517
## [205,] 69.23853  24.53379  14.51509
## [206,] 77.05590  32.15570  13.21957
## [207,] 68.37706  17.94928  15.77697
## [208,] 68.75732  16.84494  15.98992
## [209,] 77.39369  33.00304  13.10220
## [210,] 67.56568  23.33444  14.74115
## [211,] 67.74329  19.78985  15.42205
## [212,] 69.23853  24.53379  14.51509
## [213,] 67.36303  20.89419  15.20910
## [214,] 77.28109  32.72059  13.14132
## [215,] 71.74781  26.33283  14.17599
## [216,] 63.13322  14.32600  15.34926
## [217,] 76.38032  30.46101  13.45433
## [218,] 67.61654  20.15796  15.35107
## [219,] 68.37706  17.94928  15.77697
## [220,] 76.15513  29.89611  13.53258
## [221,] 67.23627  21.26230  15.13812
## [222,] 86.15087  52.70649  10.81963
## [223,] 75.92994  29.33122  13.61084
## [224,] 66.60981  14.70288  15.90236
## [225,] 76.60551  31.02591  13.37608
## [226,] 77.39369  33.00304  13.10220
## [227,] 68.00045  14.85363  16.12360
## [228,] 75.09351  28.73154  13.72387
## [229,] 72.58423  26.93251  14.06296
## [230,] 76.15513  29.89611  13.53258
## [231,] 76.71811  31.30835  13.33695
## [232,] 70.91138  25.73315  14.28903
## [233,] 68.25031  18.31740  15.70599
## [234,] 66.98277  21.99853  14.99615
## [235,] 76.60551  31.02591  13.37608
## [236,] 69.26434  15.37249  16.27385
## [237,] 67.56568  23.33444  14.74115
## [238,] 77.39369  33.00304  13.10220
## [239,] 74.11924  47.06107  12.08126
## [240,] 71.74781  26.33283  14.17599
## [241,] 77.05590  32.15570  13.21957
## [242,] 83.74455  51.57740  11.07196
## [243,] 85.24193  47.67055  11.31603
## [244,] 71.74781  26.33283  14.17599
## [245,] 75.09351  28.73154  13.72387
## [246,] 75.92994  29.33122  13.61084
## [247,] 70.91138  25.73315  14.28903
## [248,] 69.39109  15.00437  16.34484
## [249,] 76.26772  30.17856  13.49346
## [250,] 76.26772  30.17856  13.49346
## [251,] 74.11924  47.06107  12.08126
## [252,] 74.11924  47.06107  12.08126
## [253,] 67.61654  20.15796  15.35107
## [254,] 70.07496  25.13347  14.40206
## [255,] 76.94330  31.87325  13.25870
## [256,] 76.94330  31.87325  13.25870
## [257,] 76.94330  31.87325  13.25870
## [258,] 67.56568  23.33444  14.74115
## [259,] 76.15513  29.89611  13.53258
## [260,] 76.15513  29.89611  13.53258
## [261,] 76.15513  29.89611  13.53258
## [262,] 73.42066  27.53218  13.94993
## [263,] 68.63057  17.21306  15.91894
## [264,] 68.25031  18.31740  15.70599
## [265,] 57.57066  13.72301  14.46429
## [266,] 77.50629  33.28549  13.06307
## [267,] 76.49292  30.74346  13.41521
## [268,] 67.61654  20.15796  15.35107
## [269,] 67.10952  21.63042  15.06713
## [270,] 67.36303  20.89419  15.20910
## [271,] 77.39369  33.00304  13.10220
## [272,] 75.09351  28.73154  13.72387
## [273,] 86.15087  52.70649  10.81963
## [274,] 69.13759  15.74060  16.20287
## [275,] 74.25708  28.13186  13.83690
## [276,] 66.60981  14.70288  15.90236
## [277,] 72.58423  26.93251  14.06296
## [278,] 71.74781  26.33283  14.17599
## [279,] 76.49292  30.74346  13.41521
## [280,] 78.93189  49.31924  11.57661
## [281,] 67.36303  20.89419  15.20910
## [282,] 61.04726  14.09988  15.01740
## [283,] 76.49292  30.74346  13.41521
## [284,] 83.03174  43.56053  11.81519
## [285,] 84.13683  45.61554  11.56561
## [286,] 68.00045  14.85363  16.12360
## [287,] 67.10952  21.63042  15.06713
## [288,] 77.05590  32.15570  13.21957
## [289,] 67.36303  20.89419  15.20910
## [290,] 74.25708  28.13186  13.83690
## [291,] 68.40211  23.93411  14.62812
## [292,] 69.23853  24.53379  14.51509
## [293,] 81.92665  41.50552  12.06476
## [294,] 67.74329  19.78985  15.42205
## [295,] 80.82156  39.45051  12.31434
## [296,] 71.74781  26.33283  14.17599
## [297,] 76.94330  31.87325  13.25870
## [298,] 67.61654  20.15796  15.35107
## [299,] 77.50629  33.28549  13.06307
## [300,] 86.34702  49.72555  11.06646
## [301,] 76.49292  30.74346  13.41521
## [302,] 76.71811  31.30835  13.33695
## [303,] 66.98277  21.99853  14.99615
## [304,] 61.04726  14.09988  15.01740
## [305,] 67.56568  23.33444  14.74115
## [306,] 67.74329  19.78985  15.42205
## [307,] 76.71811  31.30835  13.33695
## [308,] 88.55720  53.83557  10.56731
## [309,] 78.61138  35.34050  12.81349
## [310,] 85.24193  47.67055  11.31603
## [311,] 72.58423  26.93251  14.06296
## [312,] 66.85601  22.36664  14.92517
## [313,] 67.10952  21.63042  15.06713
## [314,] 75.09351  28.73154  13.72387
## [315,] 68.40211  23.93411  14.62812
## [316,] 67.48978  20.52608  15.28008
## [317,] 68.50382  17.58117  15.84795
## [318,] 74.11924  47.06107  12.08126
## [319,] 77.16850  32.43814  13.18045
## [320,] 86.34702  49.72555  11.06646
## [321,] 70.07496  25.13347  14.40206
## [322,] 69.23853  24.53379  14.51509
## [323,] 75.92994  29.33122  13.61084
## [324,] 66.72926  22.73476  14.85418
## [325,] 68.69577  14.92900  16.23422
## [326,] 68.50382  17.58117  15.84795
## [327,] 77.05590  32.15570  13.21957
## [328,] 77.50629  33.28549  13.06307
## [329,] 67.48978  20.52608  15.28008
## [330,] 71.74781  26.33283  14.17599
## [331,] 76.71811  31.30835  13.33695
## [332,] 76.15513  29.89611  13.53258
## [333,] 75.92994  29.33122  13.61084
## [334,] 67.74329  19.78985  15.42205
## [335,] 76.71811  31.30835  13.33695
## [336,] 66.72926  22.73476  14.85418
## [337,] 67.23627  21.26230  15.13812
## [338,] 70.91138  25.73315  14.28903
## [339,] 76.94330  31.87325  13.25870
## [340,] 75.92994  29.33122  13.61084
## [341,] 74.25708  28.13186  13.83690
