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()

---

LearnerRegrNCVreg$new()

Creates a new instance of this R6 class.

Usage

LearnerRegrNCVreg$new()

---

LearnerRegrNCVreg$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.

---

LearnerRegrNCVreg$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] 36.427478 34.246119 29.827599 25.647328 22.208686 19.401789 17.131959
#>   [8] 15.317687 13.888859 12.785219 11.955037 11.353954 10.943975 10.692607
#>  [15] 10.581922 10.452297 10.224761  9.735844  9.369347  8.895112  8.501647
#>  [22]  8.180712  7.921373  7.714310  7.551428  7.425832  7.331581  7.263583
#>  [29]  7.217477  7.185648  7.098912  6.977605  6.895888  6.835868  8.317669
#>  [36]  8.471690  8.664745  8.895460  9.073026  9.192626 10.491386 10.482114
#>  [43] 10.901530 11.014503 10.968374 16.994398 25.770639 26.398818 26.882552
#>  [50] 26.928071 27.948305 27.845678 28.620873 28.569953 28.571912 28.394714
#>  [57] 28.155073 27.705260 27.985823 28.212219 28.609955 28.549214 29.580556
#>  [64] 30.117810 30.216074 30.216599 30.014509 29.950476 29.170683 29.472371
#>  [71] 29.470098 29.690527 29.688463 29.702781 29.705861 29.817493 30.174057
#>  [78] 30.173648 30.173262 30.172896 30.207315 30.182747 30.182336 30.181961
#>  [85] 30.181621 30.181312 30.181034 30.180784 30.180560 30.180362 30.180186
#>  [92] 30.180033 30.179899 30.179785 30.179687 30.179606 30.179526 30.177053
#>  [99] 30.177015 30.176985
#> 
#> $cvse
#>   [1] 11.906458 11.617580 10.465912  9.236294  8.230935  7.397853  6.694844
#>   [8]  6.089168  5.556717  5.080843  4.651076  4.261914  3.911775  3.602109
#>  [15]  3.335137  3.129422  2.963665  2.778095  2.678512  2.554949  2.443521
#>  [22]  2.343943  2.255477  2.177686  2.110265  2.052952  2.005448  1.967374
#>  [29]  1.938247  1.917207  1.894772  1.869398  1.853787  1.844513  2.432816
#>  [36]  2.436633  2.445643  2.456206  2.466660  2.474116  3.318715  3.342021
#>  [43]  3.367245  3.348207  3.334733  7.834595 11.412243 11.429553 11.390221
#>  [50] 11.385406 11.348645 11.349441 11.375149 11.382835 11.383969 10.804927
#>  [57] 10.821906 10.821961 10.831418 10.816824 11.055378 11.042429 11.825375
#>  [64] 12.141128 12.133343 12.133578 12.152274 12.153669 11.637289 11.624680
#>  [71] 11.623152 11.617250 11.615841 11.612486 11.609292 11.596900 11.609614
#>  [78] 11.608543 11.607525 11.606558 11.605473 11.604932 11.604104 11.603317
#>  [85] 11.602572 11.601864 11.601194 11.600558 11.599955 11.599385 11.598844
#>  [92] 11.598332 11.597847 11.597388 11.596954 11.596543 11.596157 11.595900
#>  [99] 11.595552 11.595224
#> 
#> $fold
#>  [1]  4  8  2  6  3 10  8  3  5  7  1  1 10  6  9  9  2  4  1  5  7
#> 
#> $lambda
#>   [1] 5.038168084 4.698612417 4.381941666 4.086613464 3.811189394 3.554327984
#>   [7] 3.314778174 3.091373219 2.883025011 2.688718774 2.507508128 2.338510472
#>  [13] 2.180902693 2.033917151 1.896837942 1.768997413 1.649772908 1.538583736
#>  [19] 1.434888341 1.338181670 1.247992704 1.163882172 1.085440409 1.012285359
#>  [25] 0.944060714 0.880434181 0.821095864 0.765756751 0.714147309 0.666016170
#>  [31] 0.621128910 0.579266900 0.540226250 0.503816808 0.469861242 0.438194167
#>  [37] 0.408661346 0.381118939 0.355432798 0.331477817 0.309137322 0.288302501
#>  [43] 0.268871877 0.250750813 0.233851047 0.218090269 0.203391715 0.189683794
#>  [49] 0.176899741 0.164977291 0.153858374 0.143488834 0.133818167 0.124799270
#>  [55] 0.116388217 0.108544041 0.101228536 0.094406071 0.088043418 0.082109586
#>  [61] 0.076575675 0.071414731 0.066601617 0.062112891 0.057926690 0.054022625
#>  [67] 0.050381681 0.046986124 0.043819417 0.040866135 0.038111894 0.035543280
#>  [73] 0.033147782 0.030913732 0.028830250 0.026887188 0.025075081 0.023385105
#>  [79] 0.021809027 0.020339172 0.018968379 0.017689974 0.016497729 0.015385837
#>  [85] 0.014348883 0.013381817 0.012479927 0.011638822 0.010854404 0.010122854
#>  [91] 0.009440607 0.008804342 0.008210959 0.007657568 0.007141473 0.006660162
#>  [97] 0.006211289 0.005792669 0.005402262 0.005038168
#> 
#> $fit
#> $beta
#>               5.0382    4.6986    4.3819    4.0866    3.8112    3.5543
#> (Intercept) 20.77619 22.710582 24.514603 26.197038 27.766083 29.229379
#> am           0.00000  0.000000  0.000000  0.000000  0.000000  0.000000
#> carb         0.00000  0.000000  0.000000  0.000000  0.000000  0.000000
#> cyl          0.00000  0.000000  0.000000  0.000000  0.000000  0.000000
#> disp         0.00000  0.000000  0.000000  0.000000  0.000000  0.000000
#> drat         0.00000  0.000000  0.000000  0.000000  0.000000  0.000000
#> gear         0.00000  0.000000  0.000000  0.000000  0.000000  0.000000
#> hp           0.00000  0.000000  0.000000  0.000000  0.000000  0.000000
#> qsec         0.00000  0.000000  0.000000  0.000000  0.000000  0.000000
#> vs           0.00000  0.000000  0.000000  0.000000  0.000000  0.000000
#> wt           0.00000 -0.624333 -1.206588 -1.749601 -2.256017 -2.728302
#>                3.3148    3.0914    2.8830    2.6887    2.5075    2.3385
#> (Intercept) 30.594054 31.866755 33.053680 34.160610 35.192937 36.155688
#> 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          0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> 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          -3.168756 -3.579526 -3.962611 -4.319877 -4.653065 -4.963797
#>                2.1809    2.0339   1.8968       1.7690      1.6498     1.5386
#> (Intercept) 37.053553 37.890905 38.67182 39.276942969 38.29166112 36.6093490
#> am           0.000000  0.000000  0.00000  0.000000000  0.00000000  0.0000000
#> carb         0.000000  0.000000  0.00000  0.000000000  0.00000000  0.0000000
#> cyl          0.000000  0.000000  0.00000  0.000000000  0.00000000  0.0000000
#> disp         0.000000  0.000000  0.00000  0.000000000  0.00000000  0.0000000
#> drat         0.000000  0.000000  0.00000  0.000000000  0.00000000  0.0000000
#> gear         0.000000  0.000000  0.00000  0.000000000  0.00000000  0.0000000
#> hp           0.000000  0.000000  0.00000  0.000000000  0.00000000  0.0000000
#> qsec         0.000000  0.000000  0.00000  0.006305897  0.08528907  0.1739173
#> vs           0.000000  0.000000  0.00000  0.000000000  0.00000000  0.0000000
#> wt          -5.253587 -5.523845 -5.77589 -6.007588251 -6.14542046 -6.1139478
#>                1.4349     1.3382    1.2480    1.1639     1.0854     1.0123
