Cross-Validated MCP- or SCAD-penalized Regression Learner

MCP- or SCAD-penalized regression models with k-fold cross validation for choosing the regularization parameter lambda. Calls ncvreg::cv.ncvreg() from package ncvreg with family set to "gaussian" (default). Poisson family is also supported. Covariates are internally standardized by ncvreg prior to model fitting.

Dictionary

This Learner can be instantiated via lrn():

lrn("regr.cv_ncvreg")

Meta Information

• Task type: “regr”

• Predict Types: “response”

• Feature Types: “integer”, “numeric”

• Required Packages: mlr3, mlr3extralearners, ncvreg

Parameters

Id	Type	Default	Levels	Range
family	character	gaussian	gaussian, poisson	-
penalty	character	MCP	MCP, SCAD, lasso	-
gamma	numeric	-		\([0, \infty)\)
alpha	numeric	1		\([0, 1]\)
lambda.min	numeric	-		\([0, \infty)\)
nlambda	integer	100		\([1, \infty)\)
lambda	untyped	-		-
eps	numeric	1e-04		\((-\infty, \infty)\)
max.iter	integer	10000		\([1, \infty)\)
convex	logical	TRUE	TRUE, FALSE	-
dfmax	integer	-		\([0, \infty)\)
penalty.factor	untyped	-		-
warn	logical	TRUE	TRUE, FALSE	-
returnX	logical	TRUE	TRUE, FALSE	-
cluster	untyped	-		-
nfolds	integer	10		\((-\infty, \infty)\)
fold	untyped	-		-
returnY	logical	FALSE	TRUE, FALSE	-
trace	logical	FALSE	TRUE, FALSE	-
pred_lambda	numeric	-		\((-\infty, \infty)\)

References

Breheny P, Huang J (2011). “Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection.” Annals of Applied Statistics, 5(1), 232–253. ISSN 1932-6157, doi:10.1214/10-AOAS388 .

See also

• Dictionary of Learners: mlr3::mlr_learners.

• as.data.table(mlr_learners) for a table of available Learners in the running session (depending on the loaded packages).

• Chapter in the mlr3book: https://mlr3book.mlr-org.com/chapters/chapter2/data_and_basic_modeling.html#sec-learners

• mlr3learners for a selection of recommended learners.

• mlr3cluster for unsupervised clustering learners.

• mlr3pipelines to combine learners with pre- and postprocessing steps.

• mlr3tuning for tuning of hyperparameters, mlr3tuningspaces for established default tuning spaces.

Author

bblodfon

Super classes

mlr3::Learner -> mlr3::LearnerRegr -> LearnerRegrNCVreg

Methods

Public methods

• LearnerRegrNCVreg$new()

• LearnerRegrNCVreg$selected_features()

• LearnerRegrNCVreg$clone()

Inherited methods

• mlr3::Learner$base_learner()
• mlr3::Learner$configure()
• mlr3::Learner$encapsulate()
• mlr3::Learner$format()
• mlr3::Learner$help()
• mlr3::Learner$predict()
• mlr3::Learner$predict_newdata()
• mlr3::Learner$print()
• mlr3::Learner$reset()
• mlr3::Learner$train()
• mlr3::LearnerRegr$predict_newdata_fast()

---

Method new()

Creates a new instance of this R6 class.

Usage

LearnerRegrNCVreg$new()

---

Method selected_features()

Returns the set of selected features which have non-zero coefficients. Calls the internal coef.cv.ncvreg() function.

Usage

LearnerRegrNCVreg$selected_features(lambda = NULL)

Arguments

lambda

(numeric(1))
Custom lambda, defaults to the lambda with the minimum CV error.

Returns

(character()) vector of feature names.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

LearnerRegrNCVreg$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# Define the Learner
learner = lrn("regr.cv_ncvreg")
print(learner)
#> 
#> ── <LearnerRegrNCVreg> (regr.cv_ncvreg): MCP- or SCAD-penalized Regression Model
#> • Model: -
#> • Parameters: list()
#> • Packages: mlr3, mlr3extralearners, and ncvreg
#> • Predict Types: [response]
#> • Feature Types: integer and numeric
#> • Encapsulation: none (fallback: -)
#> • Properties: selected_features
#> • Other settings: use_weights = 'error', predict_raw = 'FALSE'