## [342,] 66.72926  22.73476  14.85418
## [343,] 83.74455  51.57740  11.07196
## [344,] 75.09351  28.73154  13.72387
## [345,] 76.71811  31.30835  13.33695
## [346,] 67.87004  19.42174  15.49303
## [347,] 84.13683  45.61554  11.56561
## [348,] 77.50629  33.28549  13.06307
## [349,] 76.71811  31.30835  13.33695
## [350,] 74.25708  28.13186  13.83690
## [351,] 67.23627  21.26230  15.13812
## [352,] 67.74329  19.78985  15.42205
## [353,] 68.40211  23.93411  14.62812
## [354,] 72.58423  26.93251  14.06296
## [355,] 88.55720  53.83557  10.56731
## [356,] 67.74329  19.78985  15.42205
## [357,] 67.61654  20.15796  15.35107
## [358,] 65.21917  14.55213  15.68112
## [359,] 68.12355  18.68551  15.63500
## [360,] 85.24193  47.67055  11.31603
## [361,] 76.83071  31.59080  13.29783
## [362,] 77.28109  32.72059  13.14132
## [363,] 77.05590  32.15570  13.21957
## [364,] 66.72926  22.73476  14.85418
## [365,] 83.03174  43.56053  11.81519
## [366,] 78.61138  35.34050  12.81349
## [367,] 76.04253  29.61367  13.57171
## [368,] 71.74781  26.33283  14.17599
## [369,] 67.99680  19.05362  15.56402
## [370,] 76.04253  29.61367  13.57171
## [371,] 70.91138  25.73315  14.28903
## [372,] 76.49292  30.74346  13.41521
## [373,] 66.85601  22.36664  14.92517
## [374,] 73.42066  27.53218  13.94993
## [375,] 68.40211  23.93411  14.62812
## [376,] 67.48978  20.52608  15.28008
## [377,] 70.07496  25.13347  14.40206
## [378,] 74.11924  47.06107  12.08126
## [379,] 61.74258  14.17525  15.12802
## [380,] 67.10952  21.63042  15.06713
## [381,] 67.36303  20.89419  15.20910
## [382,] 76.38032  30.46101  13.45433
## [383,] 68.69577  14.92900  16.23422
## [384,] 66.85601  22.36664  14.92517
## [385,] 53.39874  13.27076  13.80057
## [386,] 67.56568  23.33444  14.74115
## [387,] 76.38032  30.46101  13.45433
## [388,] 77.39369  33.00304  13.10220
## [389,] 67.10952  21.63042  15.06713
## [390,] 67.56568  23.33444  14.74115
## [391,] 77.50629  33.28549  13.06307
## [392,] 68.63057  17.21306  15.91894
## [393,] 76.83071  31.59080  13.29783
## [394,] 70.91138  25.73315  14.28903
## [395,] 57.57066  13.72301  14.46429
## [396,] 77.05590  32.15570  13.21957
## [397,] 81.92665  41.50552  12.06476
## [398,] 76.15513  29.89611  13.53258
## [399,] 77.16850  32.43814  13.18045
## [400,] 66.85601  22.36664  14.92517
## [401,] 77.39369  33.00304  13.10220
## [402,] 67.61654  20.15796  15.35107
## [403,] 76.26772  30.17856  13.49346
## [404,] 76.04253  29.61367  13.57171
## [405,] 68.40211  23.93411  14.62812
## [406,] 76.15513  29.89611  13.53258
## [407,] 66.60981  14.70288  15.90236
## [408,] 76.04253  29.61367  13.57171
## [409,] 77.39369  33.00304  13.10220
## [410,] 71.74781  26.33283  14.17599
## [411,] 66.98277  21.99853  14.99615
## [412,] 68.63057  17.21306  15.91894
## [413,] 69.23853  24.53379  14.51509
## [414,] 67.61654  20.15796  15.35107
## [415,] 76.60551  31.02591  13.37608
## [416,] 68.88408  16.47683  16.06090
## [417,] 76.38032  30.46101  13.45433
## [418,] 76.60551  31.02591  13.37608
## [419,] 68.37706  17.94928  15.77697
## [420,] 69.01083  16.10871  16.13189
## [421,] 67.10952  21.63042  15.06713
## [422,] 67.36303  20.89419  15.20910
## [423,] 66.85601  22.36664  14.92517
## [424,] 74.25708  28.13186  13.83690
## [425,] 86.34702  49.72555  11.06646
## [426,] 70.07496  25.13347  14.40206
## [427,] 65.91449  14.62750  15.79174
## [428,] 67.48978  20.52608  15.28008
## [429,] 77.39369  33.00304  13.10220
## [430,] 76.94330  31.87325  13.25870
## [431,] 73.42066  27.53218  13.94993
## [432,] 77.39369  33.00304  13.10220
## [433,] 70.91138  25.73315  14.28903
## [434,] 76.49292  30.74346  13.41521
## [435,] 67.87004  19.42174  15.49303
## [436,] 68.50382  17.58117  15.84795
## [437,] 68.12355  18.68551  15.63500
## [438,] 80.82156  39.45051  12.31434
## [439,] 71.74781  26.33283  14.17599
## [440,] 68.69577  14.92900  16.23422
## [441,] 69.23853  24.53379  14.51509
## [442,] 77.39369  33.00304  13.10220
## [443,] 75.09351  28.73154  13.72387
## [444,] 68.88408  16.47683  16.06090
## [445,] 68.12355  18.68551  15.63500
## [446,] 70.07496  25.13347  14.40206
## [447,] 72.58423  26.93251  14.06296
## [448,] 68.63057  17.21306  15.91894
## [449,] 68.12355  18.68551  15.63500
## [450,] 74.25708  28.13186  13.83690
## [451,] 69.26434  15.37249  16.27385
## [452,] 64.52385  14.47675  15.57050
## [453,] 68.40211  23.93411  14.62812
## [454,] 76.26772  30.17856  13.49346
## [455,] 67.36303  20.89419  15.20910
## [456,] 72.58423  26.93251  14.06296
## [457,] 69.23853  24.53379  14.51509
## [458,] 67.30513  14.77825  16.01298
## [459,] 78.61138  35.34050  12.81349
## [460,] 76.52556  48.19015  11.82893
## [461,] 83.74455  51.57740  11.07196
## [462,] 73.42066  27.53218  13.94993
## [463,] 66.85601  22.36664  14.92517
## [464,] 77.05590  32.15570  13.21957
## [465,] 79.71647  37.39550  12.56392
## [466,] 69.23853  24.53379  14.51509
## [467,] 68.25031  18.31740  15.70599
## [468,] 76.38032  30.46101  13.45433
## [469,] 74.25708  28.13186  13.83690
## [470,] 74.25708  28.13186  13.83690
## [471,] 77.50629  33.28549  13.06307
## [472,] 75.92994  29.33122  13.61084
## [473,] 76.71811  31.30835  13.33695
## [474,] 75.92994  29.33122  13.61084
## [475,] 70.91138  25.73315  14.28903
## [476,] 77.16850  32.43814  13.18045
## [477,] 76.15513  29.89611  13.53258
## [478,] 76.94330  31.87325  13.25870
## [479,] 