#> (Intercept) 35.040349 33.5770944 32.212458 30.939794 29.7529031 28.6460046
#> am           0.000000  0.0000000  0.000000  0.000000  0.0000000  0.0000000
#> carb         0.000000  0.0000000  0.000000  0.000000  0.0000000  0.0000000
#> cyl          0.000000  0.0000000  0.000000  0.000000  0.0000000  0.0000000
#> disp         0.000000  0.0000000  0.000000  0.000000  0.0000000  0.0000000
#> drat         0.000000  0.0000000  0.000000  0.000000  0.0000000  0.0000000
#> gear         0.000000  0.0000000  0.000000  0.000000  0.0000000  0.0000000
#> hp           0.000000  0.0000000  0.000000  0.000000  0.0000000  0.0000000
#> qsec         0.256576  0.3336637  0.405556  0.472603  0.5351312  0.5934453
#> vs           0.000000  0.0000000  0.000000  0.000000  0.0000000  0.0000000
#> wt          -6.084595 -6.0572204 -6.031691 -6.007882 -5.9856774 -5.9649695
#>                 0.9441     0.8804     0.8211     0.7658    0.7141     0.6660
#> (Intercept) 27.6137074 26.6509835 25.7531441 24.9158160 24.134921 23.4066557
#> am           0.0000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> carb         0.0000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> cyl          0.0000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> disp         0.0000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> drat         0.0000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> gear         0.0000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> hp           0.0000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> qsec         0.6478292  0.6985478  0.7458481  0.7899606  0.831100  0.8694667
#> vs           0.0000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> wt          -5.9456573 -5.9276467 -5.9108499 -5.8951852 -5.880576 -5.8669518
#>                 0.6211     0.5793    0.5402    0.5038    0.4699    0.4382
#> (Intercept) 22.7274731 22.3904329 22.390429 22.390429 22.390429 22.390429
#> am           0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> carb         0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> cyl          0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> disp         0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> drat         0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> gear         0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> hp           0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> qsec         0.9052477  0.9230038  0.923004  0.923004  0.923004  0.923004
#> vs           0.0000000  0.0000000  0.000000  0.000000  0.000000  0.000000
#> wt          -5.8542457 -5.8479403 -5.847940 -5.847940 -5.847940 -5.847940
#>                0.4087    0.3811    0.3554      0.3315     0.3091     0.2883
#> (Intercept) 22.390429 22.390429 22.390429 23.10207259 24.4399031 25.6830696
#> am           0.000000  0.000000  0.000000  0.00000000  0.0000000  0.0000000
#> carb         0.000000  0.000000  0.000000 -0.05947358 -0.1713171 -0.2752418
#> cyl          0.000000  0.000000  0.000000  0.00000000  0.0000000  0.0000000
#> disp         0.000000  0.000000  0.000000  0.00000000  0.0000000  0.0000000
#> drat         0.000000  0.000000  0.000000  0.00000000  0.0000000  0.0000000
#> gear         0.000000  0.000000  0.000000  0.00000000  0.0000000  0.0000000
#> hp           0.000000  0.000000  0.000000  0.00000000  0.0000000  0.0000000
#> qsec         0.923004  0.923004  0.923004  0.88731722  0.8202302  0.7578902
#> vs           0.000000  0.000000  0.000000  0.00000000  0.0000000  0.0000000
#> wt          -5.847940 -5.847940 -5.847940 -5.81408094 -5.7503981 -5.6912251
#>                 0.2689     0.2508     0.2339    0.2181     0.2034     0.1897
#> (Intercept) 26.8454130 21.8050845 22.8807988 22.898107 22.9000045 22.9013295
#> am           0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.0000000
#> carb        -0.3724131 -0.3105211 -0.3941406 -0.395465 -0.3955779 -0.3956438
#> cyl          0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.0000000
#> disp         0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.0000000
#> drat         0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.0000000
#> gear         0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.0000000
#> hp           0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.0000000
#> qsec         0.6996031  1.0845376  1.0282319  1.027318  1.0272074  1.0271280
#> vs           0.0000000 -1.8293621 -1.7966078 -1.795977 -1.7957583 -1.7955833
#> wt          -5.6358967 -6.0094529 -5.9557549 -5.954884 -5.9547797 -5.9547122
#>                 0.1769     0.1650     0.1539     0.1435     0.1338      0.1248
#> (Intercept) 22.9022920 22.9030027 22.9035305 22.9039228 22.9042144  1.12333671
#> am           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  2.44823471
#> carb        -0.3956867 -0.3957167 -0.3957386 -0.3957547 -0.3957668 -0.36609312
#> cyl          0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  1.39302648
#> disp         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.00000000
#> drat         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  1.00602019
#> gear         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.00000000
#> hp           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000 -0.01287335
#> qsec         1.0270697  1.0270265  1.0269944  1.0269705  1.0269527  1.51388123
#> vs          -1.7954493 -1.7953485 -1.7952735 -1.7952177 -1.7951762 -1.21298922
#> wt          -5.9546656 -5.9546320 -5.9546073 -5.9545891 -5.9545755 -5.57123263
#>                  0.1164      0.1085      0.1012      0.0944      0.0880
#> (Intercept)  1.11803686  1.11340816  1.10937050  1.10585256  1.10279095
#> am           2.44885836  2.44940257  2.44987694  2.45028997  2.45064923
#> carb        -0.36613283 -0.36616848 -0.36620041 -0.36622893 -0.36625433
#> cyl          1.39331415  1.39356354  1.39377954  1.39396644  1.39412803
#> disp         0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> drat         1.00606140  1.00609972  1.00613513  1.00616768  1.00619745
#> gear         0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> hp          -0.01287172 -0.01287027 -0.01286898 -0.01286784 -0.01286682
#> qsec         1.51406975  1.51423402  1.51437698  1.51450124  1.51460913
#> vs          -1.21293014 -1.21287955 -1.21283624 -1.21279913 -1.21276734
