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] 21.424615 20.987197 19.989961 19.215997 18.629930 18.087857 16.699630
#>   [8] 15.667733 14.772807 14.041687 13.450172 12.976907 12.562205 12.232694
#>  [15] 11.981434 11.746803 11.335158 10.930155 10.451148  9.630281  8.750736
#>  [22]  8.058867  7.515085  7.060383  6.793426  6.597929  6.271277  6.100117
#>  [29]  6.016597  5.974016  5.925806  5.912116  5.893493  5.675423  5.549831
#>  [36]  4.832572  4.916599  4.814894  4.302505  4.261366  4.347174  4.599310
#>  [43]  4.587752  4.594928  4.812284  4.649637  4.649743  4.422918  4.347009
#>  [50]  5.211867  5.337880  5.338008  4.655697  4.632334  4.655042  4.866418
#>  [57]  4.786514  5.354664  5.354848  5.072035  5.064774  4.935553  4.935773
#>  [64]  4.857672  4.857912  4.858146  4.858373  4.858594  4.739297  4.618445
#>  [71]  5.223906  5.224092  5.224275  5.224456  5.224634  6.570515  6.890697
#>  [78]  6.891358  6.892013  6.892662  6.749676  6.750295  6.750908  6.751517
#>  [85]  6.752122  6.752722  6.753328  6.768308  6.768953  6.769588  6.770213
#>  [92]  6.770830  6.771439  6.772050  7.075885  7.076751  7.077608  7.078455
#>  [99]  7.079293  7.080122
#> 
#> $cvse
#>   [1] 8.9541715 8.9576129 8.8245936 8.7293928 8.6605152 8.5186166 7.5977776
#>   [8] 6.7922197 6.0836112 5.4648284 4.9283829 4.4681567 4.0486540 3.6985892
#>  [15] 3.4189763 3.1935010 2.9711465 2.7813281 2.6072055 2.3859023 2.2120040
#>  [22] 2.0759906 1.9690659 1.8892154 1.8467101 1.8168701 1.8174658 1.7888109
#>  [29] 1.7395725 1.7216050 1.7146169 1.7144821 1.6288097 1.5730227 1.5093635
#>  [36] 1.2175852 1.1931282 1.1300718 0.8596063 0.8409315 0.8208136 0.8677069
#>  [43] 0.8689455 0.8764560 0.9168607 0.9264935 0.9265206 0.9189374 0.9251702
#>  [50] 1.0840977 1.0743891 1.0744316 1.0351359 1.0407699 1.0600284 1.0891317
#>  [57] 1.1094245 1.4378674 1.4380054 1.4372815 1.4383522 1.4193378 1.4194644
#>  [64] 1.4302150 1.4303298 1.4304414 1.4305498 1.4306551 1.4513876 1.4618630
#>  [71] 1.9683784 1.9685782 1.9687753 1.9689697 1.9691616 3.2247314 3.2098720
#>  [78] 3.2102814 3.2106885 3.2110934 3.1987733 3.1991755 3.1995756 3.1999737
#>  [85] 3.2003696 3.2007635 3.2011574 3.2012458 3.2016312 3.2020147 3.2023964
#>  [92] 3.2027762 3.2031541 3.2035324 3.2142729 3.2146625 3.2150500 3.2154355
#>  [99] 3.2158189 3.2162004
#> 
#> $fold
#>  [1]  1  7  7  5  8  6  9  1  2  4  9  3  4  2  3  1  6 10  5  8 10
#> 
#> $lambda
#>   [1] 3.666405254 3.419301811 3.188852313 2.973934339 2.773501118 2.586576426
#>   [7] 2.412249831 2.249672266 2.098051885 1.956650210 1.824778534 1.701794569
#>  [13] 1.587099310 1.480134129 1.380378042 1.287345182 1.200582425 1.119667188
#>  [19] 1.044205367 0.973829420 0.908196577 0.846987167 0.789903067 0.736666244
#>  [25] 0.687017404 0.640714731 0.597532702 0.557260998 0.519703472 0.484677197
#>  [31] 0.452011576 0.421547509 0.393136618 0.366640525 0.341930181 0.318885231
#>  [37] 0.297393434 0.277350112 0.258657643 0.241224983 0.224967227 0.209805189
#>  [43] 0.195665021 0.182477853 0.170179457 0.158709931 0.148013413 0.138037804
#>  [49] 0.128734518 0.120058243 0.111966719 0.104420537 0.097382942 0.090819658
#>  [55] 0.084698717 0.078990307 0.073666624 0.068701740 0.064071473 0.059753270
#>  [61] 0.055726100 0.051970347 0.048467720 0.045201158 0.042154751 0.039313662
#>  [67] 0.036664053 0.034193018 0.031888523 0.029739343 0.027735011 0.025865764
#>  [73] 0.024122498 0.022496723 0.020980519 0.019566502 0.018247785 0.017017946
#>  [79] 0.015870993 0.014801341 0.013803780 0.012873452 0.012005824 0.011196672
#>  [85] 0.010442054 0.009738294 0.009081966 0.008469872 0.007899031 0.007366662