74.25708  28.13186  13.83690
## [480,] 68.40211  23.93411  14.62812
## [481,] 84.13683  45.61554  11.56561
## [482,] 77.16850  32.43814  13.18045
## [483,] 67.74329  19.78985  15.42205
## [484,] 76.71811  31.30835  13.33695
## [485,] 66.98277  21.99853  14.99615
## [486,] 66.85601  22.36664  14.92517
## [487,] 77.28109  32.72059  13.14132
## [488,] 75.92994  29.33122  13.61084
## [489,] 81.33822  50.44832  11.32428
## [490,] 66.85601  22.36664  14.92517
## [491,] 68.12355  18.68551  15.63500
## [492,] 75.09351  28.73154  13.72387
## [493,] 75.92994  29.33122  13.61084
## [494,] 73.42066  27.53218  13.94993
## [495,] 78.61138  35.34050  12.81349
## [496,] 77.39369  33.00304  13.10220
## [497,] 76.60551  31.02591  13.37608
## [498,] 73.42066  27.53218  13.94993
## [499,] 78.93189  49.31924  11.57661
## [500,] 76.83071  31.59080  13.29783
## [501,] 76.49292  30.74346  13.41521
## [502,] 77.50629  33.28549  13.06307
## [503,] 77.39369  33.00304  13.10220
## [504,] 67.48978  20.52608  15.28008
## [505,] 81.92665  41.50552  12.06476
## [506,] 67.23627  21.26230  15.13812
## [507,] 78.93189  49.31924  11.57661
## [508,] 67.56568  23.33444  14.74115
## [509,] 67.10952  21.63042  15.06713
## [510,] 68.40211  23.93411  14.62812
## [511,] 69.01083  16.10871  16.13189
## [512,] 74.11924  47.06107  12.08126
## [513,] 77.39369  33.00304  13.10220
## [514,] 67.23627  21.26230  15.13812
## [515,] 67.61654  20.15796  15.35107
## [516,] 76.26772  30.17856  13.49346
## [517,] 72.58423  26.93251  14.06296
## [518,] 83.03174  43.56053  11.81519
## [519,] 70.91138  25.73315  14.28903
## [520,] 76.04253  29.61367  13.57171
## [521,] 76.15513  29.89611  13.53258
## [522,] 66.85601  22.36664  14.92517
## [523,] 74.11924  47.06107  12.08126
## [524,] 68.25031  18.31740  15.70599
## [525,] 76.94330  31.87325  13.25870
## [526,] 75.92994  29.33122  13.61084
## [527,] 68.12355  18.68551  15.63500
## [528,] 77.16850  32.43814  13.18045
## [529,] 84.13683  45.61554  11.56561
## [530,] 73.42066  27.53218  13.94993
## [531,] 68.50382  17.58117  15.84795
## [532,] 67.48978  20.52608  15.28008
## [533,] 68.75732  16.84494  15.98992
## [534,] 68.75732  16.84494  15.98992
## [535,] 76.15513  29.89611  13.53258
## [536,] 76.04253  29.61367  13.57171
## [537,] 67.10952  21.63042  15.06713
## [538,] 67.74329  19.78985  15.42205
## [539,] 68.00045  14.85363  16.12360
## [540,] 67.61654  20.15796  15.35107
## [541,] 73.42066  27.53218  13.94993
## [542,] 83.03174  43.56053  11.81519
## [543,] 71.74781  26.33283  14.17599
## [544,] 67.99680  19.05362  15.56402
## [545,] 76.83071  31.59080  13.29783
## [546,] 70.91138  25.73315  14.28903
## [547,] 72.58423  26.93251  14.06296
## [548,] 78.61138  35.34050  12.81349
## [549,] 69.13759  15.74060  16.20287
## [550,] 76.83071  31.59080  13.29783
## [551,] 70.07496  25.13347  14.40206
## [552,] 76.15513  29.89611  13.53258
## [553,] 81.92665  41.50552  12.06476
## [554,] 68.50382  17.58117  15.84795
## [555,] 73.42066  27.53218  13.94993
## [556,] 66.72926  22.73476  14.85418
## [557,] 76.26772  30.17856  13.49346
## [558,] 76.94330  31.87325  13.25870
## [559,] 70.91138  25.73315  14.28903
## [560,] 81.33822  50.44832  11.32428
## [561,] 76.38032  30.46101  13.45433
## [562,] 77.05590  32.15570  13.21957
## [563,] 67.10952  21.63042  15.06713
## [564,] 66.98277  21.99853  14.99615
## [565,] 67.99680  19.05362  15.56402
## [566,] 70.07496  25.13347  14.40206
## [567,] 68.88408  16.47683  16.06090
## [568,] 67.48978  20.52608  15.28008
## [569,] 72.58423  26.93251  14.06296
## [570,] 76.60551  31.02591  13.37608
## [571,] 67.48978  20.52608  15.28008
## [572,] 71.74781  26.33283  14.17599
## [573,] 66.72926  22.73476  14.85418
## [574,] 68.37706  17.94928  15.77697
## [575,] 84.13683  45.61554  11.56561
## [576,] 68.40211  23.93411  14.62812
## [577,] 73.42066  27.53218  13.94993
## [578,] 67.48978  20.52608  15.28008
## [579,] 68.37706  17.94928  15.77697
## [580,] 78.93189  49.31924  11.57661
## [581,] 68.00045  14.85363  16.12360
## [582,] 75.09351  28.73154  13.72387
## [583,] 68.75732  16.84494  15.98992
## [584,] 70.91138  25.73315  14.28903
## [585,] 67.87004  19.42174  15.49303
## [586,] 49.92214  12.89389  13.24747
## [587,] 68.75732  16.84494  15.98992
## [588,] 77.50629  33.28549  13.06307
## [589,] 67.56568  23.33444  14.74115
## [590,] 69.26434  15.37249  16.27385
## [591,] 75.92994  29.33122  13.61084
## [592,] 77.16850  32.43814  13.18045
## [593,] 71.74781  26.33283  14.17599
## [594,] 85.24193  47.67055  11.31603
## [595,] 83.74455  51.57740  11.07196
## [596,] 76.83071  31.59080  13.29783
## [597,] 87.45211  51.78056  10.81688
## [598,] 76.38032  30.46101  13.45433
## [599,] 67.61654  20.15796  15.35107
## [600,] 71.74781  26.33283  14.17599
## [601,] 70.91138  25.73315  14.28903
## [602,] 81.92665  41.50552  12.06476
## [603,] 67.10952  21.63042  15.06713
## [604,] 65.91449  14.62750  15.79174
## [605,] 69.26434  15.37249  16.27385
## [606,] 76.83071  31.59080  13.29783
## [607,] 72.58423  26.93251  14.06296
## [608,] 68.37706  17.94928  15.77697
## [609,] 66.98277  21.99853  14.99615
## [610,] 84.13683  45.61554  11.56561
## [611,] 67.36303  20.89419  15.20910
## [612,] 76.04253  29.61367  13.57171
## [613,] 70.07496  25.13347  14.40206
## [614,] 87.45211  51.78056  10.81688
## [615,] 76.49292  30.74346  13.41521
## [616,] 73.42066  