# Define a Task
task = tsk("mtcars")

# Create train and test set
ids = partition(task)

# Train the learner on the training ids
learner$train(task, row_ids = ids$train)

print(learner$model)
#> $cve
#>   [1] 31.916993 30.308922 28.957101 26.296033 22.802877 19.902658 17.508849
#>   [8] 15.546817 13.952237 12.669707 11.651549 10.856769 10.250154  9.801492
#>  [15]  9.484888  9.278180  8.961687  8.728841  8.556624  8.555882  8.555882
#>  [22]  8.514714  8.577641  8.844261  9.230159  9.399054  9.369718  8.919063
#>  [29]  8.677058  8.695215  8.287103  7.905579  7.610632  7.541586  9.387084
#>  [36]  9.346906  9.624811 10.663012 11.282623 11.107372 10.327938 10.238523
#>  [43] 10.616530 10.675191 10.961242 11.376271 13.301047 14.444276 18.250926
#>  [50] 18.890889 18.892103 19.556045 19.556544 19.626736 19.322682 20.626546
#>  [57] 20.954863 20.955302 22.196434 22.935664 25.970661 25.971763 26.604974
#>  [64] 26.606082 26.607162 26.608216 26.374579 26.491570 26.290767 26.390964
#>  [71] 26.392001 26.393001 26.393966 26.394897 26.395797 26.396665 26.397504
#>  [78] 26.398314 26.401580 26.402432 27.446608 27.476685 27.415670 27.417292
#>  [85] 27.418867 27.420395 27.421880 27.373708 27.347775 27.348916 27.350028
#>  [92] 27.351112 27.352169 27.353256 27.320408 27.319807 27.319217 27.318636
#>  [99] 27.318065 27.317502
#> 
#> $cvse
#>   [1] 11.129327 11.142507 11.146322 10.407121  9.282810  8.304796  7.451962
#>   [8]  6.706519  6.053583  5.480799  4.977986  4.536828  4.150576  3.813785
#>  [15]  3.522051  3.271773  3.049247  2.877624  2.740661  2.737321  2.737321
#>  [22]  2.732888  2.707786  2.667476  2.661187  2.630718  2.586454  2.562948
#>  [29]  2.557664  2.576806  2.474682  2.418306  2.393961  2.380625  3.251885
#>  [36]  3.241982  3.220465  3.183109  3.113534  3.052807  2.957052  2.907307
#>  [43]  2.998633  3.015020  3.028066  2.998953  3.697663  3.917763  4.742201
#>  [50]  4.653370  4.653646  4.606833  4.606825  4.594630  4.617460  5.685547
#>  [57]  5.679430  5.679550  5.795446  5.847232  6.282895  6.283135  6.388259
#>  [64]  6.388514  6.388763  6.389006  6.402543  6.326444  6.338162  6.373419
#>  [71]  6.373579  6.373734  6.373884  6.374031  6.374173  6.374311  6.374446
#>  [78]  6.374576  6.375846  6.375963  6.740147  6.736210  6.746319  6.746951
#>  [85]  6.747564  6.748158  6.748733  6.760343  6.763632  6.764179  6.764710
#>  [92]  6.765225  6.765725  6.766266  6.762104  6.762021  6.761935  6.761847
#>  [99]  6.761756  6.761663
#> 
#> $fold
#>  [1]  1  2 10  3  6 10  8  6  9  3  8  9  4  1  4  7  7  1  5  5  2
#> 
#> $lambda
#>   [1] 4.617977367 4.306741149 4.016481209 3.745783819 3.493330526 3.257891740
#>   [7] 3.038320741 2.833548092 2.642576434 2.464475627 2.298378218 2.143475218
#>  [13] 1.999012162 1.864285433 1.738638835 1.621460396 1.512179392 1.410263562
#>  [19] 1.315216518 1.226575327 1.143908255 1.066812667 0.994913064 0.927859253
#>  [25] 0.865324645 0.807004660 0.752615247 0.701891498 0.654586360 0.610469430
#>  [31] 0.569325834 0.530955178 0.495170576 0.461797737 0.430674115 0.401648121
#>  [37] 0.374578382 0.349333053 0.325789174 0.303832074 0.283354809 0.264257643
#>  [43] 0.246447563 0.229837822 0.214347522 0.199901216 0.186428543 0.173863883
#>  [49] 0.162146040 0.151217939 0.141026356 0.131521652 0.122657533 0.114390825
#>  [55] 0.106681267 0.099491306 0.092785925 0.086532464 0.080700466 0.075261525
#>  [61] 0.070189150 0.065458636 0.061046943 0.056932583 0.053095518 0.049517058
#>  [67] 0.046179774 0.043067411 0.040164812 0.037457838 0.034933305 0.032578917
#>  [73] 0.030383207 0.028335481 0.026425764 0.024644756 0.022983782 0.021434752
#>  [79] 0.019990122 0.018642854 0.017386388 0.016214604 0.015121794 0.014102636
#>  [85] 0.013152165 0.012265753 0.011439083 0.010668127 0.009949131 0.009278593
#>  [91] 0.008653246 0.008070047 0.007526152 0.007018915 0.006545864 0.006104694
#>  [97] 0.005693258 0.005309552 0.004951706 0.004617977
#> 
#> $fit
#> $beta
#>               4.6180     4.3067     4.0165     3.7458    3.4933    3.2579
#> (Intercept) 19.21429 21.0741012 22.8085713 24.4261439 25.934698 27.341580
#> am           0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> carb         0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> cyl          0.00000 -0.2830154 -0.5469565 -0.7931089 -1.022671 -1.236762
#> disp         0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> drat         0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> gear         0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> hp           0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> qsec         0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> vs           0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> wt           0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#>                3.0383    2.8335    2.6426    2.4645    2.2984    2.1435
#> (Intercept) 28.653643 29.877277 31.018443 32.082697 33.075225 34.000860
#> am           0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> carb         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> cyl         -1.436424 -1.622629 -1.796285 -1.958237 -2.109273 -2.250131
#> disp         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> drat         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> gear         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> hp           0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> qsec         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> vs           0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> wt           0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#>                1.9990    1.8643    1.7386    1.6215  1.5122  1.4103  1.3152
#> (Intercept) 34.864109 35.669179 36.419990 37.120198 37.6110 37.6110 37.6110
#> am           0.000000  0.000000  0.000000  0.000000  0.0000  0.0000  0.0000
#> carb         0.000000  0.000000  0.000000  0.000000  0.0000  0.0000  0.0000
#> cyl         -2.381495 -2.504006 -2.618259 -2.724813 -2.7995 -2.7995 -2.7995
#> disp         0.000000  0.000000  0.000000  0.000000  0.0000  0.0000  0.0000
#> drat         0.000000  0.000000  0.000000  0.000000  0.0000  0.0000  0.0000
#> gear         0.000000  0.000000  0.000000  0.000000  0.0000  0.0000  0.0000
#> hp           0.000000  0.000000  0.000000  0.000000  0.0000  0.0000  0.0000
#> qsec         0.000000  0.000000  0.000000  0.000000  0.0000  0.0000  0.0000
#> vs           0.000000  0.000000  0.000000  0.000000  0.0000  0.0000  0.0000
#> wt           0.000000  0.000000  0.000000  0.000000  0.0000  0.0000  0.0000
#>              1.2266  1.1439  1.0668  0.9949       0.9279     0.8653    0.8070
#> (Intercept) 37.6110 37.6110 37.6110 37.6110 37.620033449 38.1196229 38.585630
#> am           0.0000  0.0000  0.0000  0.0000  0.000000000  0.0000000  0.000000