#> wt          -5.57136771 -5.57148294 -5.57158110 -5.57166460 -5.57173552
#>                  0.0821      0.0766      0.0714      0.0666     0.0621
#> (Intercept)  1.10012941  1.09781818  1.09581324  1.09407579  1.0925716
#> am           2.45096138  2.45123235  2.45146733  2.45167091  2.4518471
#> carb        -0.36627691 -0.36629693 -0.36631465 -0.36633031 -0.3663441
#> cyl          1.39426759  1.39438804  1.39449190  1.39458138  1.3946584
#> disp         0.00000000  0.00000000  0.00000000  0.00000000  0.0000000
#> drat         1.00622456  1.00624915  1.00627138  1.00629139  1.0063094
#> gear         0.00000000  0.00000000  0.00000000  0.00000000  0.0000000
#> hp          -0.01286593 -0.01286514 -0.01286444 -0.01286384 -0.0128633
#> qsec         1.51470269  1.51478374  1.51485387  1.51491450  1.5149669
#> vs          -1.21274010 -1.21271675 -1.21269672 -1.21267954 -1.2126648
#> wt          -5.57179568 -5.57184664 -5.57188974 -5.57192615 -5.5719569
#>                  0.0579      0.0540      0.0504      0.0470     0.0438
#> (Intercept)  1.09127070  1.09014660  1.08917620  1.08833922  1.0876180
#> am           2.45199952  2.45213120  2.45224487  2.45234293  2.4524274
#> carb        -0.36635625 -0.36636692 -0.36637628 -0.36638447 -0.3663916
#> cyl          1.39472468  1.39478163  1.39483056  1.39487255  1.3949086
#> disp         0.00000000  0.00000000  0.00000000  0.00000000  0.0000000
#> drat         1.00632546  1.00633984  1.00635264  1.00636402  1.0063741
#> gear         0.00000000  0.00000000  0.00000000  0.00000000  0.0000000
#> hp          -0.01286284 -0.01286243 -0.01286207 -0.01286177 -0.0128615
#> qsec         1.51501202  1.51505094  1.51508446  1.51511329  1.5151381
#> vs          -1.21265215 -1.21264128 -1.21263195 -1.21262393 -1.2126170
#> wt          -5.57198272 -5.57200448 -5.57202275 -5.57203807 -5.5720509
#>                  0.0409      0.0381      0.0355      0.0331       0.0309
#> (Intercept)  1.08699693  1.08646267  1.08600342  1.08560896  1.682237160
#> am           2.45250023  2.45256286  2.45261672  2.45266300  2.455355364
#> carb        -0.36639789 -0.36640334 -0.36640809 -0.36641222 -0.231796369
#> cyl          1.39493943  1.39496588  1.39498851  1.39500787  1.311567452
#> disp         0.00000000  0.00000000  0.00000000  0.00000000  0.004464464
#> drat         1.00638303  1.00639092  1.00639787  1.00640398  0.888243987
#> gear         0.00000000  0.00000000  0.00000000  0.00000000  0.000000000
#> hp          -0.01286127 -0.01286106 -0.01286089 -0.01286074 -0.015988438
#> qsec         1.51515935  1.51517761  1.51519326  1.51520666  1.543856014
#> vs          -1.21261111 -1.21260600 -1.21260161 -1.21259783 -1.111257861
#> wt          -5.57206165 -5.57207061 -5.57207809 -5.57208431 -5.933096064
#>                   0.0288       0.0269       0.0251       0.0234       0.0218
#> (Intercept)  1.686380401  1.690239590  1.693830368  1.697167855  1.700266639
#> am           2.454927745  2.454526218  2.454149656  2.453796933  2.453466932
#> carb        -0.231730917 -0.231672954 -0.231621775 -0.231576733 -0.231537232
#> cyl          1.311243638  1.310943131  1.310664553  1.310406579  1.310167941
#> disp         0.004466346  0.004468005  0.004469462  0.004470737  0.004471849
#> drat         0.888020021  0.887817830  0.887635607  0.887471674  0.887324472
#> gear         0.000000000  0.000000000  0.000000000  0.000000000  0.000000000
#> hp          -0.015987594 -0.015986779 -0.015985995 -0.015985243 -0.015984524
#> qsec         1.543784975  1.543716697  1.543651227  1.543588585  1.543528776
#> vs          -1.111390476 -1.111515419 -1.111632962 -1.111743385 -1.111846976
#> wt          -5.933266590 -5.933414324 -5.933541584 -5.933650489 -5.933742975
#>                   0.0203       0.0190       0.0177       0.0165       0.0154
#> (Intercept)  2.530846608  2.530272718  2.529593968  2.528824299  2.527976583
#> am           2.478867723  2.478791060  2.478728495  2.478678807  2.478640844
#> carb        -0.209716942 -0.209859085 -0.209994971 -0.210124704 -0.210248402
#> cyl          1.242767138  1.242819870  1.242881407  1.242950545  1.243026179
#> disp         0.004202929  0.004198278  0.004193889  0.004189752  0.004185856
#> drat         0.977219598  0.977591615  0.977940666  0.978267746  0.978573836
#> gear        -0.200792198 -0.200856460 -0.200906215 -0.200942821 -0.200967545
#> hp          -0.014746456 -0.014744182 -0.014742153 -0.014740351 -0.014738759
#> qsec         1.531580601  1.531502854  1.531432135  1.531367999  1.531310017
#> vs          -1.144780280 -1.144873243 -1.144954461 -1.145024862 -1.145085322
#> wt          -5.919129515 -5.918585713 -5.918072999 -5.917590202 -5.917136149
#>                   0.0143       0.0134       0.0125       0.0116       0.0109
#> (Intercept)  2.527062674  2.526093466  2.525078939  2.524028215  2.522949602
#> am           2.478613525  2.478595837  2.478586830  2.478585617  2.478591373
#> carb        -0.210366197 -0.210478230 -0.210584652 -0.210685621 -0.210781300
#> cyl          1.243107291  1.243192949  1.243282300  1.243374567  1.243469044
#> disp         0.004182193  0.004178752  0.004175525  0.004172501  0.004169672
#> drat         0.978859901  0.979126890  0.979375729  0.979607325  0.979822558
#> gear        -0.200981569 -0.200985993 -0.200981841 -0.200970061 -0.200951534
#> hp          -0.014737361 -0.014736141 -0.014735085 -0.014734180 -0.014733413
#> qsec         1.531257779  1.531210893  1.531168986  1.531131701  1.531098702
#> vs          -1.145136663 -1.145179660 -1.145215036 -1.145243471 -1.145265599
#> wt          -5.916709669 -5.916309596 -5.915934779 -5.915584079 -5.915256380
#>                   0.0101       0.0094       0.0088       0.0082       0.0077
#> (Intercept)  2.521850647  2.520738185  2.519618376  2.518496759  2.517378289
#> am           2.478603328  2.478620768  2.478643031  2.478669506  2.478699626
#> carb        -0.210871859 -0.210957467 -0.211038301 -0.211114534 -0.211186343
#> cyl          1.243565091  1.243662128  1.243759635  1.243857146  1.243954244
#> disp         0.004167028  0.004164561  0.004162262  0.004160123  0.004158135
#> drat         0.980022286  0.980207338  0.980378519  0.980536604  0.980682342
#> gear        -0.200927072 -0.200897427 -0.200863290 -0.200825296 -0.200784031
#> hp          -0.014732772 -0.014732246 -0.014731824 -0.014731498 -0.014731257