27.53218  13.94993
## [617,] 67.74329  19.78985  15.42205
## [618,] 68.50382  17.58117  15.84795
## [619,] 76.71811  31.30835  13.33695
## [620,] 72.58423  26.93251  14.06296
## [621,] 70.07496  25.13347  14.40206
## [622,] 72.58423  26.93251  14.06296
## [623,] 67.36303  20.89419  15.20910
## [624,] 77.16850  32.43814  13.18045
## [625,] 66.60981  14.70288  15.90236
## [626,] 75.09351  28.73154  13.72387
## [627,] 66.98277  21.99853  14.99615
## [628,] 68.25031  18.31740  15.70599
## [629,] 64.52385  14.47675  15.57050
## [630,] 66.72926  22.73476  14.85418
## [631,] 70.91138  25.73315  14.28903
## [632,] 67.30513  14.77825  16.01298
## [633,] 67.23627  21.26230  15.13812
## [634,] 70.07496  25.13347  14.40206
## [635,] 74.25708  28.13186  13.83690
## [636,] 67.10952  21.63042  15.06713
## [637,] 66.72926  22.73476  14.85418
## [638,] 80.82156  39.45051  12.31434
## [639,] 67.48978  20.52608  15.28008
## [640,] 67.74329  19.78985  15.42205
## [641,] 68.50382  17.58117  15.84795
## [642,] 67.48978  20.52608  15.28008
## [643,] 66.85601  22.36664  14.92517
## [644,] 67.99680  19.05362  15.56402
## [645,] 68.12355  18.68551  15.63500
## [646,] 67.61654  20.15796  15.35107
## [647,] 67.74329  19.78985  15.42205
## [648,] 67.48978  20.52608  15.28008
## [649,] 70.91138  25.73315  14.28903
## [650,] 76.49292  30.74346  13.41521
## [651,] 68.69577  14.92900  16.23422
## [652,] 77.39369  33.00304  13.10220
## [653,] 69.23853  24.53379  14.51509
## [654,] 67.48978  20.52608  15.28008
## [655,] 67.23627  21.26230  15.13812
## [656,] 67.99680  19.05362  15.56402
## [657,] 68.25031  18.31740  15.70599
## [658,] 67.30513  14.77825  16.01298
## [659,] 69.13759  15.74060  16.20287
## [660,] 76.71811  31.30835  13.33695
## [661,] 81.33822  50.44832  11.32428
## [662,] 68.63057  17.21306  15.91894
## [663,] 67.36303  20.89419  15.20910
## [664,] 87.45211  51.78056  10.81688
## [665,] 72.58423  26.93251  14.06296
## [666,] 76.15513  29.89611  13.53258
## [667,] 70.07496  25.13347  14.40206
## [668,] 70.07496  25.13347  14.40206
## [669,] 74.11924  47.06107  12.08126
## [670,] 77.05590  32.15570  13.21957
## [671,] 72.58423  26.93251  14.06296
## [672,] 69.23853  24.53379  14.51509
## [673,] 68.75732  16.84494  15.98992
## [674,] 86.34702  49.72555  11.06646
## [675,] 68.12355  18.68551  15.63500
## [676,] 70.07496  25.13347  14.40206
## [677,] 68.25031  18.31740  15.70599
## [678,] 74.25708  28.13186  13.83690
## [679,] 68.00045  14.85363  16.12360
## [680,] 69.39109  15.00437  16.34484
## [681,] 68.50382  17.58117  15.84795
## [682,] 83.03174  43.56053  11.81519
## [683,] 69.23853  24.53379  14.51509
## [684,] 67.48978  20.52608  15.28008
## [685,] 63.13322  14.32600  15.34926
## [686,] 71.74781  26.33283  14.17599
## [687,] 67.87004  19.42174  15.49303
## [688,] 66.98277  21.99853  14.99615
## [689,] 71.74781  26.33283  14.17599
## [690,] 77.28109  32.72059  13.14132
## [691,] 68.25031  18.31740  15.70599
## [692,] 68.69577  14.92900  16.23422
## [693,] 76.94330  31.87325  13.25870
## [694,] 86.15087  52.70649  10.81963
## [695,] 71.74781  26.33283  14.17599
## [696,] 67.48978  20.52608  15.28008
## [697,] 71.74781  26.33283  14.17599
## [698,] 68.00045  14.85363  16.12360
## [699,] 73.42066  27.53218  13.94993
## [700,] 68.37706  17.94928  15.77697
## [701,] 76.15513  29.89611  13.53258
## [702,] 69.39109  15.00437  16.34484
## [703,] 68.50382  17.58117  15.84795
## [704,] 76.83071  31.59080  13.29783
## [705,] 76.94330  31.87325  13.25870
## [706,] 74.25708  28.13186  13.83690
## [707,] 69.13759  15.74060  16.20287
## [708,] 86.15087  52.70649  10.81963
## [709,] 77.39369  33.00304  13.10220
## [710,] 84.13683  45.61554  11.56561
## [711,] 83.74455  51.57740  11.07196
## [712,] 68.50382  17.58117  15.84795
## [713,] 64.52385  14.47675  15.57050
## [714,] 76.26772  30.17856  13.49346
## [715,] 63.82854  14.40138  15.45988
## [716,] 74.25708  28.13186  13.83690
## [717,] 76.26772  30.17856  13.49346
## [718,] 66.85601  22.36664  14.92517
## [719,] 76.15513  29.89611  13.53258
## [720,] 76.49292  30.74346  13.41521
## [721,] 83.03174  43.56053  11.81519
## [722,] 74.25708  28.13186  13.83690
## [723,] 70.07496  25.13347  14.40206
## [724,] 73.42066  27.53218  13.94993
## [725,] 79.71647  37.39550  12.56392
## [726,] 84.13683  45.61554  11.56561
## [727,] 71.74781  26.33283  14.17599
## [728,] 67.10952  21.63042  15.06713
## [729,] 84.13683  45.61554  11.56561
## [730,] 67.61654  20.15796  15.35107
## [731,] 70.07496  25.13347  14.40206
## [732,] 84.13683  45.61554  11.56561
## [733,] 68.12355  18.68551  15.63500
## [734,] 85.24193  47.67055  11.31603
## [735,] 75.09351  28.73154  13.72387
## [736,] 70.91138  25.73315  14.28903
## [737,] 77.50629  33.28549  13.06307
## [738,] 86.34702  49.72555  11.06646
## [739,] 67.61654  20.15796  15.35107
## [740,] 67.56568  23.33444  14.74115
## [741,] 73.42066  27.53218  13.94993
## [742,] 67.23627  21.26230  15.13812
## [743,] 67.56568  23.33444  14.74115
## [744,] 67.23627  21.26230  15.13812
## [745,] 66.72926  22.73476  14.85418
## [746,] 67.61654  20.15796  15.35107
## [747,] 68.40211  23.93411  14.62812
## [748,] 71.74781  26.33283  14.17599
## [749,] 69.23853  24.53379  14.51509
## [750,] 77.05590  32.15570  13.21957
## [751,] 67.87004  19.42174  15.49303
## [752,] 80.82156  39.45051  12.31434
## [753,] 78.61138  