#> carb         0.0000  0.0000  0.0000  0.0000  0.000000000  0.0000000  0.000000
#> cyl         -2.7995 -2.7995 -2.7995 -2.7995 -2.796053122 -2.5573134 -2.334507
#> disp         0.0000  0.0000  0.0000  0.0000  0.000000000  0.0000000  0.000000
#> drat         0.0000  0.0000  0.0000  0.0000  0.000000000  0.0000000  0.000000
#> gear         0.0000  0.0000  0.0000  0.0000  0.000000000  0.0000000  0.000000
#> hp           0.0000  0.0000  0.0000  0.0000  0.000000000  0.0000000  0.000000
#> qsec         0.0000  0.0000  0.0000  0.0000  0.000000000  0.0000000  0.000000
#> vs           0.0000  0.0000  0.0000  0.0000  0.000000000  0.0000000  0.000000
#> wt           0.0000  0.0000  0.0000  0.0000 -0.009445264 -0.6260605 -1.201452
#>                0.7526    0.7019    0.6546      0.6105      0.5693     0.5310
#> (Intercept) 39.020097 39.425416 39.547617 39.54811416 39.55058058 39.5529591
#> am           0.000000  0.000000  0.000000  0.00000000  0.00000000  0.0000000
#> carb         0.000000  0.000000  0.000000 -0.02460781 -0.07243039 -0.1169348
#> cyl         -2.126952 -1.933151 -1.874324 -1.86416550 -1.84525138 -1.8276954
#> disp         0.000000  0.000000  0.000000  0.00000000  0.00000000  0.0000000
#> drat         0.000000  0.000000  0.000000  0.00000000  0.00000000  0.0000000
#> gear         0.000000  0.000000  0.000000  0.00000000  0.00000000  0.0000000
#> hp           0.000000  0.000000  0.000000  0.00000000  0.00000000  0.0000000
#> qsec         0.000000  0.000000  0.000000  0.00000000  0.00000000  0.0000000
#> vs           0.000000  0.000000  0.000000  0.00000000  0.00000000  0.0000000
#> wt          -1.737563 -2.238042 -2.389713 -2.38810240 -2.38380038 -2.3797318
#>                 0.4952     0.4618     0.4307     0.4016     0.3746     0.3493
#> (Intercept) 39.5551804 39.5572521 39.5591842 39.5609862 39.5626666 39.5640391
#> am           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> carb        -0.1584382 -0.1971443 -0.2332418 -0.2669064 -0.2983021 -0.3275505
#> cyl         -1.8113251 -1.7960582 -1.7818203 -1.7685419 -1.7561584 -1.7445156
#> disp         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> drat         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> gear         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> hp           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> qsec         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> vs           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> wt          -2.3759351 -2.3723942 -2.3690919 -2.3660122 -2.3631401 -2.3606152
#>                 0.3258     0.3038     0.2834     0.2643     0.2464     0.2298
#> (Intercept) 39.5654967 29.6831147 29.6819893 29.6813399 29.6809714 29.6807665
#> am           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> carb        -0.3548666 -0.6775456 -0.6776264 -0.6776753 -0.6777045 -0.6777218
#> cyl         -1.7337388 -1.3889388 -1.3887856 -1.3886915 -1.3886342 -1.3885997
#> disp         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> drat         0.0000000  1.8769200  1.8770996  1.8772015  1.8772582  1.8772889
#> gear         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> hp           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> qsec         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> vs           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> wt          -2.3581198 -1.7669708 -1.7670522 -1.7671066 -1.7671426 -1.7671660
#>                 0.2143     0.1999    0.1864    0.1739    0.1621    0.1512
#> (Intercept) 29.6806554 29.6805971 38.833734 38.834671 38.835731 38.836780
#> am           0.0000000  0.0000000  2.060614  2.060006  2.059605  2.059361
#> carb        -0.6777318 -0.6777376  0.000000  0.000000  0.000000  0.000000
#> cyl         -1.3885792 -1.3885672 -1.767438 -1.767312 -1.767224 -1.767167
#> disp         0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> drat         1.8773051  1.8773131  2.246591  2.246220  2.245867  2.245552
#> gear         0.0000000  0.0000000 -2.669314 -2.668999 -2.668773 -2.668617
#> hp           0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> qsec         0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> vs           0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> wt          -1.7671811 -1.7671907 -2.023427 -2.023850 -2.024176 -2.024418
#>                0.1410    0.1315    0.1227    0.1144    0.1067    0.0995
#> (Intercept) 38.837737 38.838562 38.839241 12.050639 12.042605 12.035142
#> am           2.059230  2.059176  2.059173  2.305128  2.305349  2.305554
#> carb         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> cyl         -1.767131 -1.767113 -1.767105 -1.176787 -1.176491 -1.176217
#> disp         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> drat         2.245286  2.245070  2.244902  2.635207  2.635194  2.635181
#> gear        -2.668516 -2.668456 -2.668425 -1.669084 -1.668738 -1.668417
#> hp           0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> qsec         0.000000  0.000000  0.000000  1.147791  1.148104  1.148394
#> vs           0.000000  0.000000  0.000000 -2.340062 -2.340319 -2.340559
#> wt          -2.024591 -2.024709 -2.024784 -2.480660 -2.480843 -2.481013
#>                0.0928    0.0865    0.0807    0.0753       0.0702       0.0655
#> (Intercept) 12.028209 12.021768 12.015784 12.005242  6.308535652  6.316121962
#> am           2.305744  2.305921  2.306085  2.306400  2.024102074  2.023925631
#> carb         0.000000  0.000000  0.000000  0.000000  0.000000000  0.000000000
#> cyl         -1.175962 -1.175726 -1.175506 -1.175119 -1.237713965 -1.237994455
#> disp         0.000000  0.000000  0.000000  0.000000  0.007940645  0.007940313
#> drat         2.635169  2.635158  2.635148  2.635103  2.538696526  2.538560233
#> gear        -1.668119 -1.667842 -1.667584 -1.667125 -1.089395491 -1.089666201
#> hp           0.000000  0.000000  0.000000  0.000000  0.000000000  0.000000000
#> qsec         1.148665  1.148915  1.149149  1.149563  1.414692634  1.414424219
#> vs          -2.340781 -2.340988 -2.341179 -2.341523 -2.423331216 -2.423189079
#> wt          -2.481171 -2.481317 -2.481453 -2.481694 -3.149178014 -3.149015731
#>                   0.0610     0.0569      0.0531     0.0495      0.0462
#> (Intercept)  6.323366354  2.7443311  2.74028554  2.7363725  2.73258771
#> am           2.023767588  1.9479402  1.94783750  1.9477381  1.94764205
#> carb         0.000000000  0.2608052  0.26095767  0.2611052  0.26124787
#> cyl         -1.238254574 -1.3394343 -1.33949953 -1.3395626 -1.33962369
#> disp         0.007939787  0.0121411  0.01214547  0.0121497  0.01215378
#> drat         2.538445051  2.5244252  2.52434627  2.5242699  2.52419611
#> gear        -1.089939241 -1.1933319 -1.19320807 -1.1930883 -1.19297246
#> hp           0.000000000  0.0000000  0.00000000  0.0000000  0.00000000