#> qsec         1.531069667  1.531044294  1.531022295  1.531003402  1.530987357
#> vs          -1.145282014 -1.145293268 -1.145299878 -1.145302321 -1.145301044
#> wt          -5.914950584 -5.914665621 -5.914400445 -5.914154038 -5.913925414
#>                  0.0071      0.0067       0.0062       0.0058       0.0054
#> (Intercept)  2.51626737  2.51516792  2.514083376  2.513016737  2.511970613
#> am           2.47873287  2.47876877  2.478806868  2.478846779  2.478888133
#> carb        -0.21125390 -0.21131739 -0.211376974 -0.211432828 -0.211485119
#> cyl          1.24405056  1.24414577  1.244239575  1.244331739  1.244422042
#> disp         0.00415629  0.00415458  0.004152999  0.004151538  0.004150192
#> drat         0.98081645  0.98093963  0.981052531  0.981155798  0.981250037
#> gear        -0.20074003 -0.20069377 -0.200645714 -0.200596254 -0.200545758
#> hp          -0.01473109 -0.01473100 -0.014730970 -0.014730994 -0.014731069
#> qsec         1.53097392  1.53096287  1.530953996  1.530947096  1.530941985
#> vs          -1.14529646 -1.14528894 -1.145278856 -1.145266519 -1.145252232
#> wt          -5.91371362 -5.91351772 -5.913336829 -5.913170087 -5.913016665
#>                   0.0050
#> (Intercept)  2.510947243
#> am           2.478930597
#> carb        -0.211534013
#> cyl          1.244510298
#> disp         0.004148953
#> drat         0.981335828
#> gear        -0.200494558
#> hp          -0.014731187
#> qsec         1.530938493
#> vs          -1.145236270
#> wt          -5.912875767
#> 
#> $iter
#>   [1]   0   3   2   2   2   2   2   2   2   2   2   2   2   2   2   5   4   3
#>  [19]   3   3   3   3   3   3   3   3   3   3   3   3   3   3   1   1   1   1
#>  [37]   1   1   1  20  23  22  22  65  25   3   1   1   1   1   1   1   1 164
#>  [55]   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1
#>  [73]   1  71   1   1   1   1   1  57   1   1   1   1   1   1   1   1   1   1
#>  [91]   1   1   1   1   1   1   1   1   1   1
#> 
#> $lambda
#>   [1] 5.038168084 4.698612417 4.381941666 4.086613464 3.811189394 3.554327984
#>   [7] 3.314778174 3.091373219 2.883025011 2.688718774 2.507508128 2.338510472
#>  [13] 2.180902693 2.033917151 1.896837942 1.768997413 1.649772908 1.538583736
#>  [19] 1.434888341 1.338181670 1.247992704 1.163882172 1.085440409 1.012285359
#>  [25] 0.944060714 0.880434181 0.821095864 0.765756751 0.714147309 0.666016170
#>  [31] 0.621128910 0.579266900 0.540226250 0.503816808 0.469861242 0.438194167
#>  [37] 0.408661346 0.381118939 0.355432798 0.331477817 0.309137322 0.288302501
#>  [43] 0.268871877 0.250750813 0.233851047 0.218090269 0.203391715 0.189683794
#>  [49] 0.176899741 0.164977291 0.153858374 0.143488834 0.133818167 0.124799270
#>  [55] 0.116388217 0.108544041 0.101228536 0.094406071 0.088043418 0.082109586
#>  [61] 0.076575675 0.071414731 0.066601617 0.062112891 0.057926690 0.054022625
#>  [67] 0.050381681 0.046986124 0.043819417 0.040866135 0.038111894 0.035543280
#>  [73] 0.033147782 0.030913732 0.028830250 0.026887188 0.025075081 0.023385105
#>  [79] 0.021809027 0.020339172 0.018968379 0.017689974 0.016497729 0.015385837
#>  [85] 0.014348883 0.013381817 0.012479927 0.011638822 0.010854404 0.010122854
#>  [91] 0.009440607 0.008804342 0.008210959 0.007657568 0.007141473 0.006660162
#>  [97] 0.006211289 0.005792669 0.005402262 0.005038168
#> 
#> $penalty
#> [1] "MCP"
#> 
#> $family
#> [1] "gaussian"
#> 
#> $gamma
#> [1] 3
#> 
#> $alpha
#> [1] 1
#> 
#> $convex.min
#> [1] 39
#> 
#> $loss
#>   [1] 697.43810 595.10940 509.49623 438.19310 379.12320 330.49461 290.76217
#>   [8] 258.59445 232.84511 212.52795 196.79534 184.91952 176.27632 170.33106
#>  [15] 166.62637 163.87424 152.70924 141.76806 132.66531 125.13411 118.94374
#>  [22] 113.89531 109.81745 106.56266 104.00405 102.03260 100.55471  99.49015
#>  [29]  98.77019  98.33607  98.13761  98.11308  98.11308  98.11308  98.11308
#>  [36]  98.11308  98.11308  98.11308  98.11308  96.69533  94.59349  93.30088
#>  [43]  92.66777  87.86582  87.65361  87.65353  87.65353  87.65353  87.65353
#>  [50]  87.65353  87.65353  87.65353  87.65353  77.75505  77.75504  77.75503
#>  [57]  77.75503  77.75502  77.75502  77.75502  77.75502  77.75502  77.75501
#>  [64]  77.75501  77.75501  77.75501  77.75501  77.75501  77.75501  77.75501
#>  [71]  77.75501  77.75501  77.75501  77.41572  77.41571  77.41570  77.41570
#>  [78]  77.41569  77.41569  77.35153  77.35152  77.35151  77.35150  77.35149
#>  [85]  77.35148  77.35147  77.35146  77.35146  77.35145  77.35145  77.35145
#>  [92]  77.35144  77.35144  77.35144  77.35143  77.35143  77.35143  77.35143
#>  [99]  77.35143  77.35142
#> 
#> $linear.predictors
#>      5.0382   4.6986   4.3819   4.0866   3.8112   3.5543   3.3148   3.0914
#> 1  20.77619 21.07483 21.35334 21.61308 21.85532 22.08123 22.29191 22.48840
#> 2  20.77619 20.91562 21.04566 21.16693 21.28003 21.38551 21.48388 21.57562
#> 3  20.77619 21.26213 21.71532 22.13796 22.53212 22.89972 23.24254 23.56225
#> 4  20.77619 20.70335 20.63542 20.57207 20.51299 20.45789 20.40650 20.35858
#> 5  20.77619 20.55039 20.33981 20.14342 19.96026 19.78945 19.63016 19.48160
#> 6  20.77619 20.48171 20.20708 19.95096 19.71210 19.48934 19.28159 19.08785
#> 7  20.77619 20.74393 20.71385 20.68579 20.65963 20.63523 20.61247 20.59125
#> 8  20.77619 20.56288 20.36394 20.17841 20.00538 19.84402 19.69353 19.55319
#> 9  20.77619 20.56288 20.36394 20.17841 20.00538 19.84402 19.69353 19.55319
#> 10 20.77619 20.16955 19.60379 19.07616 18.58409 18.12519 17.69722 17.29808
#> 11 20.77619 20.38182 20.01403 19.67103 19.35114 19.05281 18.77459 18.51512
#> 12 20.77619 19.43283 18.18002 17.01163 15.92199 14.90579 13.95808 13.07424
#> 13 20.77619 21.33705 21.86011 22.34792 22.80285 23.22711 23.62279 23.99180
#> 14 20.77619 21.70228 22.56596 23.37143 24.12262 24.82317 25.47651 26.08582
#> 15 20.77619 21.56493 22.30051 22.98652 23.62629 24.22295 24.77939 25.29832
#> 16 20.77619 20.31002 19.87527 19.46982 19.09170 18.73906 18.41019 18.10348
#> 17 20.77619 21.37451 21.93250 22.45289 22.93821 23.39081 23.81292 24.20657
#> 18 20.77619 20.73145 20.68972 20.65080 20.61451 20.58066 20.54910 20.51966
#> 19 20.77619 20.98118 21.17235 21.35064 21.51692 21.67198 21.81660 21.95147
#> 20 20.77619 20.48171 20.20708 19.95096 19.71210 19.48934 19.28159 19.08785
#> 21 20.77619 20.97494 21.16029 21.33315 21.49436 21.64470 21.78491 21.91567