35.34050  12.81349
## [754,] 76.04253  29.61367  13.57171
## [755,] 76.15513  29.89611  13.53258
## [756,] 76.15513  29.89611  13.53258
## [757,] 67.61654  20.15796  15.35107
## [758,] 77.05590  32.15570  13.21957
## [759,] 70.07496  25.13347  14.40206
## [760,] 73.42066  27.53218  13.94993
## [761,] 74.25708  28.13186  13.83690
## [762,] 66.72926  22.73476  14.85418
## [763,] 67.61654  20.15796  15.35107
## [764,] 76.52556  48.19015  11.82893
## [765,] 73.42066  27.53218  13.94993
## [766,] 85.24193  47.67055  11.31603
## [767,] 66.85601  22.36664  14.92517
## [768,] 66.72926  22.73476  14.85418
## [769,] 67.87004  19.42174  15.49303
## [770,] 76.83071  31.59080  13.29783
## [771,] 76.49292  30.74346  13.41521
## [772,] 77.28109  32.72059  13.14132
## [773,] 69.13759  15.74060  16.20287
## [774,] 77.39369  33.00304  13.10220
## [775,] 67.99680  19.05362  15.56402
## [776,] 76.52556  48.19015  11.82893
## [777,] 76.52556  48.19015  11.82893
## 
## $lenb
## [1] 11
## 
## $coefficients
##             [,1]        [,2]        [,3]
## [1,] 108.3290089 19.22534476 22.53956356
## [2,]  -2.8160983 -3.10871746  0.61252244
## [3,]  -0.6953199 -0.07537447 -0.11062012
## [4,]   0.9924947  1.77256055 -0.21045012
## [5,]   0.9631794  0.23156479 -0.04204800
## [6,]  -0.8220740  0.29273901 -0.18160363
## [7,]  -0.7238287 -0.31723049  0.07390526
## 
## $x
##        [,1] [,2] [,3] [,4] [,5] [,6] [,7]
##   [1,]    1    0   34    0    1   22    0
##   [2,]    1    0   38    0    0   18    0
##   [3,]    1    0   40    0    0   16    0
##   [4,]    1    0   35    0    0   21    0
##   [5,]    1    0   79    0    0    0    0
##   [6,]    1    0   39    0    0   17    0
##   [7,]    1    0   31    0    4   25    0
##   [8,]    1    0   21    0   14   35    3
##   [9,]    1    0   14    0   21   42   10
##  [10,]    1    0   42    0    0   14    0
##  [11,]    1    0   21    0   14   35    3
##  [12,]    1    0   18    0   17   38    6
##  [13,]    1    0   20    0   15   36    4
##  [14,]    1    0   26    0    9   30    0
##  [15,]    1    0   39    0    0   17    0
##  [16,]    1    0   25    0   10   31    0
##  [17,]    1    6    0   16   41   62   30
##  [18,]    1    0   35    0    0   21    0
##  [19,]    1    0   48    0    0    8    0
##  [20,]    1    0   60    0    0    0    0
##  [21,]    1    0   46    0    0   10    0
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## [406,]    1    0   22    0   13   34    2
## [407,]    1    0   60    0    0    0    0
## [408,]    1    0   23    0   12   33    1
## [409,]    1    0   11    0   24   45   13
## [410,]    1    0   29    0    6   27    0
## [411,]    1    0   37    0    0   19    0
## [412,]    1    0   50    0    0    6    0
## [413,]    1    0   32    0    3   24    0
## [414,]    1    0   42    0    0   14    0
## [415,]    1    0   18    0   17   38    6
## [416,]    1    0   52    0    0    4    0
## [417,]    1    0   20    0   15   36    4
## [418,]    1    0   18    0   17   38    6
## [419,]    1    0   48    0    0    8    0
## [420,]    1    0   53    0    0    3    0
## [421,]    1    0   38    0    0   18    0
## [422,]    1    0   40    0    0   16    0
## [423,]    1    0   36    0    0   20    0
## [424,]    1    0   26    0    9   30    0
## [425,]    1    0    2    8   33   54   22
## [426,]    1    0   31    0    4   25    0
## [427,]    1    0   61    0    0    0    0
## [428,]    1    0   41    0    0   15    0
## [429,]    1    0   11    0   24   45   13
## [430,]    1    0   15    0   20   41    9
## [431,]    1    0   27    0    8   29    0
## [432,]    1    0   11    0   24   45   13
## [433,]    1    0   30    0    5   26    0
## [434,]    1    0   19    0   16   37    5
## [435,]    1    0   44    0    0   12    0
## [436,]    1    0   49    0    0    7    0
## [437,]    1    0   46    0    0   10    0
## [438,]    1    0    7    3   28   49   17
## [439,]    1    0   29    0    6   27    0
## [440,]    1    0   57    0    0    0    0
## [441,]    1    0   32    0    3   24    0
## [442,]    1    0   11    0   24   45   13
## [443,]    1    0   25    0   10   31    0
## [444,]    1    0   52    0    0    4    0
## [445,]    1    0   46    0    0   10    0
## [446,]    1    0   31    0    4   25    0
## [447,]    1    0   28    0    7   28    0
## [448,]    1    0   50    0    0    6    0
## [449,]    1    0   46    0    0   10    0
## [450,]    1    0   26    0    9   30    0
## [451,]    1    0   55    0    0    1    0
## [452,]    1    0   63    0    0    0    0
## [453,]    1    0   33    0    2   23    0
## [454,]    1    0   21    0   14   35    3
## [455,]    1    0   40    0    0   16    0
## [456,]    1    0   28    0    7   28    0
## [457,]    1    0   32    0    3   24    0
## [458,]    1    0   59    0    0    0    0
## [459,]    1    0    9    1   26   47   15
## [460,]    1    5    0   15   40   61   29
## [461,]    1    2    0   12   37   58   26
## [462,]    1    0   27    0    8   29    0
## [463,]    1    0   36    0    0   20    0
## [464,]    1    0   14    0   21   42   10
## [465,]    1    0    8    2   27   48   16
## [466,]    1    0   32    0    3   24    0
## [467,]    1    0   47    0    0    9    0
## [468,]    1    0   20    0   15   36    4
## [469,]    1    0   26    0    9   30    0
## [470,]    1    0   26    0    9   30    0
## [471,]    1    0   10    