#> qsec         1.414164492  1.7060304  1.70630129  1.7065633  1.70681676
#> vs          -2.423049088 -2.8139661 -2.81430583 -2.8146345 -2.81495236
#> wt          -3.148843505 -3.7850343 -3.78559273 -3.7861329 -3.78665539
#>                  0.0431      0.0402      0.0375      0.0349     0.0326
#> (Intercept)  2.72892687  2.72538593  2.72196096  2.71864816  2.7154438
#> am           1.94754909  1.94745918  1.94737222  1.94728810  1.9472067
#> carb         0.26138588  0.26151937  0.26164848  0.26177337  0.2618942
#> cyl         -1.33968273 -1.33973984 -1.33979508 -1.33984850 -1.3399002
#> disp         0.01215774  0.01216156  0.01216526  0.01216884  0.0121723
#> drat         2.52412472  2.52405567  2.52398890  2.52392432  2.5238619
#> gear        -1.19286042 -1.19275205 -1.19264724 -1.19254587 -1.1924478
#> hp           0.00000000  0.00000000  0.00000000  0.00000000  0.0000000
#> qsec         1.70706190  1.70729901  1.70752834  1.70775017  1.7079647
#> vs          -2.81525983 -2.81555725 -2.81584492 -2.81612318 -2.8163923
#> wt          -3.78716074 -3.78764953 -3.78812231 -3.78857958 -3.7890219
#>                  0.0304      0.0283      0.0264      0.0246      0.0230
#> (Intercept)  2.71234445  2.70934656  2.70644682  2.70364204  2.70092909
#> am           1.94712805  1.94705193  1.94697831  1.94690710  1.94683823
#> carb         0.26201100  0.26212400  0.26223331  0.26233903  0.26244129
#> cyl         -1.33995015 -1.33999849 -1.34004524 -1.34009046 -1.34013419
#> disp         0.01217564  0.01217888  0.01218201  0.01218504  0.01218797
#> drat         2.52380145  2.52374303  2.52368652  2.52363188  2.52357902
#> gear        -1.19235298 -1.19226125 -1.19217252 -1.19208670 -1.19200369
#> hp           0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> qsec         1.70817226  1.70837300  1.70856715  1.70875495  1.70893660
#> vs          -2.81665264 -2.81690445 -2.81714800 -2.81738358 -2.81761143
#> wt          -3.78944968 -3.78986345 -3.79026367 -3.79065078 -3.79102520
#>                 0.0214      0.0200      0.0186      0.0174      0.0162
#> (Intercept)  2.6983050  2.69576677  2.69331168  2.69093697  2.68864002
#> am           1.9467716  1.94670718  1.94664486  1.94658458  1.94652628
#> carb         0.2625402  0.26263586  0.26272839  0.26281789  0.26290445
#> cyl         -1.3401765 -1.34021739 -1.34025695 -1.34029522 -1.34033223
#> disp         0.0121908  0.01219354  0.01219619  0.01219876  0.01220124
#> drat         2.5235279  2.52347846  2.52343064  2.52338439  2.52333965
#> gear        -1.1919234 -1.19184573 -1.19177061 -1.19169795 -1.19162766
#> hp           0.0000000  0.00000000  0.00000000  0.00000000  0.00000000
#> qsec         1.7091123  1.70928224  1.70944661  1.70960560  1.70975938
#> vs          -2.8178318 -2.81804500 -2.81825120 -2.81845063 -2.81864353
#> wt          -3.7913873 -3.79173763 -3.79207643 -3.79240413 -3.79272110
#>                  0.0151      0.0141     0.0132      0.0123      0.0114
#> (Intercept)  2.68641828  2.68426928  2.6821906  2.68018008  2.67823535
#> am           1.94646989  1.94641535  1.9463626  1.94631157  1.94626222
#> carb         0.26298818  0.26306916  0.2631475  0.26322326  0.26329653
#> cyl         -1.34036802 -1.34040264 -1.3404361 -1.34046850 -1.34049982
#> disp         0.01220363  0.01220595  0.0122082  0.01221037  0.01221247
#> drat         2.52329638  2.52325454  2.5232141  2.52317491  2.52313704
#> gear        -1.19155968 -1.19149392 -1.1914303 -1.19136879 -1.19130928
#> hp           0.00000000  0.00000000  0.0000000  0.00000000  0.00000000
#> qsec         1.70990813  1.71005200  1.7101912  1.71032576  1.71045595
#> vs          -2.81883012 -2.81901059 -2.8191851 -2.81935398 -2.81951729
#> wt          -3.79302768 -3.79332421 -3.7936110 -3.79388845 -3.79415678
#>                 0.0107      0.0099      0.0093     0.0087      0.0081
#> (Intercept)  2.6763543  2.67453484  2.67277496  2.6710727  2.66942621
#> am           1.9462145  1.94616832  1.94612366  1.9460805  1.94603869
#> carb         0.2633674  0.26343597  0.26350228  0.2635664  0.26362845
#> cyl         -1.3405301 -1.34055941 -1.34058775 -1.3406152 -1.34064166
#> disp         0.0122145  0.01221646  0.01221836  0.0122202  0.01222197
#> drat         2.5231004  2.52306500  2.52303073  2.5229976  2.52296554
#> gear        -1.1912517 -1.19119604 -1.19114218 -1.1910901 -1.19103969
#> hp           0.0000000  0.00000000  0.00000000  0.0000000  0.00000000
#> qsec         1.7105819  1.71070368  1.71082150  1.7109355  1.71104567
#> vs          -2.8196752 -2.81982802 -2.81997580 -2.8201187 -2.82025698
#> wt          -3.7944163 -3.79466735 -3.79491016 -3.7951450 -3.79537217
#>                  0.0075      0.0070      0.0065      0.0061      0.0057
#> (Intercept)  2.66783362  2.66629319  2.66480320  2.66336202  2.66196803
#> am           1.94599829  1.94595921  1.94592141  1.94588484  1.94584948
#> carb         0.26368845  0.26374648  0.26380262  0.26385691  0.26390942
#> cyl         -1.34066730 -1.34069209 -1.34071608 -1.34073927 -1.34076171
#> disp         0.01222369  0.01222536  0.01222696  0.01222852  0.01223002
#> drat         2.52293453  2.52290455  2.52287554  2.52284749  2.52282035
#> gear        -1.19099095 -1.19094381 -1.19089821 -1.19085410 -1.19081143
#> hp           0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> qsec         1.71115228  1.71125540  1.71135514  1.71145161  1.71154493
#> vs          -2.82039070 -2.82052004 -2.82064514 -2.82076614 -2.82088318
#> wt          -3.79559188 -3.79580440 -3.79600996 -3.79620878 -3.79640109
#>                  0.0053      0.0050      0.0046
#> (Intercept)  2.66061969  2.65931551  2.65805405
#> am           1.94581528  1.94578219  1.94575019
#> carb         0.26396022  0.26400935  0.26405687
#> cyl         -1.34078341 -1.34080440 -1.34082469
#> disp         0.01223148  0.01223289  0.01223425
#> drat         2.52279410  2.52276872  2.52274416
#> gear        -1.19077017 -1.19073025 -1.19069164
#> hp           0.00000000  0.00000000  0.00000000
#> qsec         1.71163518  1.71172248  1.71180692
#> vs          -2.82099638 -2.82110588 -2.82121178
#> wt          -3.79658709 -3.79676701 -3.79694102
#> 
#> $iter
#>   [1]   0   2   2   2   2   2   2   2   2   2   2   2   2   2   2   2   2   1
#>  [19]   1   1   1   1   1   8  28  28  27  27  10   5   5   5   5   5   5   5
#>  [37]   5   4   4  31   1   1   1   1   1   1  74   1   1   1   1   1   1 163
#>  [55]   1   1   1   1   1   2  67   1   1 124   1   1   1   1   1   1   1   1
#>  [73]   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1
#>  [91]   1   1   1   1   1   1   1   1   1   1
#> 
#> $lambda
#>   [1] 4.617977367 4.306741149 4.016481209 3.745783819 3.493330526 3.257891740
#>   [7] 3.038320741 2.833548092 2.642576434 2.464475627 2.298378218 2.143475218
#>  [13] 1.999012162 1.864285433 1.738638835 1.621460396 1.512179392 1.410263562