#>      2.8830   2.6887   2.5075   2.3385    2.1809    2.0339    1.8968    1.7690
#> 1  22.67164 22.84253 23.00191 23.15054 23.289156 23.418430 23.538991 23.640857
#> 2  21.66117 21.74096 21.81537 21.88477 21.949491 22.009849 22.066139 22.112453
#> 3  23.86042 24.13849 24.39783 24.63968 24.865232 25.075584 25.271758 25.456691
#> 4  20.31389 20.27220 20.23333 20.19708 20.163272 20.131742 20.102337 20.085133
#> 5  19.34305 19.21383 19.09333 18.98095 18.876143 18.778400 18.687244 18.618193
#> 6  18.90716 18.73865 18.58149 18.43493 18.298249 18.170777 18.051896 17.929738
#> 7  20.57146 20.55300 20.53578 20.51973 20.504755 20.490792 20.477770 20.497445
#> 8  19.42230 19.30023 19.18639 19.08023 18.981215 18.888877 18.802761 18.726237
#> 9  19.42230 19.30023 19.18639 19.08023 18.981215 18.888877 18.802761 18.730021
#> 10 16.92585 16.57871 16.25496 15.95303 15.671455 15.408854 15.163951 14.935781
#> 11 18.27314 18.04747 17.83700 17.64073 17.457675 17.286961 17.127753 16.979623
#> 12 12.24997 11.48125 10.76435 10.09575  9.472223  8.890716  8.348401  7.850485
#> 13 24.33594 24.65688 24.95619 25.23533 25.495662 25.738445 25.964865 26.183025
#> 14 26.65406 27.18401 27.67824 28.13916 28.569011 28.969895 29.343760 29.691473
#> 15 25.78229 26.23364 26.65456 27.04712 27.413222 27.754649 28.073065 28.378506
#> 16 17.81744 17.55068 17.30190 17.06989 16.853512 16.651719 16.463526 16.285282
#> 17 24.57369 24.91607 25.23538 25.53316 25.810878 26.069876 26.311418 26.526013
#> 18 20.49220 20.46660 20.44272 20.42045 20.399683 20.380315 20.362252 20.324324
#> 19 22.07725 22.19455 22.30395 22.40597 22.501118 22.589853 22.672608 22.733665
#> 20 18.90716 18.73865 18.58149 18.43493 18.298249 18.170777 18.051896 17.921919
#> 21 22.03762 22.15135 22.25742 22.35633 22.448582 22.534615 22.614849 22.693137
#>       1.6498    1.5386    1.4349    1.3382    1.2480    1.1639    1.0854
#> 1  23.594518 23.453484 23.321951 23.199282 23.084880 22.978189 22.878689
#> 2  22.075197 21.991821 21.914061 21.841542 21.773911 21.710837 21.652014
#> 3  25.621515 25.661591 25.698967 25.733825 25.766333 25.796650 25.824924
#> 4  20.192154 20.333959 20.466213 20.589553 20.704581 20.811856 20.911902
#> 5  18.753051 18.971697 19.175617 19.365792 19.543151 19.708556 19.862813
#> 6  17.703489 17.537405 17.382508 17.238051 17.103329 16.977688 16.860514
#> 7  20.886706 21.333120 21.749465 22.137749 22.499865 22.837575 23.152525
#> 8  18.712205 18.760055 18.804683 18.846302 18.885117 18.921316 18.955075
#> 9  18.763378 18.864406 18.958628 19.046501 19.128451 19.204877 19.276153
#> 10 14.763830 14.751742 14.740469 14.729956 14.720151 14.711007 14.702480
#> 11 16.870330 16.865268 16.860547 16.856144 16.852037 16.848208 16.844636
#> 12  7.561701  7.638156  7.709461  7.775961  7.837979  7.895817  7.949757
#> 13 26.432314 26.544834 26.649774 26.747642 26.838914 26.924035 27.003418
#> 14 29.946361 29.956272 29.965515 29.974135 29.982175 29.989673 29.996665
#> 15 28.712067 28.851209 28.980979 29.102003 29.214870 29.320131 29.418297
#> 16 16.116698 16.066510 16.019702 15.976048 15.935337 15.897370 15.861961
#> 17 26.564789 26.429920 26.304134 26.186827 26.077425 25.975397 25.880245
#> 18 20.047370 19.749935 19.472535 19.213830 18.972561 18.747552 18.537709
#> 19 22.590827 22.369432 22.162948 21.970382 21.790793 21.623308 21.467111
#> 20 17.597730 17.321748 17.064354 16.824308 16.600440 16.391660 16.196951
#> 21 22.793769 22.847436 22.897488 22.944167 22.987700 23.028299 23.066161
#>       1.0123    0.9441    0.8804    0.8211    0.7658    0.7141   0.6660
#> 1  22.785894 22.699354 22.618646 22.543377 22.473182 22.407717 22.34666
#> 2  21.597156 21.545995 21.498283 21.453785 21.412287 21.373586 21.33749
#> 3  25.851292 25.875884 25.898817 25.920206 25.940152 25.958755 25.97610
#> 4  21.005204 21.092219 21.173368 21.249049 21.319629 21.385452 21.44684
#> 5  20.006674 20.140839 20.265962 20.382652 20.491478 20.592969 20.68762
#> 6  16.751237 16.649325 16.554282 16.465644 16.382980 16.305887 16.23399
#> 7  23.446248 23.720175 23.975641 24.213889 24.436079 24.643295 24.83655
#> 8  18.986558 19.015920 19.043303 19.068841 19.092657 19.114868 19.13558
#> 9  19.342626 19.404618 19.462432 19.516350 19.566633 19.613528 19.65726
#> 10 14.694527 14.687110 14.680193 14.673742 14.667726 14.662115 14.65688
#> 11 16.841306 16.838199 16.835302 16.832601 16.830081 16.827731 16.82554
#> 12  8.000061  8.046975  8.090728  8.131531  8.169585  8.205073  8.23817
#> 13 27.077452 27.146496 27.210886 27.270937 27.326941 27.379170 27.42788
#> 14 30.003186 30.009267 30.014939 30.020228 30.025161 30.029762 30.03405
#> 15 29.509847 29.595227 29.674853 29.749112 29.818366 29.882953 29.94319
#> 16 15.828939 15.798143 15.769422 15.742636 15.717656 15.694360 15.67263
#> 17 25.791506 25.708748 25.631568 25.559589 25.492461 25.429857 25.37147
#> 18 18.342008 18.159497 17.989286 17.830547 17.682507 17.544444 17.41569
#> 19 21.321441 21.185589 21.058893 20.940736 20.830542 20.727774 20.63193
#> 20 16.015365 15.846017 15.688082 15.540792 15.403429 15.275324 15.15585
#> 21 23.101472 23.134403 23.165114 23.193756 23.220468 23.245379 23.26861
#>       0.6211    0.5793    0.5402    0.5038    0.4699    0.4382    0.4087
#> 1  22.289726 22.261471 22.261471 22.261471 22.261471 22.261471 22.261471
#> 2  21.303832 21.287129 21.287128 21.287128 21.287128 21.287128 21.287128
#> 3  25.992283 26.000312 26.000312 26.000312 26.000312 26.000312 26.000312
#> 4  21.504088 21.532498 21.532498 21.532498 21.532498 21.532498 21.532498
#> 5  20.775891 20.819696 20.819696 20.819696 20.819696 20.819696 20.819696
#> 6  16.166939 16.133666 16.133665 16.133665 16.133665 16.133665 16.133665
#> 7  25.016771 25.106207 25.106208 25.106208 25.106208 25.106208 25.106208
#> 8  19.154901 19.164487 19.164487 19.164487 19.164487 19.164487 19.164487
#> 9  19.698049 19.718289 19.718290 19.718290 19.718290 19.718290 19.718290
#> 10 14.652003 14.649581 14.649581 14.649581 14.649581 14.649581 14.649581
#> 11 16.823496 16.822482 16.822482 16.822482 16.822482 16.822482 16.822482
#> 12  8.269037  8.284354  8.284354  8.284354  8.284354  8.284354  8.284354
#> 13 27.473305 27.495848 27.495848 27.495848 27.495848 27.495848 27.495848
#> 14 30.038054 30.040039 30.040039 30.040039 30.040039 30.040039 30.040039
#> 15 29.999361 30.027237 30.027238 30.027238 30.027238 30.027238 30.027238