#>  [91] 0.006870174 0.006407147 0.005975327 0.005572610 0.005197035 0.004846772
#>  [97] 0.004520116 0.004215475 0.003931366 0.003666405
#> 
#> $fit
#> $beta
#>               3.6664     3.4193     3.1889    2.9739    2.7735    2.5866
#> (Intercept) 17.79524 19.3221432 20.7461400 22.074164 23.312684 24.467732
#> am           0.00000  0.0000000  0.0000000  0.000000  0.000000  0.000000
#> carb         0.00000  0.0000000  0.0000000  0.000000  0.000000  0.000000
#> cyl          0.00000  0.0000000  0.0000000  0.000000  0.000000  0.000000
#> disp         0.00000  0.0000000  0.0000000  0.000000  0.000000  0.000000
#> drat         0.00000  0.0000000  0.0000000  0.000000  0.000000  0.000000
#> gear         0.00000  0.0000000  0.0000000  0.000000  0.000000  0.000000
#> hp           0.00000  0.0000000  0.0000000  0.000000  0.000000  0.000000
#> qsec         0.00000  0.0000000  0.0000000  0.000000  0.000000  0.000000
#> vs           0.00000  0.0000000  0.0000000  0.000000  0.000000  0.000000
#> wt           0.00000 -0.4243424 -0.8200855 -1.189157 -1.533354 -1.854353
#>                2.4122    2.2497   2.0981    1.9567    1.8248    1.7018
#> (Intercept) 25.544933 26.549535 27.48643 28.360181 29.175044 29.934988
#> am           0.000000  0.000000  0.00000  0.000000  0.000000  0.000000
#> carb         0.000000  0.000000  0.00000  0.000000  0.000000  0.000000
#> cyl          0.000000  0.000000  0.00000  0.000000  0.000000  0.000000
#> disp         0.000000  0.000000  0.00000  0.000000  0.000000  0.000000
#> drat         0.000000  0.000000  0.00000  0.000000  0.000000  0.000000
#> gear         0.000000  0.000000  0.00000  0.000000  0.000000  0.000000
#> hp           0.000000  0.000000  0.00000  0.000000  0.000000  0.000000
#> qsec         0.000000  0.000000  0.00000  0.000000  0.000000  0.000000
#> vs           0.000000  0.000000  0.00000  0.000000  0.000000  0.000000
#> wt          -2.153719 -2.432908 -2.69328 -2.936104 -3.162563 -3.373759
#>                1.5871    1.4801    1.3804    1.2873    1.2006      1.1197
#> (Intercept) 30.643715 31.304676 31.921090 32.495960 32.898907 31.96845602
#> am           0.000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> carb         0.000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> cyl          0.000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> disp         0.000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> drat         0.000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> gear         0.000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> hp           0.000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> qsec         0.000000  0.000000  0.000000  0.000000  0.000000  0.05157456
#> vs           0.000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> wt          -3.570722 -3.754409 -3.925717 -4.085479 -4.197462 -4.19289031
#>                 1.0442     0.9738    0.9082     0.8470     0.7899     0.7367
#> (Intercept) 30.7654170 29.6434555 28.597110 27.6212856 26.7112281 25.4276389
#> am           0.0000000  0.0000000  0.000000  0.0000000  0.0000000  0.0000000
#> carb         0.0000000  0.0000000  0.000000  0.0000000  0.0000000  0.0000000
#> cyl          0.0000000  0.0000000  0.000000  0.0000000  0.0000000  0.0000000
#> disp         0.0000000  0.0000000  0.000000  0.0000000  0.0000000  0.0000000
#> drat         0.0000000  0.0000000  0.000000  0.0000000  0.0000000  0.1060387
#> gear         0.0000000  0.0000000  0.000000  0.0000000  0.0000000  0.0000000
#> hp           0.0000000  0.0000000  0.000000  0.0000000  0.0000000  0.0000000
#> qsec         0.1182586  0.1804485  0.238447  0.2925366  0.3429808  0.3859306