#>  [19] 1.315216518 1.226575327 1.143908255 1.066812667 0.994913064 0.927859253
#>  [25] 0.865324645 0.807004660 0.752615247 0.701891498 0.654586360 0.610469430
#>  [31] 0.569325834 0.530955178 0.495170576 0.461797737 0.430674115 0.401648121
#>  [37] 0.374578382 0.349333053 0.325789174 0.303832074 0.283354809 0.264257643
#>  [43] 0.246447563 0.229837822 0.214347522 0.199901216 0.186428543 0.173863883
#>  [49] 0.162146040 0.151217939 0.141026356 0.131521652 0.122657533 0.114390825
#>  [55] 0.106681267 0.099491306 0.092785925 0.086532464 0.080700466 0.075261525
#>  [61] 0.070189150 0.065458636 0.061046943 0.056932583 0.053095518 0.049517058
#>  [67] 0.046179774 0.043067411 0.040164812 0.037457838 0.034933305 0.032578917
#>  [73] 0.030383207 0.028335481 0.026425764 0.024644756 0.022983782 0.021434752
#>  [79] 0.019990122 0.018642854 0.017386388 0.016214604 0.015121794 0.014102636
#>  [85] 0.013152165 0.012265753 0.011439083 0.010668127 0.009949131 0.009278593
#>  [91] 0.008653246 0.008070047 0.007526152 0.007018915 0.006545864 0.006104694
#>  [97] 0.005693258 0.005309552 0.004951706 0.004617977
#> 
#> $penalty
#> [1] "MCP"
#> 
#> $family
#> [1] "gaussian"
#> 
#> $gamma
#> [1] 3
#> 
#> $alpha
#> [1] 1
#> 
#> $convex.min
#> [1] 23
#> 
#> $loss
#>   [1] 594.62571 508.65397 436.72583 376.82029 327.19256 286.33711 252.95578
#>   [8] 225.92999 204.29660 187.22708 174.00929 164.03179 156.77017 151.77524
#>  [15] 148.66274 147.10445 146.78570 146.78570 146.78570 146.78570 146.78570
#>  [22] 146.78570 146.78570 146.46863 128.48561 116.53097 109.58544 106.75202
#>  [29] 106.58934 105.49068 103.53681 101.93353 100.62515  99.56741  98.72226
#>  [36]  98.05696  97.54339  97.15777  96.87847  88.44692  88.44692  88.44692
#>  [43]  88.44692  88.44692  88.44692  88.44692  80.72820  80.72819  80.72819
#>  [50]  80.72818  80.72818  80.72818  80.72818  75.06260  75.06259  75.06257
#>  [57]  75.06257  75.06256  75.06255  75.06254  73.60554  73.60553  73.60552
#>  [64]  73.04885  73.04884  73.04882  73.04880  73.04879  73.04878  73.04877
#>  [71]  73.04876  73.04874  73.04873  73.04873  73.04872  73.04871  73.04870
#>  [78]  73.04869  73.04869  73.04868  73.04868  73.04867  73.04867  73.04866
#>  [85]  73.04866  73.04865  73.04865  73.04865  73.04864  73.04864  73.04864
#>  [92]  73.04863  73.04863  73.04863  73.04863  73.04862  73.04862  73.04862
#>  [99]  73.04862  73.04862
#> 
#> $linear.predictors
#>      4.6180   4.3067   4.0165   3.7458   3.4933   3.2579   3.0383   2.8335
#> 1  19.21429 19.94204 20.62075 21.25371 21.84401 22.39453 22.90795 23.38676
#> 2  19.21429 19.37601 19.52683 19.66749 19.79867 19.92101 20.03510 20.14150
#> 3  19.21429 18.80998 18.43292 18.08127 17.75333 17.44748 17.16225 16.89624
#> 4  19.21429 19.37601 19.52683 19.66749 19.79867 19.92101 20.03510 20.14150
#> 5  19.21429 18.80998 18.43292 18.08127 17.75333 17.44748 17.16225 16.89624
#> 6  19.21429 19.94204 20.62075 21.25371 21.84401 22.39453 22.90795 23.38676
#> 7  19.21429 19.37601 19.52683 19.66749 19.79867 19.92101 20.03510 20.14150
#> 8  19.21429 19.37601 19.52683 19.66749 19.79867 19.92101 20.03510 20.14150
#> 9  19.21429 18.80998 18.43292 18.08127 17.75333 17.44748 17.16225 16.89624
#> 10 19.21429 18.80998 18.43292 18.08127 17.75333 17.44748 17.16225 16.89624
#> 11 19.21429 18.80998 18.43292 18.08127 17.75333 17.44748 17.16225 16.89624
#> 12 19.21429 18.80998 18.43292 18.08127 17.75333 17.44748 17.16225 16.89624
#> 13 19.21429 19.94204 20.62075 21.25371 21.84401 22.39453 22.90795 23.38676
#> 14 19.21429 19.94204 20.62075 21.25371 21.84401 22.39453 22.90795 23.38676
#> 15 19.21429 18.80998 18.43292 18.08127 17.75333 17.44748 17.16225 16.89624
#> 16 19.21429 18.80998 18.43292 18.08127 17.75333 17.44748 17.16225 16.89624
#> 17 19.21429 18.80998 18.43292 18.08127 17.75333 17.44748 17.16225 16.89624
#> 18 19.21429 19.94204 20.62075 21.25371 21.84401 22.39453 22.90795 23.38676
#> 19 19.21429 18.80998 18.43292 18.08127 17.75333 17.44748 17.16225 16.89624
#> 20 19.21429 19.37601 19.52683 19.66749 19.79867 19.92101 20.03510 20.14150
#> 21 19.21429 18.80998 18.43292 18.08127 17.75333 17.44748 17.16225 16.89624
#>      2.6426   2.4645   2.2984   2.1435   1.9990   1.8643   1.7386   1.6215
#> 1  23.83330 24.24975 24.63813 25.00034 25.33813 25.65316 25.94695 26.22095
#> 2  20.24073 20.33328 20.41958 20.50007 20.57514 20.64515 20.71043 20.77132
#> 3  16.64816 16.41680 16.20104 15.99981 15.81215 15.63713 15.47392 15.32170
#> 4  20.24073 20.33328 20.41958 20.50007 20.57514 20.64515 20.71043 20.77132
#> 5  16.64816 16.41680 16.20104 15.99981 15.81215 15.63713 15.47392 15.32170
#> 6  23.83330 24.24975 24.63813 25.00034 25.33813 25.65316 25.94695 26.22095
#> 7  20.24073 20.33328 20.41958 20.50007 20.57514 20.64515 20.71043 20.77132
#> 8  20.24073 20.33328 20.41958 20.50007 20.57514 20.64515 20.71043 20.77132
#> 9  16.64816 16.41680 16.20104 15.99981 15.81215 15.63713 15.47392 15.32170
#> 10 16.64816 16.41680 16.20104 15.99981 15.81215 15.63713 15.47392 15.32170
#> 11 16.64816 16.41680 16.20104 15.99981 15.81215 15.63713 15.47392 15.32170
#> 12 16.64816 16.41680 16.20104 15.99981 15.81215 15.63713 15.47392 15.32170
#> 13 23.83330 24.24975 24.63813 25.00034 25.33813 25.65316 25.94695 26.22095
#> 14 23.83330 24.24975 24.63813 25.00034 25.33813 25.65316 25.94695 26.22095
#> 15 16.64816 16.41680 16.20104 15.99981 15.81215 15.63713 15.47392 15.32170
#> 16 16.64816 16.41680 16.20104 15.99981 15.81215 15.63713 15.47392 15.32170
#> 17 16.64816 16.41680 16.20104 15.99981 15.81215 15.63713 15.47392 15.32170
#> 18 23.83330 24.24975 24.63813 25.00034 25.33813 25.65316 25.94695 26.22095
#> 19 16.64816 16.41680 16.20104 15.99981 15.81215 15.63713 15.47392 15.32170
#> 20 20.24073 20.33328 20.41958 20.50007 20.57514 20.64515 20.71043 20.77132
#> 21 16.64816 16.41680 16.20104 15.99981 15.81215 15.63713 15.47392 15.32170
#>    1.5122 1.4103 1.3152 1.2266 1.1439 1.0668 0.9949   0.9279   0.8653   0.8070
#> 1  26.413 26.413 26.413 26.413 26.413 26.413 26.413 26.41391 26.43791 26.46023
#> 2  20.814 20.814 20.814 20.814 20.814 20.814 20.814 20.81335 20.76296 20.71592
#> 3  15.215 15.215 15.215 15.215 15.215 15.215 15.215 15.21912 15.50747 15.77658
#> 4  20.814 20.814 20.814 20.814 20.814 20.814 20.814 20.81103 20.60957 20.42156
#> 5  15.215 15.215 15.215 15.215 15.215 15.215 15.215 15.21789 15.42608 15.62039
#> 6  26.413 26.413 26.413 26.413 26.413 26.413 26.413 26.40569 25.89324 25.41497
#> 7  20.814 20.814 20.814 20.814 20.814 20.814 20.814 20.81122 20.62209 20.44559
#> 8  20.814 20.814 20.814 20.814 20.814 20.814 20.814 20.81122 20.62209 20.44559
#> 9  15.215 15.215 15.215 15.215 15.215 15.215 15.215 15.21638 15.32591 15.42816
#> 10 15.215 15.215 15.215 15.215 15.215 15.215 15.215 15.21591 15.29461 15.36809
#> 11 15.215 15.215 15.215 15.215 15.215 15.215 15.215 15.20202 14.37430 13.60195
#> 12 15.215 15.215 15.215 15.215 15.215 15.215 15.215 15.20112 14.31482 13.48781