#> 16 15.652372 15.642317 15.642317 15.642317 15.642317 15.642317 15.642317
#> 17 25.317024 25.290004 25.290003 25.290003 25.290003 25.290003 25.290003
#> 18 17.295606 17.236017 17.236016 17.236016 17.236016 17.236016 17.236016
#> 19 20.542552 20.498197 20.498196 20.498196 20.498196 20.498196 20.498196
#> 20 15.044432 14.989141 14.989140 14.989140 14.989140 14.989140 14.989140
#> 21 23.290277 23.301029 23.301029 23.301029 23.301029 23.301029 23.301029
#>       0.3811    0.3554    0.3315    0.3091    0.2883    0.2689    0.2508
#> 1  22.261471 22.261471 22.236528 22.189582 22.145965 22.105179 22.669723
#> 2  21.287128 21.287128 21.250835 21.182559 21.119121 21.059803 21.744654
#> 3  26.000312 26.000312 26.066905 26.192147 26.308521 26.417334 25.906516
#> 4  21.532498 21.532498 21.599775 21.726332 21.843924 21.953877 21.428222
#> 5  20.819696 20.819696 20.867433 20.957264 21.040728 21.118773 20.801845
#> 6  16.133665 16.133665 16.163014 16.218161 16.269409 16.317323 16.288330
#> 7  25.106208 25.106208 24.988335 24.766788 24.560912 24.368424 25.260815
#> 8  19.164487 19.164487 19.101645 18.983479 18.873678 18.771013 17.908159
#> 9  19.718290 19.718290 19.634035 19.475617 19.328412 19.190775 18.558881
#> 10 14.649581 14.649581 14.699662 14.793838 14.881347 14.963169 15.286003
#> 11 16.822482 16.822482 16.853913 16.913019 16.967941 17.019294 17.546124
#> 12  8.284354  8.284354  8.294217  8.312785  8.330036  8.346167  8.513359
#> 13 27.495848 27.495848 27.527687 27.587593 27.643254 27.695300 27.560353
#> 14 30.040039 30.040039 30.026500 30.001040 29.977383 29.955264 29.735051
#> 15 30.027238 30.027238 30.031373 30.039187 30.046444 30.053232 30.220154
#> 16 15.642317 15.642317 15.756743 15.971914 16.171853 16.358797 16.569063
#> 17 25.290003 25.290003 25.359190 25.489262 25.610130 25.723140 26.435592
#> 18 17.236016 17.236016 17.299641 17.419212 17.530326 17.634213 17.238830
#> 19 20.498196 20.498196 20.393644 20.196967 20.014223 19.843349 20.106107
#> 20 14.989140 14.989140 14.824846 14.515807 14.228658 13.960162 13.701419
#> 21 23.301029 23.301029 23.324081 23.367445 23.407737 23.445412 22.820801
#>       0.2339    0.2181    0.2034    0.1897    0.1769    0.1650    0.1539
#> 1  22.624855 22.624112 22.624003 22.623935 22.623888 22.623856 22.623832
#> 2  21.681948 21.680915 21.680771 21.680675 21.680608 21.680560 21.680524
#> 3  26.008094 26.009730 26.009909 26.010022 26.010099 26.010154 26.010194
#> 4  21.531126 21.532784 21.532963 21.533070 21.533141 21.533190 21.533226
#> 5  20.873987 20.875145 20.875264 20.875326 20.875362 20.875386 20.875403
#> 6  16.329384 16.330035 16.330094 16.330139 16.330173 16.330199 16.330219
#> 7  25.081792 25.078908 25.078583 25.078346 25.078169 25.078036 25.077938
#> 8  17.836475 17.835397 17.835387 17.835403 17.835422 17.835438 17.835450
#> 9  18.453414 18.451788 18.451712 18.451680 18.451663 18.451654 18.451647
#> 10 15.349689 15.350675 15.350726 15.350746 15.350756 15.350761 15.350765
#> 11 17.580292 17.580799 17.580792 17.580774 17.580756 17.580741 17.580730
#> 12  8.524132  8.524292  8.524288  8.524276  8.524264  8.524254  8.524246
#> 13 27.607064 27.607810 27.607880 27.607917 27.607938 27.607952 27.607962
#> 14 29.720220 29.720000 29.720002 29.720008 29.720015 29.720020 29.720024
#> 15 30.223055 30.223090 30.223074 30.223052 30.223031 30.223015 30.223002
#> 16 16.723994 16.726427 16.726606 16.726705 16.726768 16.726811 16.726842
#> 17 26.518675 26.519943 26.519983 26.519995 26.519998 26.519999 26.519999
#> 18 17.333856 17.335382 17.335548 17.335672 17.335766 17.335836 17.335889
#> 19 19.956108 19.953724 19.953511 19.953397 19.953328 19.953282 19.953249
#> 20 13.477814 13.474300 13.474045 13.473925 13.473860 13.473819 13.473791
#> 21 22.864024 22.864745 22.864860 22.864939 22.864995 22.865036 22.865066
#>      0.1435    0.1338    0.1248    0.1164    0.1085    0.1012    0.0944
#> 1  22.62381 22.623802 23.294624 23.294604 23.294584 23.294565 23.294547
#> 2  21.68050 21.680478 22.721733 22.721784 22.721827 22.721863 22.721893
#> 3  26.01022 26.010247 25.488621 25.488620 25.488620 25.488621 25.488623
#> 4  21.53325 21.533272 21.103225 21.103207 21.103190 21.103175 21.103160
#> 5  20.87542 20.875424 20.661541 20.661615 20.661679 20.661733 20.661779
#> 6  16.33023 16.330244 14.969109 14.968986 14.968879 14.968785 14.968704
#> 7  25.07786 25.077809 24.589396 24.589434 24.589469 24.589500 24.589529
#> 8  17.83546 17.835466 17.703298 17.702971 17.702685 17.702435 17.702216
#> 9  18.45164 18.451638 18.611626 18.611413 18.611225 18.611061 18.610917
#> 10 15.35077 15.350769 15.607165 15.607197 15.607225 15.607248 15.607268
#> 11 17.58072 17.580716 17.804161 17.804276 17.804376 17.804461 17.804535
#> 12  8.52424  8.524236  9.082392  9.082369  9.082351  9.082337  9.082326
#> 13 27.60797 27.607975 28.038072 28.038215 28.038340 28.038449 28.038544
#> 14 29.72003 29.720030 30.528307 30.528322 30.528335 30.528346 30.528355
#> 15 30.22299 30.222985 30.876257 30.876534 30.876776 30.876986 30.877169
#> 16 16.72687 16.726882 16.771354 16.771383 16.771407 16.771429 16.771447
#> 17 26.52000 26.520000 25.056065 25.055649 25.055290 25.054978 25.054709
#> 18 17.33593 17.335958 18.388723 18.389097 18.389427 18.389715 18.389968
#> 19 19.95323 19.953207 19.154973 19.154767 19.154584 19.154423 19.154282
#> 20 13.47377 13.473756 13.249144 13.249412 13.249646 13.249849 13.250027
#> 21 22.86509 22.865106 22.600214 22.600146 22.600089 22.600041 22.600002
#>       0.0880    0.0821    0.0766    0.0714    0.0666    0.0621    0.0579
#> 1  23.294530 23.294514 23.294500 23.294486 23.294474 23.294464 23.294454
#> 2  22.721918 22.721940 22.721958 22.721973 22.721985 22.721996 22.722005
#> 3  25.488626 25.488629 25.488632 25.488635 25.488638 25.488641 25.488644
#> 4  21.103147 21.103135 21.103124 21.103114 21.103105 21.103097 21.103090
#> 5  20.661818 20.661851 20.661879 20.661902 20.661922 20.661939 20.661954
#> 6  14.968633 14.968571 14.968518 14.968471 14.968431 14.968396 14.968365
#> 7  24.589555 24.589578 24.589599 24.589617 24.589634 24.589648 24.589661
#> 8  17.702026 17.701861 17.701717 17.701592 17.701483 17.701389 17.701308
#> 9  18.610792 18.610682 18.610587 18.610504 18.610432 18.610369 18.610315
#> 10 15.607286 15.607300 15.607313 15.607324 15.607333 15.607341 15.607348
#> 11 17.804597 17.804651 17.804698 17.804737 17.804771 17.804800 17.804824