#> vs           0.0000000  0.0000000  0.000000  0.0000000  0.0000000  0.0000000
#> wt          -4.1869788 -4.1814656 -4.176324 -4.1715290 -4.1670572 -4.1217956
#>                 0.6870     0.6407     0.5975    0.5573     0.5197    0.4847
#> (Intercept) 23.0886585 20.9094746 18.8748821 16.977403 14.8632045 14.695097
#> am           0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.000000
#> carb         0.0000000  0.0000000  0.0000000  0.000000 -0.8931233 -0.924055
#> cyl          0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.000000
#> disp         0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.000000
#> drat         0.4832506  0.8345293  1.1626721  1.468702  4.1962245  4.246397
#> gear         0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.000000
#> hp           0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.000000
#> qsec         0.4152669  0.4426422  0.4681554  0.491949  0.0000000  0.000000
#> vs           0.0000000  0.0000000  0.0000000  0.000000  0.0000000  0.000000
#> wt          -3.9717303 -3.8319769 -3.7014332 -3.579687 -2.3240555 -2.296373
#>                 0.4520     0.4215     0.3931     0.3666     0.3419     0.3189
#> (Intercept) 14.6932449 14.6922283 14.6916701 14.6913637 14.6911954 14.6911031
#> am           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> carb        -0.9241315 -0.9241735 -0.9241965 -0.9242092 -0.9242161 -0.9242199
#> cyl          0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> disp         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> drat         4.2468202  4.2470526  4.2471802  4.2472503  4.2472888  4.2473099
#> 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          -2.2961878 -2.2960860 -2.2960301 -2.2959994 -2.2959825 -2.2959733
#>                0.2974     0.2774     0.2587     0.2412     0.2250     0.2098
#> (Intercept) 14.691052 14.6910245 14.6910092 14.0806219 14.3257106 14.5534581
#> am           0.000000  0.0000000  0.0000000  2.2355192  2.4263996  2.6036787
#> carb        -0.924222 -0.9242232 -0.9242238 -1.2450335 -1.2346743 -1.2250256
#> cyl          0.000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> disp         0.000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> drat         4.247321  4.2473278  4.2473313  3.9115109  3.7457402  3.5916685
#> gear         0.000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> hp           0.000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> qsec         0.000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> vs           0.000000  0.0000000  0.0000000  0.1590397  0.4392069  0.6997581
#> wt          -2.295968 -2.2959654 -2.2959639 -1.6774690 -1.6336984 -1.5930272
#>                 0.1957    0.1825    0.1702    0.1587    0.1480      0.1380
#> (Intercept) 14.7667461 14.964768 14.993042 14.993649 14.993989 12.17239201
#> am           2.7698030  2.923938  2.944772  2.945491  2.946027  3.52952853
#> carb        -1.2160137 -1.207623 -1.206413 -1.206435 -1.206457 -1.61909284
#> cyl          0.0000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> disp         0.0000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> drat         3.4474126  3.313448  3.295007  3.294627  3.294372  3.79908539
#> gear         0.0000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> hp           0.0000000  0.000000  0.000000  0.000000  0.000000  0.01380978
#> qsec         0.0000000  0.000000  0.000000  0.000000  0.000000  0.00000000
#> vs           0.9435397  1.170100  1.200637  1.200994  1.201249  1.63420887
#> wt          -1.5549366 -1.519574 -1.514961 -1.514828 -1.514717 -1.52796935