#> 13 26.413 26.413 26.413 26.413 26.413 26.413 26.413 26.41504 26.51304 26.60441
#> 14 26.413 26.413 26.413 26.413 26.413 26.413 26.413 26.42057 26.87928 27.30726
#> 15 15.215 15.215 15.215 15.215 15.215 15.215 15.215 15.21836 15.45738 15.68046
#> 16 15.215 15.215 15.215 15.215 15.215 15.215 15.215 15.21916 15.51060 15.78259
#> 17 15.215 15.215 15.215 15.215 15.215 15.215 15.215 15.21529 15.25391 15.28999
#> 18 26.413 26.413 26.413 26.413 26.413 26.413 26.413 26.41561 26.55060 26.67650
#> 19 15.215 15.215 15.215 15.215 15.215 15.215 15.215 15.22167 15.67650 16.10097
#> 20 20.814 20.814 20.814 20.814 20.814 20.814 20.814 20.81755 21.04155 21.25057
#> 21 15.215 15.215 15.215 15.215 15.215 15.215 15.215 15.21789 15.42608 15.62039
#>      0.7526   0.7019   0.6546   0.6105   0.5693   0.5310   0.4952   0.4618
#> 1  26.48114 26.50055 26.50619 26.52645 26.56673 26.60426 26.63927 26.67192
#> 2  20.67212 20.63120 20.61875 20.66076 20.74272 20.81901 20.89016 20.95651
#> 3  16.02726 16.26134 16.33242 16.37050 16.44344 16.51125 16.57449 16.63346
#> 4  20.24642 20.08288 20.03327 20.07568 20.15869 20.23598 20.30806 20.37527
#> 5  15.80138 15.97040 16.02175 16.01083 15.98868 15.96801 15.94874 15.93076
#> 6  24.96946 24.55346 24.42714 24.42419 24.42039 24.41696 24.41377 24.41079
#> 7  20.28117 20.12764 20.08106 20.04962 19.98908 19.93277 19.88026 19.83129
#> 8  20.28117 20.12764 20.08106 20.04962 19.98908 19.93277 19.88026 19.83129
#> 9  15.52337 15.61231 15.63940 15.65334 15.67970 15.70419 15.72703 15.74832
#> 10 15.43649 15.50041 15.51991 15.53394 15.56051 15.58520 15.60823 15.62970
#> 11 12.88227 12.21049 12.00704 11.99882 11.98390 11.97006 11.95717 11.94514
#> 12 12.71720 11.99787 11.78001 11.77195 11.75743 11.74399 11.73145 11.71976
#> 13 26.68965 26.76912 26.79296 26.81302 26.85278 26.88983 26.92438 26.95661
#> 14 27.70612 28.07837 28.19094 28.18545 28.17488 28.16504 28.15587 28.14731
#> 15 15.88826 16.08230 16.14124 16.17945 16.25273 16.32087 16.38441 16.44367
#> 16 16.03595 16.27253 16.34437 16.38244 16.45535 16.52315 16.58637 16.64532
#> 17 15.32355 15.35493 15.36458 15.40332 15.47800 15.54746 15.61223 15.67264
#> 18 26.79390 26.90340 26.93634 26.93170 26.92338 26.91568 26.90850 26.90181
#> 19 16.49640 16.86561 16.97764 16.96607 16.94220 16.91991 16.89911 16.87972
#> 20 21.44533 21.62713 21.68217 21.60043 21.44136 21.29332 21.15526 21.02650
#> 21 15.80138 15.97040 16.02175 15.91240 15.69896 15.50027 15.31499 15.14218
#>      0.4307   0.4016   0.3746   0.3493   0.3258   0.3038   0.2834   0.2643
#> 1  26.70237 26.73076 26.75725 26.78180 26.80484 26.57658 26.57649 26.57644
#> 2  21.01839 21.07610 21.12992 21.18002 21.22684 20.77204 20.77204 20.77205
#> 3  16.68846 16.73976 16.78759 16.83230 16.87392 17.05043 17.05066 17.05080
#> 4  20.43796 20.49643 20.55095 20.60167 20.64910 19.73852 19.73844 19.73840
#> 5  15.91400 15.89836 15.88378 15.87032 15.85763 15.57825 15.57831 15.57835
#> 6  24.40802 24.40543 24.40301 24.40051 24.39841 24.06147 24.06120 24.06103
#> 7  19.78562 19.74303 19.70331 19.66623 19.63167 19.91845 19.91834 19.91827
#> 8  19.78562 19.74303 19.70331 19.66623 19.63167 19.91845 19.91834 19.91827
#> 9  15.76818 15.78671 15.80398 15.82017 15.83520 15.71031 15.71042 15.71048
#> 10 15.64973 15.66841 15.68582 15.70214 15.71729 15.62196 15.62206 15.62213
#> 11 11.93392 11.92346 11.91371 11.90448 11.89599 12.08420 12.08408 12.08400
#> 12 11.70886 11.69869 11.68921 11.68022 11.67197 12.47941 12.47934 12.47928
#> 13 26.98666 27.01469 27.04082 27.06507 27.08781 27.22031 27.22027 27.22025
#> 14 28.13934 28.13190 28.12496 28.11848 28.11244 29.17183 29.17191 29.17195
#> 15 16.49893 16.55048 16.59854 16.64345 16.68527 16.17707 16.17722 16.17732
#> 16 16.70031 16.75159 16.79941 16.84410 16.88571 17.05927 17.05949 17.05963
#> 17 15.72898 15.78152 15.83052 15.87625 15.91888 16.20342 16.20360 16.20371
#> 18 26.89556 26.88974 26.88431 26.87916 26.87443 27.30571 27.30565 27.30562
#> 19 16.86163 16.84477 16.82904 16.81456 16.80088 18.18073 18.18100 18.18117
#> 20 20.90643 20.79444 20.69001 20.59274 20.50187 19.18415 19.18388 19.18372
#> 21 14.98103 14.83074 14.69057 14.56011 14.43817 13.48745 13.48725 13.48713
#>      0.2464   0.2298   0.2143   0.1999   0.1864   0.1739   0.1621   0.1512
#> 1  26.57640 26.57638 26.57637 26.57636 27.10236 27.10205 27.10185 27.10173
#> 2  20.77205 20.77206 20.77206 20.77206 20.63534 20.63548 20.63561 20.63573
#> 3  17.05088 17.05093 17.05097 17.05099 16.80246 16.80273 16.80293 16.80309
#> 4  19.73838 19.73837 19.73836 19.73836 19.42069 19.42085 19.42101 19.42117
#> 5  15.57838 15.57840 15.57841 15.57841 16.67421 16.67440 16.67454 16.67465
#> 6  24.06092 24.06086 24.06082 24.06080 22.92191 22.92190 22.92187 22.92184
#> 7  19.91823 19.91820 19.91819 19.91818 19.39789 19.39794 19.39793 19.39788
#> 8  19.91823 19.91820 19.91819 19.91818 19.39789 19.39794 19.39793 19.39788
#> 9  15.71053 15.71055 15.71057 15.71058 16.03594 16.03611 16.03625 16.03636
#> 10 15.62217 15.62219 15.62221 15.62222 15.93477 15.93492 15.93505 15.93514
#> 11 12.08395 12.08392 12.08390 12.08389 12.64580 12.64539 12.64509 12.64487
#> 12 12.47925 12.47922 12.47921 12.47920 13.12756 13.12699 13.12655 13.12621
#> 13 27.22023 27.22022 27.22021 27.22021 27.86189 27.86154 27.86130 27.86114
#> 14 29.17197 29.17199 29.17199 29.17199 30.95520 30.95478 30.95443 30.95414
#> 15 16.17738 16.17742 16.17744 16.17746 15.76441 15.76479 15.76511 15.76537
#> 16 17.05972 17.05977 17.05980 17.05982 16.81257 16.81285 16.81306 16.81321
#> 17 16.20378 16.20382 16.20385 16.20386 15.82571 15.82583 15.82593 15.82601
#> 18 27.30559 27.30558 27.30557 27.30556 26.10029 26.10015 26.10003 26.09993
#> 19 18.18127 18.18132 18.18136 18.18138 16.47462 16.47463 16.47460 16.47455
#> 20 19.18363 19.18357 19.18354 19.18352 19.47091 19.47106 19.47120 19.47132
#> 21 13.48706 13.48701 13.48699 13.48698 14.13757 14.13766 14.13774 14.13780
#>      0.1410   0.1315   0.1227   0.1144   0.1067   0.0995   0.0928   0.0865
#> 1  27.10168 27.10166 27.10167 26.38302 26.38286 26.38272 26.38258 26.38245
#> 2  20.63582 20.63590 20.63595 20.09677 20.09674 20.09672 20.09669 20.09667
#> 3  16.80319 16.80327 16.80331 16.93192 16.93194 16.93196 16.93198 16.93199
#> 4  19.42130 19.42142 19.42151 19.54102 19.54120 19.54136 19.54151 19.54165
#> 5  16.67471 16.67476 16.67478 15.41316 15.41278 15.41243 15.41211 15.41181
#> 6  22.92181 22.92178 22.92175 23.09352 23.09341 23.09332 23.09323 23.09315
#> 7  19.39781 19.39774 19.39767 18.77463 18.77454 18.77445 18.77437 18.77430
#> 8  19.39781 19.39774 19.39767 19.46331 19.46340 19.46349 19.46357 19.46365
#> 9  16.03644 16.03650 16.03653 16.66743 16.66758 16.66772 16.66785 16.66797
#> 10 15.93521 15.93526 15.93529 17.00252 17.00278 17.00303 17.00326 17.00347
#> 11 12.64472 12.64463 12.64457 12.96406 12.96405 12.96405 12.96404 12.96403
#> 12 13.12597 13.12580 13.12569 12.87620 12.87599 12.87580 12.87563 12.87546