#> 12  9.082318  9.082312  9.082308  9.082305  9.082304  9.082303  9.082302
#> 13 28.038627 28.038700 28.038763 28.038818 28.038866 28.038907 28.038943
#> 14 30.528363 30.528370 30.528376 30.528381 30.528385 30.528389 30.528392
#> 15 30.877327 30.877465 30.877584 30.877688 30.877777 30.877854 30.877921
#> 16 16.771463 16.771477 16.771489 16.771500 16.771509 16.771516 16.771523
#> 17 25.054476 25.054275 25.054102 25.053952 25.053824 25.053713 25.053618
#> 18 18.390190 18.390384 18.390552 18.390700 18.390828 18.390940 18.391036
#> 19 19.154157 19.154048 19.153953 19.153869 19.153796 19.153732 19.153677
#> 20 13.250181 13.250314 13.250430 13.250531 13.250617 13.250692 13.250757
#> 21 22.599969 22.599942 22.599920 22.599902 22.599887 22.599874 22.599864
#>       0.0540    0.0504    0.0470    0.0438    0.0409    0.0381    0.0355
#> 1  23.294445 23.294437 23.294430 23.294424 23.294418 23.294413 23.294409
#> 2  22.722012 22.722019 22.722024 22.722028 22.722032 22.722035 22.722037
#> 3  25.488646 25.488649 25.488651 25.488653 25.488655 25.488657 25.488659
#> 4  21.103084 21.103078 21.103073 21.103069 21.103065 21.103061 21.103058
#> 5  20.661966 20.661976 20.661984 20.661992 20.661998 20.662003 20.662007
#> 6  14.968339 14.968316 14.968296 14.968279 14.968264 14.968252 14.968241
#> 7  24.589672 24.589682 24.589690 24.589698 24.589704 24.589710 24.589714
#> 8  17.701238 17.701177 17.701125 17.701080 17.701041 17.701007 17.700979
#> 9  18.610268 18.610228 18.610193 18.610162 18.610136 18.610114 18.610095
#> 10 15.607353 15.607358 15.607362 15.607366 15.607369 15.607371 15.607373
#> 11 17.804845 17.804863 17.804878 17.804891 17.804902 17.804911 17.804919
#> 12  9.082302  9.082303  9.082303  9.082304  9.082305  9.082306  9.082307
#> 13 28.038974 28.039001 28.039025 28.039045 28.039062 28.039077 28.039090
#> 14 30.528395 30.528397 30.528399 30.528401 30.528402 30.528403 30.528405
#> 15 30.877978 30.878027 30.878070 30.878107 30.878138 30.878165 30.878188
#> 16 16.771529 16.771534 16.771538 16.771542 16.771545 16.771548 16.771550
#> 17 25.053536 25.053466 25.053406 25.053354 25.053310 25.053272 25.053240
#> 18 18.391121 18.391194 18.391257 18.391311 18.391359 18.391399 18.391435
#> 19 19.153628 19.153586 19.153550 19.153518 19.153491 19.153467 19.153446
#> 20 13.250813 13.250861 13.250902 13.250938 13.250968 13.250994 13.251017
#> 21 22.599856 22.599850 22.599844 22.599840 22.599837 22.599834 22.599832
#>       0.0331   0.0309    0.0288    0.0269    0.0251    0.0234    0.0218
#> 1  23.294405 23.36671 23.366647 23.366589 23.366534 23.366482 23.366433
#> 2  22.722040 22.71833 22.718183 22.718049 22.717925 22.717811 22.717705
#> 3  25.488660 25.42216 25.422217 25.422269 25.422318 25.422363 25.422406
#> 4  21.103056 21.27514 21.275232 21.275314 21.275386 21.275449 21.275505
#> 5  20.662010 20.67412 20.674116 20.674114 20.674111 20.674105 20.674098
#> 6  14.968231 15.06242 15.062666 15.062892 15.063099 15.063289 15.063463
#> 7  24.589719 24.61032 24.610467 24.610605 24.610731 24.610848 24.610954
#> 8  17.700954 17.61950 17.619480 17.619471 17.619468 17.619470 17.619476
#> 9  18.610078 18.54581 18.545751 18.545701 18.545659 18.545623 18.545594
#> 10 15.607375 15.27507 15.274873 15.274696 15.274538 15.274398 15.274273
#> 11 17.804925 17.60109 17.600941 17.600800 17.600673 17.600557 17.600451
#> 12  9.082308  9.28952  9.289567  9.289609  9.289645  9.289676  9.289704
#> 13 28.039101 27.96703 27.966910 27.966804 27.966706 27.966615 27.966532
#> 14 30.528406 30.70488 30.704789 30.704703 30.704623 30.704547 30.704475
#> 15 30.878208 30.90288 30.902746 30.902623 30.902505 30.902394 30.902289
#> 16 16.771552 16.94478 16.944803 16.944825 16.944843 16.944856 16.944867
#> 17 25.053212 25.02289 25.023198 25.023492 25.023768 25.024027 25.024271
#> 18 18.391465 18.37541 18.375168 18.374939 18.374726 18.374528 18.374344
#> 19 19.153429 19.17612 19.176327 19.176513 19.176684 19.176842 19.176987
#> 20 13.251036 13.26697 13.267026 13.267075 13.267116 13.267150 13.267177
#> 21 22.599830 22.47887 22.478892 22.478917 22.478943 22.478970 22.478998
#>       0.0203    0.0190    0.0177    0.0165    0.0154    0.0143    0.0134
#> 1  23.387493 23.387435 23.387382 23.387333 23.387288 23.387247 23.387210
#> 2  22.735800 22.735837 22.735875 22.735914 22.735952 22.735991 22.736029
#> 3  25.438243 25.438267 25.438288 25.438305 25.438319 25.438330 25.438338
#> 4  21.246583 21.246331 21.246094 21.245873 21.245666 21.245473 21.245293
#> 5  20.613354 20.613198 20.613055 20.612925 20.612806 20.612699 20.612603
#> 6  15.197731 15.197605 15.197473 15.197337 15.197198 15.197057 15.196915
#> 7  24.584030 24.583985 24.583939 24.583892 24.583845 24.583798 24.583752
#> 8  17.588050 17.588280 17.588499 17.588705 17.588901 17.589086 17.589260
#> 9  18.506998 18.507182 18.507358 18.507526 18.507687 18.507840 18.507986
#> 10 15.304972 15.305330 15.305669 15.305989 15.306292 15.306578 15.306848
#> 11 17.623792 17.623949 17.624100 17.624244 17.624381 17.624511 17.624635
#> 12  9.318141  9.318046  9.317954  9.317865  9.317779  9.317696  9.317616
#> 13 27.965467 27.965519 27.965572 27.965624 27.965675 27.965725 27.965774
#> 14 30.787917 30.787882 30.787847 30.787813 30.787779 30.787747 30.787714
#> 15 30.904143 30.904049 30.903965 30.903888 30.903819 30.903758 30.903703
#> 16 16.915948 16.915767 16.915600 16.915445 16.915301 16.915168 16.915045
#> 17 24.960615 24.960730 24.960834 24.960926 24.961007 24.961079 24.961141
#> 18 18.259331 18.259347 18.259374 18.259410 18.259454 18.259505 18.259563
#> 19 19.113895 19.113758 19.113628 19.113505 19.113388 19.113277 19.113173
#> 20 13.284316 13.284114 13.283921 13.283737 13.283562 13.283395 13.283237
#> 21 22.563182 22.563388 22.563576 22.563746 22.563900 22.564039 22.564164
#>      0.0125    0.0116    0.0109    0.0101    0.0094    0.0088    0.0082
#> 1  23.38718 23.387145 23.387117 23.387092 23.387069 23.387048 23.387030
#> 2  22.73607 22.736105 22.736142 22.736178 22.736214 22.736249 22.736283
#> 3  25.43834 25.438348 25.438350 25.438350 25.438349 25.438346 25.438343
#> 4  21.24513 21.244970 21.244825 21.244691 21.244567 21.244453 21.244347
#> 5  20.61252 20.612438 20.612369 20.612308 20.612253 20.612206 20.612164
#> 6  15.19677 15.196629 15.196486 15.196345 15.196206 15.196069 15.195934
#> 7  24.58371 24.583659 24.583614 24.583570 24.583526 24.583483 24.583442