0   25   46   14
## [472,]    1    0   24    0   11   32    0
## [473,]    1    0   17    0   18   39    7
## [474,]    1    0   24    0   11   32    0
## [475,]    1    0   30    0    5   26    0
## [476,]    1    0   13    0   22   43   11
## [477,]    1    0   22    0   13   34    2
## [478,]    1    0   15    0   20   41    9
## [479,]    1    0   26    0    9   30    0
## [480,]    1    0   33    0    2   23    0
## [481,]    1    0    4    6   31   52   20
## [482,]    1    0   13    0   22   43   11
## [483,]    1    0   43    0    0   13    0
## [484,]    1    0   17    0   18   39    7
## [485,]    1    0   37    0    0   19    0
## [486,]    1    0   36    0    0   20    0
## [487,]    1    0   12    0   23   44   12
## [488,]    1    0   24    0   11   32    0
## [489,]    1    3    0   13   38   59   27
## [490,]    1    0   36    0    0   20    0
## [491,]    1    0   46    0    0   10    0
## [492,]    1    0   25    0   10   31    0
## [493,]    1    0   24    0   11   32    0
## [494,]    1    0   27    0    8   29    0
## [495,]    1    0    9    1   26   47   15
## [496,]    1    0   11    0   24   45   13
## [497,]    1    0   18    0   17   38    6
## [498,]    1    0   27    0    8   29    0
## [499,]    1    4    0   14   39   60   28
## [500,]    1    0   16    0   19   40    8
## [501,]    1    0   19    0   16   37    5
## [502,]    1    0   10    0   25   46   14
## [503,]    1    0   11    0   24   45   13
## [504,]    1    0   41    0    0   15    0
## [505,]    1    0    6    4   29   50   18
## [506,]    1    0   39    0    0   17    0
## [507,]    1    4    0   14   39   60   28
## [508,]    1    0   34    0    1   22    0
## [509,]    1    0   38    0    0   18    0
## [510,]    1    0   33    0    2   23    0
## [511,]    1    0   53    0    0    3    0
## [512,]    1    6    0   16   41   62   30
## [513,]    1    0   11    0   24   45   13
## [514,]    1    0   39    0    0   17    0
## [515,]    1    0   42    0    0   14    0
## [516,]    1    0   21    0   14   35    3
## [517,]    1    0   28    0    7   28    0
## [518,]    1    0    5    5   30   51   19
## [519,]    1    0   30    0    5   26    0
## [520,]    1    0   23    0   12   33    1
## [521,]    1    0   22    0   13   34    2
## [522,]    1    0   36    0    0   20    0
## [523,]    1    6    0   16   41   62   30
## [524,]    1    0   47    0    0    9    0
## [525,]    1    0   15    0   20   41    9
## [526,]    1    0   24    0   11   32    0
## [527,]    1    0   46    0    0   10    0
## [528,]    1    0   13    0   22   43   11
## [529,]    1    0    4    6   31   52   20
## [530,]    1    0   27    0    8   29    0
## [531,]    1    0   49    0    0    7    0
## [532,]    1    0   41    0    0   15    0
## [533,]    1    0   51    0    0    5    0
## [534,]    1    0   51    0    0    5    0
## [535,]    1    0   22    0   13   34    2
## [536,]    1    0   23    0   12   33    1
## [537,]    1    0   38    0    0   18    0
## [538,]    1    0   43    0    0   13    0
## [539,]    1    0   58    0    0    0    0
## [540,]    1    0   42    0    0   14    0
## [541,]    1    0   27    0    8   29    0
## [542,]    1    0    5    5   30   51   19
## [543,]    1    0   29    0    6   27    0
## [544,]    1    0   45    0    0   11    0
## [545,]    1    0   16    0   19   40    8
## [546,]    1    0   30    0    5   26    0
## [547,]    1    0   28    0    7   28    0
## [548,]    1    0    9    1   26   47   15
## [549,]    1    0   54    0    0    2    0
## [550,]    1    0   16    0   19   40    8
## [551,]    1    0   31    0    4   25    0
## [552,]    1    0   22    0   13   34    2
## [553,]    1    0    6    4   29   50   18
## [554,]    1    0   49    0    0    7    0
## [555,]    1    0   27    0    8   29    0
## [556,]    1    0   35    0    0   21    0
## [557,]    1    0   21    0   14   35    3
## [558,]    1    0   15    0   20   41    9
## [559,]    1    0   30    0    5   26    0
## [560,]    1    3    0   13   38   59   27
## [561,]    1    0   20    0   15   36    4
## [562,]    1    0   14    0   21   42   10
## [563,]    1    0   38    0    0   18    0
## [564,]    1    0   37    0    0   19    0
## [565,]    1    0   45    0    0   11    0
## [566,]    1    0   31    0    4   25    0
## [567,]    1    0   52    0    0    4    0
## [568,]    1    0   41    0    0   15    0
## [569,]    1    0   28    0    7   28    0
## [570,]    1    0   18    0   17   38    6
## [571,]    1    0   41    0    0   15    0
## [572,]    1    0   29    0    6   27    0
## [573,]    1    0   35    0    0   21    0
## [574,]    1    0   48    0    0    8    0
## [575,]    1    0    4    6   31   52   20
## [576,]    1    0   33    0    2   23    0
## [577,]    1    0   27    0    8   29    0
## [578,]    1    0   41    0    0   15    0
## [579,]    1    0   48    0    0    8    0
## [580,]    1    4    0   14   39   60   28
## [581,]    1    0   58    0    0    0    0
## [582,]    1    0   25    0   10   31    0
## [583,]    1    0   51    0    0    5    0
## [584,]    1    0   30    0    5   26    0
## [585,]    1    0   44    0    0   12    0
## [586,]    1    0   84    0    0    0    0
## [587,]    1    0   51    0    0    5    0
## [588,]    1    0   10    0   25   46   14
## [589,]    1    0   34    0    1   22    0
## [590,]    1    0   