#> 13 27.86104 27.86099 27.86097 28.27390 28.27403 28.27415 28.27426 28.27436
#> 14 30.95392 30.95375 30.95363 30.87461 30.87454 30.87447 30.87441 30.87435
#> 15 15.76557 15.76571 15.76582 15.53357 15.53353 15.53350 15.53347 15.53344
#> 16 16.81332 16.81339 16.81344 17.26571 17.26582 17.26592 17.26601 17.26610
#> 17 15.82606 15.82610 15.82613 15.77722 15.77718 15.77714 15.77710 15.77707
#> 18 26.09985 26.09979 26.09975 26.83666 26.83653 26.83641 26.83630 26.83620
#> 19 16.47449 16.47443 16.47437 16.49590 16.49608 16.49624 16.49640 16.49654
#> 20 19.47142 19.47149 19.47155 19.40840 19.40839 19.40837 19.40835 19.40834
#> 21 14.13786 14.13790 14.13793 13.82647 13.82662 13.82675 13.82688 13.82700
#>      0.0807   0.0753   0.0702   0.0655   0.0610   0.0569   0.0531   0.0495
#> 1  26.38233 26.38213 26.25378 26.25394 26.25410 26.00627 26.00608 26.00590
#> 2  20.09665 20.09661 20.43562 20.43565 20.43567 20.47855 20.47865 20.47875
#> 3  16.93201 16.93203 17.23906 17.23903 17.23900 17.30933 17.30945 17.30957
#> 4  19.54178 19.54203 19.69311 19.69303 19.69294 19.67345 19.67350 19.67356
#> 5  15.41153 15.41103 15.31265 15.31295 15.31324 15.47723 15.47726 15.47729
#> 6  23.09308 23.09294 23.35742 23.35755 23.35765 23.46349 23.46363 23.46376
#> 7  18.77423 18.77409 18.43958 18.43960 18.43963 18.29409 18.29387 18.29367
#> 8  19.46372 19.46383 19.28840 19.28826 19.28813 19.31770 19.31765 19.31761
#> 9  16.66808 16.66828 16.27462 16.27452 16.27444 16.23774 16.23764 16.23756
#> 10 17.00367 17.00402 16.68304 16.68284 16.68266 16.73090 16.73088 16.73087
#> 11 12.96403 12.96402 13.22799 13.22799 13.22798 13.42224 13.42243 13.42261
#> 12 12.87531 12.87504 12.64410 12.64424 12.64437 12.47610 12.47592 12.47574
#> 13 28.27446 28.27464 28.19955 28.19945 28.19935 28.15254 28.15251 28.15248
#> 14 30.87429 30.87418 30.83193 30.83188 30.83183 31.11620 31.11631 31.11641
#> 15 15.53341 15.53337 15.45132 15.45141 15.45150 15.25617 15.25605 15.25594
#> 16 17.26618 17.26632 17.20624 17.20616 17.20608 17.12604 17.12600 17.12595
#> 17 15.77703 15.77698 16.14600 16.14603 16.14604 16.13650 16.13659 16.13667
#> 18 26.83610 26.83593 27.02262 27.02277 27.02291 26.92400 26.92402 26.92404
#> 19 16.49667 16.49690 17.01456 17.01431 17.01406 16.70684 16.70676 16.70668
#> 20 19.40833 19.40832 19.00536 19.00549 19.00560 19.11164 19.11164 19.11163
#> 21 13.82711 13.82731 13.77302 13.77291 13.77280 14.08299 14.08315 14.08331
#>      0.0462   0.0431   0.0402   0.0375   0.0349   0.0326   0.0304   0.0283
#> 1  26.00572 26.00555 26.00539 26.00523 26.00508 26.00493 26.00479 26.00465
#> 2  20.47884 20.47894 20.47903 20.47911 20.47920 20.47928 20.47936 20.47943
#> 3  17.30968 17.30979 17.30990 17.31001 17.31011 17.31020 17.31030 17.31039
#> 4  19.67361 19.67367 19.67372 19.67377 19.67381 19.67386 19.67390 19.67394
#> 5  15.47732 15.47735 15.47738 15.47740 15.47743 15.47745 15.47748 15.47750
#> 6  23.46389 23.46402 23.46414 23.46426 23.46438 23.46449 23.46460 23.46470
#> 7  18.29347 18.29328 18.29309 18.29291 18.29274 18.29257 18.29241 18.29225
#> 8  19.31756 19.31752 19.31747 19.31743 19.31739 19.31735 19.31731 19.31727
#> 9  16.23747 16.23739 16.23731 16.23723 16.23716 16.23708 16.23702 16.23695
#> 10 16.73086 16.73086 16.73085 16.73084 16.73083 16.73082 16.73081 16.73080
#> 11 13.42278 13.42294 13.42310 13.42326 13.42341 13.42356 13.42370 13.42383
#> 12 12.47557 12.47540 12.47524 12.47508 12.47493 12.47478 12.47464 12.47451
#> 13 28.15244 28.15241 28.15238 28.15236 28.15233 28.15230 28.15228 28.15225
#> 14 31.11651 31.11661 31.11671 31.11680 31.11689 31.11697 31.11706 31.11714
#> 15 15.25583 15.25573 15.25563 15.25553 15.25544 15.25534 15.25526 15.25517
#> 16 17.12591 17.12587 17.12584 17.12580 17.12576 17.12573 17.12570 17.12567
#> 17 16.13675 16.13683 16.13690 16.13697 16.13704 16.13711 16.13718 16.13724
#> 18 26.92405 26.92407 26.92409 26.92411 26.92412 26.92414 26.92415 26.92417
#> 19 16.70660 16.70653 16.70645 16.70638 16.70632 16.70625 16.70619 16.70612
#> 20 19.11163 19.11162 19.11162 19.11161 19.11161 19.11160 19.11160 19.11159
#> 21 14.08347 14.08362 14.08376 14.08391 14.08404 14.08417 14.08430 14.08442
#>      0.0264   0.0246   0.0230   0.0214   0.0200   0.0186   0.0174   0.0162
#> 1  26.00451 26.00438 26.00426 26.00414 26.00402 26.00390 26.00379 26.00369
#> 2  20.47950 20.47958 20.47964 20.47971 20.47977 20.47984 20.47990 20.47995
#> 3  17.31048 17.31056 17.31064 17.31072 17.31080 17.31088 17.31095 17.31102
#> 4  19.67399 19.67403 19.67406 19.67410 19.67414 19.67417 19.67421 19.67424
#> 5  15.47752 15.47754 15.47756 15.47758 15.47760 15.47762 15.47764 15.47766
#> 6  23.46480 23.46490 23.46499 23.46508 23.46517 23.46526 23.46534 23.46542
#> 7  18.29210 18.29195 18.29181 18.29167 18.29154 18.29141 18.29129 18.29117
#> 8  19.31724 19.31720 19.31717 19.31714 19.31711 19.31708 19.31705 19.31702
#> 9  16.23688 16.23682 16.23676 16.23670 16.23664 16.23659 16.23653 16.23648
#> 10 16.73080 16.73079 16.73078 16.73077 16.73077 16.73076 16.73076 16.73075
#> 11 13.42397 13.42409 13.42422 13.42433 13.42445 13.42456 13.42467 13.42477
#> 12 12.47437 12.47425 12.47412 12.47400 12.47389 12.47378 12.47367 12.47356
#> 13 28.15223 28.15220 28.15218 28.15216 28.15214 28.15212 28.15210 28.15208
#> 14 31.11721 31.11729 31.11736 31.11743 31.11750 31.11756 31.11763 31.11769
#> 15 15.25509 15.25501 15.25493 15.25486 15.25478 15.25471 15.25465 15.25458
#> 16 17.12563 17.12560 17.12558 17.12555 17.12552 17.12549 17.12547 17.12544
#> 17 16.13730 16.13736 16.13742 16.13747 16.13752 16.13758 16.13763 16.13767
#> 18 26.92418 26.92420 26.92421 26.92422 26.92424 26.92425 26.92426 26.92427
#> 19 16.70607 16.70601 16.70595 16.70590 16.70585 16.70580 16.70575 16.70570
#> 20 19.11159 19.11158 19.11158 19.11158 19.11157 19.11157 19.11157 19.11156
#> 21 14.08454 14.08466 14.08477 14.08488 14.08498 14.08508 14.08518 14.08527
#>      0.0151   0.0141   0.0132   0.0123   0.0114   0.0107   0.0099   0.0093
#> 1  26.00359 26.00349 26.00339 26.00330 26.00321 26.00312 26.00303 26.00295
#> 2  20.48001 20.48006 20.48012 20.48017 20.48022 20.48026 20.48031 20.48035
#> 3  17.31108 17.31115 17.31121 17.31127 17.31133 17.31139 17.31145 17.31150
#> 4  19.67427 19.67430 19.67433 19.67436 19.67439 19.67441 19.67444 19.67447
#> 5  15.47767 15.47769 15.47771 15.47772 15.47774 15.47775 15.47776 15.47778
#> 6  23.46549 23.46557 23.46564 23.46571 23.46578 23.46584 23.46591 23.46597
#> 7  18.29105 18.29094 18.29083 18.29072 18.29062 18.29052 18.29043 18.29033
#> 8  19.31699 19.31697 19.31694 19.31692 19.31689 19.31687 19.31685 19.31683
#> 9  16.23643 16.23638 16.23634 16.23629 16.23625 16.23621 16.23616 16.23612
#> 10 16.73074 16.73074 16.73073 16.73073 16.73072 16.73072 16.73071 16.73071
#> 11 13.42487 13.42497 13.42507 13.42516 13.42525 13.42533 13.42541 13.42549
#> 12 12.47346 12.47336 12.47327 12.47318 12.47309 12.47300 12.47292 12.47284