#>                  0.1287      0.1201      0.1120      0.1044      0.0974
#> (Intercept)  1.57523056  1.57336991  1.57164982  1.57005966  1.56858962
#> am           2.48777369  2.48801934  2.48824643  2.48845637  2.48865045
#> carb        -2.68673262 -2.68697737 -2.68720364 -2.68741282 -2.68760619
#> cyl          0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> disp         0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> drat         4.14237386  4.14241648  4.14245587  4.14249229  4.14252596
#> gear         2.95337253  2.95375989  2.95411800  2.95444906  2.95475510
#> hp           0.01949469  0.01949747  0.01950005  0.01950243  0.01950463
#> qsec         0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> vs           0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> wt          -0.84351155 -0.84332782 -0.84315798 -0.84300097 -0.84285581
#>                  0.0908        0.0847       0.0790       0.0737       0.0687
#> (Intercept)  1.56723063  1.568246e+00  6.852977666  6.853470254  6.853950434
#> am           2.48882987  2.488546e+00  2.869352960  2.869655607  2.869934050
#> carb        -2.68778496 -2.688009e+00 -3.123136623 -3.123236879 -3.123318177
#> cyl          0.00000000  0.000000e+00  0.000000000  0.000000000  0.000000000
#> disp         0.00000000 -5.688766e-06 -0.009579489 -0.009576521 -0.009574059
#> drat         4.14255709  4.141962e+00  4.215207587  4.214785855  4.214421610
#> gear         2.95503803  2.955436e+00  2.732642822  2.733119412  2.733502882
#> hp           0.01950667  1.951291e-02  0.029792257  0.029789385  0.029787017
#> qsec         0.00000000  0.000000e+00 -0.322323014 -0.322373241 -0.322414977
#> vs           0.00000000  0.000000e+00  0.712082712  0.712378943  0.712641821
#> wt          -0.84272163 -8.424551e-01  0.000000000  0.000000000  0.000000000
#>                  0.0641       0.0598      0.0557      0.0520      0.0485
#> (Intercept)  6.85441309  6.854854468 28.18235114 28.18257327 28.18279116
#> am           2.87018866  2.870420193  2.02569456  2.02572390  2.02575268
#> carb        -3.12338327 -3.123434602 -4.39602987 -4.39629071 -4.39654656
#> cyl          0.00000000  0.000000000 -1.39498945 -1.39500775 -1.39502570
#> disp        -0.00957203 -0.009570369 -0.02330122 -0.02330333 -0.02330540
#> drat         4.21410808  4.213839123  4.30680768  4.30692387  4.30703784
#> gear         2.73380781  2.734046820  3.35352619  3.35382328  3.35411471
#> hp           0.02978508  0.029783493  0.05209160  0.05209447  0.05209729
#> qsec        -0.32244945 -0.322477740 -1.30389678 -1.30400143 -1.30410407
#> vs           0.71287434  0.713079360  0.00000000  0.00000000  0.00000000
#> wt           0.00000000  0.000000000  2.22312328  2.22348227  2.22383441
#>                  0.0452      0.0422      0.0393      0.0367      0.0342
#> (Intercept) 28.18300489 28.18321453 28.18342016 28.18362186 28.18381971
#> am           2.02578090  2.02580859  2.02583575  2.02586239  2.02588853
#> carb        -4.39679753 -4.39704370 -4.39728517 -4.39752203 -4.39775437
#> cyl         -1.39504331 -1.39506059 -1.39507753 -1.39509415 -1.39511045
#> disp        -0.02330743 -0.02330942 -0.02331137 -0.02331329 -0.02331517
#> drat         4.30714964  4.30725930  4.30736686  4.30747237  4.30757586
#> gear         3.35440056  3.35468096  3.35495600  3.35522579  3.35549042
#> hp           0.05210005  0.05210276  0.05210542  0.05210803  0.05211059
#> qsec        -1.30420476 -1.30430352 -1.30440039 -1.30449542 -1.30458862
#> vs           0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> wt           2.22417981  2.22451862  2.22485096  2.22517695  2.22549671