55    0    0    1    0
## [591,]    1    0   24    0   11   32    0
## [592,]    1    0   13    0   22   43   11
## [593,]    1    0   29    0    6   27    0
## [594,]    1    0    3    7   32   53   21
## [595,]    1    2    0   12   37   58   26
## [596,]    1    0   16    0   19   40    8
## [597,]    1    0    1    9   34   55   23
## [598,]    1    0   20    0   15   36    4
## [599,]    1    0   42    0    0   14    0
## [600,]    1    0   29    0    6   27    0
## [601,]    1    0   30    0    5   26    0
## [602,]    1    0    6    4   29   50   18
## [603,]    1    0   38    0    0   18    0
## [604,]    1    0   61    0    0    0    0
## [605,]    1    0   55    0    0    1    0
## [606,]    1    0   16    0   19   40    8
## [607,]    1    0   28    0    7   28    0
## [608,]    1    0   48    0    0    8    0
## [609,]    1    0   37    0    0   19    0
## [610,]    1    0    4    6   31   52   20
## [611,]    1    0   40    0    0   16    0
## [612,]    1    0   23    0   12   33    1
## [613,]    1    0   31    0    4   25    0
## [614,]    1    0    1    9   34   55   23
## [615,]    1    0   19    0   16   37    5
## [616,]    1    0   27    0    8   29    0
## [617,]    1    0   43    0    0   13    0
## [618,]    1    0   49    0    0    7    0
## [619,]    1    0   17    0   18   39    7
## [620,]    1    0   28    0    7   28    0
## [621,]    1    0   31    0    4   25    0
## [622,]    1    0   28    0    7   28    0
## [623,]    1    0   40    0    0   16    0
## [624,]    1    0   13    0   22   43   11
## [625,]    1    0   60    0    0    0    0
## [626,]    1    0   25    0   10   31    0
## [627,]    1    0   37    0    0   19    0
## [628,]    1    0   47    0    0    9    0
## [629,]    1    0   63    0    0    0    0
## [630,]    1    0   35    0    0   21    0
## [631,]    1    0   30    0    5   26    0
## [632,]    1    0   59    0    0    0    0
## [633,]    1    0   39    0    0   17    0
## [634,]    1    0   31    0    4   25    0
## [635,]    1    0   26    0    9   30    0
## [636,]    1    0   38    0    0   18    0
## [637,]    1    0   35    0    0   21    0
## [638,]    1    0    7    3   28   49   17
## [639,]    1    0   41    0    0   15    0
## [640,]    1    0   43    0    0   13    0
## [641,]    1    0   49    0    0    7    0
## [642,]    1    0   41    0    0   15    0
## [643,]    1    0   36    0    0   20    0
## [644,]    1    0   45    0    0   11    0
## [645,]    1    0   46    0    0   10    0
## [646,]    1    0   42    0    0   14    0
## [647,]    1    0   43    0    0   13    0
## [648,]    1    0   41    0    0   15    0
## [649,]    1    0   30    0    5   26    0
## [650,]    1    0   19    0   16   37    5
## [651,]    1    0   57    0    0    0    0
## [652,]    1    0   11    0   24   45   13
## [653,]    1    0   32    0    3   24    0
## [654,]    1    0   41    0    0   15    0
## [655,]    1    0   39    0    0   17    0
## [656,]    1    0   45    0    0   11    0
## [657,]    1    0   47    0    0    9    0
## [658,]    1    0   59    0    0    0    0
## [659,]    1    0   54    0    0    2    0
## [660,]    1    0   17    0   18   39    7
## [661,]    1    3    0   13   38   59   27
## [662,]    1    0   50    0    0    6    0
## [663,]    1    0   40    0    0   16    0
## [664,]    1    0    1    9   34   55   23
## [665,]    1    0   28    0    7   28    0
## [666,]    1    0   22    0   13   34    2
## [667,]    1    0   31    0    4   25    0
## [668,]    1    0   31    0    4   25    0
## [669,]    1    6    0   16   41   62   30
## [670,]    1    0   14    0   21   42   10
## [671,]    1    0   28    0    7   28    0
## [672,]    1    0   32    0    3   24    0
## [673,]    1    0   51    0    0    5    0
## [674,]    1    0    2    8   33   54   22
## [675,]    1    0   46    0    0   10    0
## [676,]    1    0   31    0    4   25    0
## [677,]    1    0   47    0    0    9    0
## [678,]    1    0   26    0    9   30    0
## [679,]    1    0   58    0    0    0    0
## [680,]    1    0   56    0    0    0    0
## [681,]    1    0   49    0    0    7    0
## [682,]    1    0    5    5   30   51   19
## [683,]    1    0   32    0    3   24    0
## [684,]    1    0   41    0    0   15    0
## [685,]    1    0   65    0    0    0    0
## [686,]    1    0   29    0    6   27    0
## [687,]    1    0   44    0    0   12    0
## [688,]    1    0   37    0    0   19    0
## [689,]    1    0   29    0    6   27    0
## [690,]    1    0   12    0   23   44   12
## [691,]    1    0   47    0    0    9    0
## [692,]    1    0   57    0    0    0    0
## [693,]    1    0   15    0   20   41    9
## [694,]    1    1    0   11   36   57   25
## [695,]    1    0   29    0    6   27    0
## [696,]    1    0   41    0    0   15    0
## [697,]    1    0   29    0    6   27    0
## [698,]    1    0   58    0    0    0    0
## [699,]    1    0   27    0    8   29    0
## [700,]    1    0   48    0    0    8    0
## [701,]    1    0   22    0   13   34    2
## [702,]    1    0   56    0    0    0    0
## [703,]    1    0   49    0    0    7    0
## [704,]    1    0   16    0   19   40    8
## [705,]    1    0   15    0   20   41    9
## [706,]    1    0   26    0    9   30    0
## [707,]    1    0   54    0    0    2    0
## [708,]    1    1    0   11   36   57   25
## [709,]    1    