#> 13 28.15206 28.15204 28.15203 28.15201 28.15199 28.15198 28.15196 28.15195
#> 14 31.11775 31.11781 31.11786 31.11792 31.11797 31.11802 31.11807 31.11811
#> 15 15.25452 15.25446 15.25440 15.25434 15.25428 15.25423 15.25418 15.25413
#> 16 17.12542 17.12540 17.12538 17.12535 17.12533 17.12531 17.12529 17.12527
#> 17 16.13772 16.13777 16.13781 16.13785 16.13789 16.13793 16.13797 16.13801
#> 18 26.92428 26.92429 26.92430 26.92431 26.92432 26.92433 26.92434 26.92435
#> 19 16.70565 16.70561 16.70557 16.70553 16.70549 16.70545 16.70541 16.70538
#> 20 19.11156 19.11156 19.11155 19.11155 19.11155 19.11155 19.11154 19.11154
#> 21 14.08536 14.08545 14.08554 14.08562 14.08570 14.08578 14.08585 14.08592
#>      0.0087   0.0081   0.0075   0.0070   0.0065   0.0061   0.0057   0.0053
#> 1  26.00287 26.00280 26.00272 26.00265 26.00258 26.00252 26.00245 26.00239
#> 2  20.48040 20.48044 20.48048 20.48052 20.48055 20.48059 20.48063 20.48066
#> 3  17.31155 17.31160 17.31165 17.31170 17.31174 17.31178 17.31183 17.31187
#> 4  19.67449 19.67451 19.67454 19.67456 19.67458 19.67460 19.67462 19.67464
#> 5  15.47779 15.47780 15.47781 15.47783 15.47784 15.47785 15.47786 15.47787
#> 6  23.46603 23.46608 23.46614 23.46619 23.46624 23.46629 23.46634 23.46639
#> 7  18.29024 18.29016 18.29007 18.28999 18.28992 18.28984 18.28977 18.28970
#> 8  19.31681 19.31679 19.31677 19.31675 19.31673 19.31671 19.31669 19.31668
#> 9  16.23609 16.23605 16.23601 16.23598 16.23595 16.23591 16.23588 16.23585
#> 10 16.73070 16.73070 16.73070 16.73069 16.73069 16.73068 16.73068 16.73068
#> 11 13.42557 13.42565 13.42572 13.42579 13.42586 13.42592 13.42598 13.42605
#> 12 12.47276 12.47269 12.47261 12.47254 12.47248 12.47241 12.47235 12.47229
#> 13 28.15193 28.15192 28.15191 28.15189 28.15188 28.15187 28.15186 28.15185
#> 14 31.11816 31.11820 31.11825 31.11829 31.11833 31.11836 31.11840 31.11844
#> 15 15.25408 15.25403 15.25399 15.25394 15.25390 15.25386 15.25382 15.25378
#> 16 17.12526 17.12524 17.12522 17.12521 17.12519 17.12517 17.12516 17.12515
#> 17 16.13804 16.13808 16.13811 16.13814 16.13817 16.13820 16.13823 16.13826
#> 18 26.92436 26.92436 26.92437 26.92438 26.92439 26.92439 26.92440 26.92441
#> 19 16.70534 16.70531 16.70527 16.70524 16.70521 16.70518 16.70515 16.70513
#> 20 19.11154 19.11154 19.11153 19.11153 19.11153 19.11153 19.11153 19.11152
#> 21 14.08599 14.08606 14.08613 14.08619 14.08625 14.08631 14.08637 14.08642
#>      0.0050   0.0046
#> 1  26.00233 26.00227
#> 2  20.48069 20.48072
#> 3  17.31191 17.31194
#> 4  19.67466 19.67468
#> 5  15.47788 15.47789
#> 6  23.46643 23.46648
#> 7  18.28963 18.28956
#> 8  19.31666 19.31665
#> 9  16.23582 16.23579
#> 10 16.73067 16.73067
#> 11 13.42610 13.42616
#> 12 12.47223 12.47217
#> 13 28.15184 28.15183
#> 14 31.11847 31.11851
#> 15 15.25375 15.25371
#> 16 17.12513 17.12512
#> 17 16.13829 16.13832
#> 18 26.92441 26.92442
#> 19 16.70510 16.70507
#> 20 19.11152 19.11152
#> 21 14.08648 14.08653
#> 
#> $penalty.factor
#>  [1] 1 1 1 1 1 1 1 1 1 1
#> 
#> $n
#> [1] 21
#> 
#> $y
#>  [1] 22.8 21.4 18.7 18.1 14.3 24.4 19.2 17.8 17.3 15.2 10.4 14.7 32.4 30.4 15.5
#> [16] 15.2 19.2 26.0 15.8 19.7 15.0
#> 
#> $X
#>               am        carb        cyl        disp        drat       gear
#>  [1,]  1.4142136 -1.12763391 -1.5588457 -1.25777566  0.59763321  0.4291975
#>  [2,] -0.7071068 -1.12763391 -0.3464102  0.02766764 -0.75204961 -0.8583951
#>  [3,] -0.7071068 -0.55006532  0.8660254  0.90176908 -0.62935117 -0.8583951
#>  [4,] -0.7071068 -1.12763391 -0.3464102 -0.25512989 -1.31295675 -0.8583951
#>  [5,] -0.7071068  0.60507186  0.8660254  0.90176908 -0.52418108 -0.8583951
#>  [6,] -0.7071068 -0.55006532 -1.5588457 -0.92613129  0.31717963  0.4291975
#>  [7,] -0.7071068  0.60507186 -0.3464102 -0.74702619  0.72033164  0.4291975
#>  [8,] -0.7071068  0.60507186 -0.3464102 -0.74702619  0.72033164  0.4291975
#>  [9,] -0.7071068  0.02750327  0.8660254  0.18020691 -0.76957796 -0.8583951
#> [10,] -0.7071068  0.02750327  0.8660254  0.18020691 -0.76957796 -0.8583951
#> [11,] -0.7071068  0.60507186  0.8660254  1.86156673 -1.01497483 -0.8583951
#> [12,] -0.7071068  0.60507186  0.8660254  1.58733883 -0.48912438 -0.8583951
#> [13,]  1.4142136 -1.12763391 -1.5588457 -1.50886558  1.00078522  0.4291975
#> [14,]  1.4142136 -0.55006532 -1.5588457 -1.53457445  2.49069482  0.4291975
#> [15,] -0.7071068 -0.55006532  0.8660254  0.54184495 -1.31295675 -0.8583951
#> [16,] -0.7071068 -0.55006532  0.8660254  0.42187025 -0.62935117 -0.8583951
#> [17,] -0.7071068 -0.55006532  0.8660254  1.24455395 -0.75204961 -0.8583951
#> [18,]  1.4142136 -0.55006532 -1.5588457 -1.15236931  1.61427741  1.7167902
#> [19,]  1.4142136  0.60507186  0.8660254  0.82464248  1.24618209  1.7167902
#> [20,]  1.4142136  1.76020904 -0.3464102 -0.94069964  0.19448120  1.7167902
#> [21,]  1.4142136  2.91534622  0.8660254  0.39616138  0.05425441  1.7167902
#>                hp         qsec         vs          wt
#>  [1,] -0.90124282  0.634112625  1.2747549 -1.20015627
#>  [2,] -0.66041671  1.161179055  1.2747549 -0.16186227
#>  [3,]  0.26038902 -0.375568851 -0.7844645  0.09916136
#>  [4,] -0.73124792  1.656494496  1.2747549  0.12236346
#>  [5,]  1.25202596 -1.124892210 -0.7844645  0.24997501
#>  [6,] -1.34039632  1.516790141  1.2747549 -0.19086490
#>  [7,] -0.47625556  0.437256488  1.2747549  0.09916136
#>  [8,] -0.47625556  0.818268366  1.2747549  0.09916136
#>  [9,]  0.33122023 -0.007257369 -0.7844645  0.43559182
#> [10,]  0.33122023  0.246750549 -0.7844645  0.49359707
#> [11,]  0.68537628  0.234050153 -0.7844645  2.19895146
#> [12,]  1.03953233 -0.121560932 -0.7844645  2.30916144
#> [13,] -1.28373135  1.180229649  1.2747549 -1.33936888
#> [14,] -1.48205874  0.576960843  1.2747549 -2.01803032
#> [15,] -0.09376703 -0.470821820 -0.7844645  0.19196976
#> [16,] -0.09376703 -0.197763308 -0.7844645  0.09336083
#> [17,]  0.26038902 -0.356518257 -0.7844645  0.56900390
#> [18,] -0.92957531 -0.578775185 -0.7844645 -1.40897518
#> [19,]  1.52118455 -1.975818737 -0.7844645 -0.21406700
#> [20,]  0.26038902 -1.340798941 -0.7844645 -0.67810901
#> [21,]  2.52698773 -1.912316757 -0.7844645  0.24997501
#> attr(,"center")
#>  [1]   0.3333333   2.9523810   6.5714286 254.7714286   3.5090476   3.6666667
#>  [7] 156.6190476  17.6114286   0.3809524   3.3545238
#> attr(,"scale")
#>  [1]   0.4714045   1.7313961   1.6495722 116.6912619   0.5705044   0.7766432
#>  [7]  70.5903516   1.5747541   0.4856209   0.8619909
#> attr(,"nonsingular")
#>  [1]  1  2  3  4  5  6  7  8  9 10
#> 
#> attr(,"class")
#> [1] "ncvreg"
#> 
#> $min
#> [1] 34
#> 
#> $lambda.min
#> [1] 0.4617977
#> 
#> $null.dev
#> [1] 28.31551
#> 
#> $Bias
#> [1] 2.724912
#> 
#> attr(,"class")
#> [1] "cv.ncvreg"


# Make predictions for the test rows
predictions = learner$predict(task, row_ids = ids$test)

# Score the predictions
predictions$score()
#> regr.mse 
#> 8.286242