#>                  0.0319      0.0297      0.0277      0.0259      0.0241
#> (Intercept) 28.18401378 28.18420414 28.18439086 28.18457401 28.18475366
#> am           2.02591416  2.02593930  2.02596397  2.02598816  2.02601189
#> carb        -4.39798226 -4.39820580 -4.39842508 -4.39864016 -4.39885113
#> cyl         -1.39512644 -1.39514212 -1.39515751 -1.39517260 -1.39518740
#> disp        -0.02331701 -0.02331882 -0.02332059 -0.02332233 -0.02332404
#> drat         4.30767738  4.30777696  4.30787463  4.30797044  4.30806442
#> gear         3.35575000  3.35600461  3.35625437  3.35649936  3.35673966
#> hp           0.05211309  0.05211556  0.05211797  0.05212034  0.05212266
#> qsec        -1.30468005 -1.30476973 -1.30485770 -1.30494399 -1.30502863
#> vs           0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> wt           2.22581036  2.22611802  2.22641980  2.22671582  2.22700619
#>                  0.0225      0.0210      0.0196      0.0182      0.0170
#> (Intercept) 28.18492988 28.18510273 28.18527228 28.18543859 28.18560172
#> am           2.02603517  2.02605800  2.02608040  2.02610237  2.02612392
#> carb        -4.39905808 -4.39926107 -4.39946018 -4.39965550 -4.39984707
#> cyl         -1.39520192 -1.39521616 -1.39523013 -1.39524384 -1.39525728
#> disp        -0.02332571 -0.02332736 -0.02332897 -0.02333055 -0.02333210
#> drat         4.30815660  4.30824703  4.30833572  4.30842273  4.30850806
#> gear         3.35697537  3.35720659  3.35743338  3.35765585  3.35787406
#> hp           0.05212494  0.05212717  0.05212936  0.05213152  0.05213362
#> qsec        -1.30511165 -1.30519309 -1.30527297 -1.30535133 -1.30542819
#> vs           0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> wt           2.22729101  2.22757038  2.22784442  2.22811323  2.22837690
#>                  0.0159      0.0148      0.0138      0.0129      0.0120
#> (Intercept) 28.18576173 28.18591869 28.18607265 28.18622366 28.18637179
#> am           2.02614505  2.02616579  2.02618613  2.02620608  2.02622564
#> carb        -4.40003499 -4.40021932 -4.40040013 -4.40057749 -4.40075146
#> cyl         -1.39527046 -1.39528340 -1.39529608 -1.39530853 -1.39532073
#> disp        -0.02333362 -0.02333511 -0.02333657 -0.02333800 -0.02333941
#> drat         4.30859177  4.30867388  4.30875443  4.30883343  4.30891092
#> gear         3.35808811  3.35829806  3.35850401  3.35870602  3.35890417
#> hp           0.05213569  0.05213772  0.05213971  0.05214167  0.05214358
#> qsec        -1.30550358 -1.30557753 -1.30565006 -1.30572121 -1.30579101
#> vs           0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> wt           2.22863553  2.22888923  2.22913807  2.22938217  2.22962160
#>                  0.0112      0.0104      0.0097      0.0091      0.0085
#> (Intercept) 28.72517194 28.72985113 28.73434241 28.73865315 28.74279043
#> am           1.91733904  1.91695468  1.91658846  1.91623938  1.91590652
#> carb        -4.40704253 -4.40724292 -4.40744312 -4.40764304 -4.40784261
#> cyl         -1.45355736 -1.45386733 -1.45416476 -1.45445019 -1.45472412
#> disp        -0.02341975 -0.02342234 -0.02342491 -0.02342746 -0.02342998
#> drat         4.30968170  4.30971767  4.30975691  4.30979920  4.30984430
#> gear         3.36950790  3.36959031  3.36967634  3.36976599  3.36985923
#> hp           0.05245782  0.05246172  0.05246558  0.05246937  0.05247311
#> qsec        -1.31230745 -1.31249451 -1.31267702 -1.31285512 -1.31302896
#> vs          -0.14647333 -0.14675520 -0.14702536 -0.14728440 -0.14753286
#> wt           2.22997878  2.23033579  2.23069032  2.23104224  2.23139141
#>                  0.0079      0.0074      0.0069      0.0064      0.0060