0   11    0   24   45   13
## [710,]    1    0    4    6   31   52   20
## [711,]    1    2    0   12   37   58   26
## [712,]    1    0   49    0    0    7    0
## [713,]    1    0   63    0    0    0    0
## [714,]    1    0   21    0   14   35    3
## [715,]    1    0   64    0    0    0    0
## [716,]    1    0   26    0    9   30    0
## [717,]    1    0   21    0   14   35    3
## [718,]    1    0   36    0    0   20    0
## [719,]    1    0   22    0   13   34    2
## [720,]    1    0   19    0   16   37    5
## [721,]    1    0    5    5   30   51   19
## [722,]    1    0   26    0    9   30    0
## [723,]    1    0   31    0    4   25    0
## [724,]    1    0   27    0    8   29    0
## [725,]    1    0    8    2   27   48   16
## [726,]    1    0    4    6   31   52   20
## [727,]    1    0   29    0    6   27    0
## [728,]    1    0   38    0    0   18    0
## [729,]    1    0    4    6   31   52   20
## [730,]    1    0   42    0    0   14    0
## [731,]    1    0   31    0    4   25    0
## [732,]    1    0    4    6   31   52   20
## [733,]    1    0   46    0    0   10    0
## [734,]    1    0    3    7   32   53   21
## [735,]    1    0   25    0   10   31    0
## [736,]    1    0   30    0    5   26    0
## [737,]    1    0   10    0   25   46   14
## [738,]    1    0    2    8   33   54   22
## [739,]    1    0   42    0    0   14    0
## [740,]    1    0   34    0    1   22    0
## [741,]    1    0   27    0    8   29    0
## [742,]    1    0   39    0    0   17    0
## [743,]    1    0   34    0    1   22    0
## [744,]    1    0   39    0    0   17    0
## [745,]    1    0   35    0    0   21    0
## [746,]    1    0   42    0    0   14    0
## [747,]    1    0   33    0    2   23    0
## [748,]    1    0   29    0    6   27    0
## [749,]    1    0   32    0    3   24    0
## [750,]    1    0   14    0   21   42   10
## [751,]    1    0   44    0    0   12    0
## [752,]    1    0    7    3   28   49   17
## [753,]    1    0    9    1   26   47   15
## [754,]    1    0   23    0   12   33    1
## [755,]    1    0   22    0   13   34    2
## [756,]    1    0   22    0   13   34    2
## [757,]    1    0   42    0    0   14    0
## [758,]    1    0   14    0   21   42   10
## [759,]    1    0   31    0    4   25    0
## [760,]    1    0   27    0    8   29    0
## [761,]    1    0   26    0    9   30    0
## [762,]    1    0   35    0    0   21    0
## [763,]    1    0   42    0    0   14    0
## [764,]    1    5    0   15   40   61   29
## [765,]    1    0   27    0    8   29    0
## [766,]    1    0    3    7   32   53   21
## [767,]    1    0   36    0    0   20    0
## [768,]    1    0   35    0    0   21    0
## [769,]    1    0   44    0    0   12    0
## [770,]    1    0   16    0   19   40    8
## [771,]    1    0   19    0   16   37    5
## [772,]    1    0   12    0   23   44   12
## [773,]    1    0   54    0    0    2    0
## [774,]    1    0   11    0   24   45   13
## [775,]    1    0   45    0    0   11    0
## [776,]    1    5    0   15   40   61   29
## [777,]    1    5    0   15   40   61   29
## 
## attr(,"class")
## [1] "mars"

In the above case, we set prune to false. This gives us the fit with all of the potential terms added. Our next version will set prune to true and look at the fully trimmed result.

model2 <- mars(x=df.response,y=df.covariate,trace.mars=F,prune=T)

If we look right toward the bottom of the model2 we see the ‘best model’ has a series of 1s and 0s. This is the trimmed output. In fact, the model object has an attribute which is the terms used.

model1$selected.terms
## [1]  1  2  3  4  6  8 10
print("versus")
## [1] "versus"
model2$selected.terms
## [1] 1 2 3 4

EARTH

I mentioned earlier that earth was a commonly used term for MARS models due to copyright. IN this case, we haven an R package called earth which has the same functionality and additional features.

library('earth')
## Warning: package 'earth' was built under R version 3.4.4
## Loading required package: plotmo
## Warning: package 'plotmo' was built under R version 3.4.4
## Loading required package: plotrix
## Loading required package: TeachingDemos
model3 <- earth(Grad.Rate ~ Books + Personal + PhD,data=df,pmethod="none")
summary(model3)
## Call: earth(formula=Grad.Rate~Books+Personal+PhD, data=df, pmethod="none")
## 
##                  coefficients
## (Intercept)       -20.7926168
## h(600-Books)        0.0080392
## h(Books-600)       -0.5353051
## h(Books-610)        0.8387684
## h(Books-650)       -0.3970726
## h(Books-720)        0.1004191
## h(Personal-600)     0.0440688
## h(Personal-1000)   -0.0250295
## h(Personal-1840)    0.0070376
## h(3176-Personal)    0.0327879
## h(Personal-3176)   -0.0203139
## h(76-PhD)          -0.1680282
## h(PhD-76)           0.6858917
## h(PhD-98)          -4.5352969
## 
## Selected 14 of 14 terms, and 3 of 3 predictors (pmethod="none")
## Termination condition: Reached nk 21
## Importance: PhD, Personal, Books
## Number of terms at each degree of interaction: 1 13 (additive model)
## GCV 247.5995    RSS 179246.7    GRSq 0.1619694    RSq 0.2171853
plotmo(model3)
##  plotmo grid:    Books Personal PhD
##                    500     1200  75

model4 <- earth(Grad.Rate ~ Books + Personal + PhD,data=df)
plotmo(model4)
##  plotmo grid:    Books Personal PhD
##                    500     1200  75