#> 8  17.58942 17.589578 17.589723 17.589859 17.589986 17.590105 17.590216
#> 9  18.50813 18.508257 18.508382 18.508501 18.508613 18.508718 18.508818
#> 10 15.30710 15.307340 15.307564 15.307774 15.307971 15.308155 15.308326
#> 11 17.62475 17.624865 17.624971 17.625071 17.625166 17.625255 17.625339
#> 12  9.31754  9.317467  9.317396  9.317329  9.317265  9.317204  9.317146
#> 13 27.96582 27.965870 27.965916 27.965960 27.966004 27.966046 27.966086
#> 14 30.78768 30.787653 30.787624 30.787595 30.787568 30.787541 30.787515
#> 15 30.90366 30.903613 30.903576 30.903544 30.903516 30.903493 30.903474
#> 16 16.91493 16.914827 16.914732 16.914644 16.914564 16.914491 16.914425
#> 17 24.96120 24.961242 24.961281 24.961314 24.961342 24.961363 24.961380
#> 18 18.25963 18.259693 18.259764 18.259838 18.259914 18.259993 18.260072
#> 19 19.11307 19.112980 19.112892 19.112809 19.112732 19.112658 19.112590
#> 20 13.28309 13.282945 13.282811 13.282684 13.282564 13.282451 13.282345
#> 21 22.56428 22.564376 22.564465 22.564543 22.564612 22.564672 22.564724
#>      0.0077    0.0071    0.0067   0.0062    0.0058    0.0054    0.0050
#> 1  23.38701 23.386999 23.386986 23.38698 23.386966 23.386957 23.386950
#> 2  22.73632 22.736348 22.736379 22.73641 22.736438 22.736465 22.736492
#> 3  25.43834 25.438332 25.438325 25.43832 25.438310 25.438302 25.438294
#> 4  21.24425 21.244161 21.244079 21.24400 21.243936 21.243874 21.243817
#> 5  20.61213 20.612098 20.612072 20.61205 20.612033 20.612019 20.612008
#> 6  15.19580 15.195673 15.195547 15.19542 15.195306 15.195191 15.195079
#> 7  24.58340 24.583362 24.583324 24.58329 24.583252 24.583218 24.583185
#> 8  17.59032 17.590417 17.590506 17.59059 17.590667 17.590739 17.590805
#> 9  18.50891 18.509001 18.509084 18.50916 18.509236 18.509304 18.509368
#> 10 15.30849 15.308636 15.308775 15.30890 15.309024 15.309135 15.309238
#> 11 17.62542 17.625494 17.625564 17.62563 17.625691 17.625749 17.625803
#> 12  9.31709  9.317037  9.316987  9.31694  9.316895  9.316853  9.316813
#> 13 27.96613 27.966163 27.966200 27.96623 27.966268 27.966300 27.966331
#> 14 30.78749 30.787467 30.787444 30.78742 30.787402 30.787382 30.787363
#> 15 30.90346 30.903445 30.903435 30.90343 30.903423 30.903421 30.903420
#> 16 16.91436 16.914310 16.914260 16.91422 16.914176 16.914141 16.914110
#> 17 24.96139 24.961401 24.961406 24.96141 24.961406 24.961402 24.961396
#> 18 18.26015 18.260233 18.260314 18.26039 18.260473 18.260552 18.260630
#> 19 19.11253 19.112465 19.112409 19.11236 19.112308 19.112262 19.112220
#> 20 13.28225 13.282152 13.282064 13.28198 13.281905 13.281834 13.281767
#> 21 22.56477 22.564807 22.564838 22.56486 22.564885 22.564900 22.564912
#> 
#> $penalty.factor
#>  [1] 1 1 1 1 1 1 1 1 1 1
#> 
#> $n
#> [1] 21
#> 
#> $y
#>  [1] 21.0 21.0 22.8 21.4 18.1 14.3 22.8 19.2 17.8 16.4 17.3 10.4 32.4 30.4 33.9
#> [16] 19.2 26.0 15.8 19.7 15.0 21.4
#> 
#> $X
#>               am       carb       cyl       disp       drat       gear
#>  [1,]  0.9534626  0.5640761  0.000000 -0.4553431  0.3555064  0.2013468
#>  [2,]  0.9534626  0.5640761  0.000000 -0.4553431  0.3555064  0.2013468
#>  [3,]  0.9534626 -1.1281521 -1.224745 -0.9181452  0.2653417  0.2013468
#>  [4,] -1.0488088 -1.1281521  0.000000  0.4168610 -1.1231942 -1.2080809
#>  [5,] -1.0488088 -1.1281521  0.000000  0.1231596 -1.7002481 -1.2080809
#>  [6,] -1.0488088  0.5640761  1.224745  1.3246652 -0.8887660 -1.2080809
#>  [7,] -1.0488088 -0.5640761 -1.224745 -0.6262239  0.3915723  0.2013468
#>  [8,] -1.0488088  0.5640761  0.000000 -0.3877028  0.3915723  0.2013468
#>  [9,] -1.0488088  0.5640761  0.000000 -0.3877028  0.3915723  0.2013468
#> [10,] -1.0488088  0.0000000  1.224745  0.5752817 -1.1412271 -1.2080809
#> [11,] -1.0488088  0.0000000  1.224745  0.5752817 -1.1412271 -1.2080809
#> [12,] -1.0488088  0.5640761  1.224745  2.3214699 -1.3936882 -1.2080809
#> [13,]  0.9534626 -1.1281521 -1.224745 -1.1789164  0.6800992  0.2013468
#> [14,]  0.9534626 -0.5640761 -1.224745 -1.2056166  2.2128986  0.2013468
#> [15,]  0.9534626 -1.1281521 -1.224745 -1.2465568  0.9325603  0.2013468
#> [16,] -1.0488088 -0.5640761  1.224745  1.6806669 -1.1231942 -1.2080809
#> [17,]  0.9534626 -0.5640761 -1.224745 -0.8086747  1.3112519  1.6107745
#> [18,]  0.9534626  0.5640761  1.224745  1.2445648  0.9325603  1.6107745
#> [19,]  0.9534626  1.6922282  0.000000 -0.5888437 -0.1494157  1.6107745
#> [20,]  0.9534626  2.8203804  1.224745  0.7995628 -0.2936792  1.6107745
#> [21,]  0.9534626 -0.5640761 -1.224745 -0.8024447  0.7341980  0.2013468
#>               hp        qsec         vs          wt
#>  [1,] -0.4720668 -0.73027344 -0.9534626 -0.58633350
#>  [2,] -0.4720668 -0.44256772 -0.9534626 -0.27375850
#>  [3,] -0.7124775  0.37431101  1.0488088 -0.95406879
#>  [4,] -0.4720668  0.80073199  1.0488088  0.14300817
#>  [5,] -0.5427758  1.20146495  1.0488088  0.44332533
#>  [6,]  1.4370765 -1.04880477 -0.9534626  0.57816160
#>  [7,] -0.6841939  2.57834232  1.0488088  0.06333219
#>  [8,] -0.2882234  0.21504535  1.0488088  0.41880964
#>  [9,] -0.2882234  0.52330147  1.0488088  0.41880964
#> [10,]  0.5178593 -0.24733884 -0.9534626  1.19105375
#> [11,]  0.5178593 -0.14458680 -0.9534626  0.77428709
#> [12,]  0.8714044  0.05064208 -0.9534626  2.63747924
#> [13,] -1.0943061  0.81614479  1.0488088 -1.10116291
#> [14,] -1.2922913  0.32807259  1.0488088 -1.81824673
#> [15,] -1.1084479  1.03706168  1.0488088 -1.54857418
#> [16,]  0.4471503 -0.42715492 -0.9534626  0.91525228
#> [17,] -0.7407611 -0.60697099 -0.9534626 -1.17470996
#> [18,]  1.7057707 -1.73724346 -0.9534626  0.08784788
#> [19,]  0.4471503 -1.22348325 -0.9534626 -0.40246585
#> [20,]  2.7098387 -1.68586744 -0.9534626  0.57816160
#> [21,] -0.4862086  0.36917341  1.0488088 -0.39020801
#> attr(,"center")
#>  [1]   0.5238095   3.0000000   6.0000000 211.1619048   3.7028571   3.8571429
#>  [7] 143.3809524  17.8814286   0.4761905   3.0983333
#> attr(,"scale")
#>  [1]   0.4994328   1.7728105   1.6329932 112.3590269   0.5545409   0.7095078
#>  [7]  70.7123457   1.9464333   0.4994328   0.8158042
#> attr(,"nonsingular")
#>  [1]  1  2  3  4  5  6  7  8  9 10
#> 
#> attr(,"class")
#> [1] "ncvreg"
#> 
#> $min
#> [1] 34
#> 
#> $lambda.min
#> [1] 0.5038168
#> 
#> $null.dev
#> [1] 33.21134
#> 
#> $Bias
#> [1] 2.412679
#> 
#> 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 
#> 10.57311