#> (Intercept) 28.74676108 28.75057166 28.75422846 28.75773756 28.76110481
#> am           1.91558904  1.91528616  1.91499713  1.91472128  1.91445797
#> carb        -4.40804174 -4.40824036 -4.40843837 -4.40863571 -4.40883231
#> cyl         -1.45498704 -1.45523939 -1.45548162 -1.45571416 -1.45593738
#> disp        -0.02343247 -0.02343493 -0.02343737 -0.02343978 -0.02344215
#> drat         4.30989199  4.30994206  4.30999431  4.31004855  4.31010458
#> gear         3.36995601  3.37005626  3.37015991  3.37026684  3.37037694
#> hp           0.05247679  0.05248042  0.05248398  0.05248749  0.05249094
#> qsec        -1.31319866 -1.31336436 -1.31352617 -1.31368422 -1.31383861
#> vs          -0.14777126 -0.14800005 -0.14821967 -0.14843054 -0.14863304
#> wt           2.23173772  2.23208106  2.23242133  2.23275843  2.23309228
#>                  0.0056      0.0052      0.0048      0.0045      0.0042
#> (Intercept) 28.76433583 28.76743604 28.77041067 28.77326473 28.77600307
#> am           1.91420659  1.91396659  1.91373742  1.91351860  1.91330964
#> carb        -4.40902807 -4.40922293 -4.40941683 -4.40960969 -4.40980143
#> cyl         -1.45615169 -1.45635744 -1.45655499 -1.45674466 -1.45692680
#> disp        -0.02344450 -0.02344681 -0.02344909 -0.02345134 -0.02345356
#> drat         4.31016225  4.31022137  4.31028180  4.31034338  4.31040599
#> gear         3.37049009  3.37060616  3.37072498  3.37084643  3.37097034
#> hp           0.05249434  0.05249768  0.05250097  0.05250419  0.05250737
#> qsec        -1.31398945 -1.31413684 -1.31428087 -1.31442165 -1.31455925
#> vs          -0.14882754 -0.14901437 -0.14919386 -0.14936632 -0.14953203
#> wt           2.23342281  2.23374994  2.23407362  2.23439379  2.23471040
#>                  0.0039      0.0037
#> (Intercept) 28.77863035 28.78115106
#> am           1.91311010  1.91291956
#> carb        -4.40999201 -4.41018136
#> cyl         -1.45710170 -1.45726966
#> disp        -0.02345574 -0.02345789
#> drat         4.31046948  4.31053373
#> gear         3.37109656  3.37122493
#> hp           0.05251049  0.05251355
#> qsec        -1.31469378 -1.31482530
#> vs          -0.14969128 -0.14984434
#> wt           2.23502341  2.23533277
#> 
#> $iter
#>   [1]   0   3   3   3   3   3   2   2   2   2   2   2   2   2   2   2   2   3
#>  [19]   2   2   2   2   2  13  14  13  13  13  37   7   1   1   1   1   1   1
#>  [37]   1   1   1  61  27  26  26  25   8   1   1  43  87   1   1   1   1   1
#>  [55]   2  65   1   1   1   1 271   1   1   1   1   1   1   1   1   1   1   1
#>  [73]   1   1   1   1   1   1   1   1   1   1   1  52   1   1   1   1   1   1
#>  [91]   1   1   1   1   1   1   1   1   1   1
#> 
#> $lambda
#>   [1] 3.666405254 3.419301811 3.188852313 2.973934339 2.773501118 2.586576426
#>   [7] 2.412249831 2.249672266 2.098051885 1.956650210 1.824778534 1.701794569
#>  [13] 1.587099310 1.480134129 1.380378042 1.287345182 1.200582425 1.119667188
#>  [19] 1.044205367 0.973829420 0.908196577 0.846987167 0.789903067 0.736666244
#>  [25] 0.687017404 0.640714731 0.597532702 0.557260998 0.519703472 0.484677197
#>  [31] 0.452011576 0.421547509 0.393136618 0.366640525 0.341930181 0.318885231
#>  [37] 0.297393434 0.277350112 0.258657643 0.241224983 0.224967227 0.209805189
#>  [43] 0.195665021 0.182477853 0.170179457 0.158709931 0.148013413 0.138037804
#>  [49] 0.128734518 0.120058243 0.111966719 0.104420537 0.097382942 0.090819658
#>  [55] 0.084698717 0.078990307 0.073666624 0.068701740 0.064071473 0.059753270
#>  [61] 0.055726100 0.051970347 0.048467720 0.045201158 0.042154751 0.039313662
#>  [67] 0.036664053 0.034193018 0.031888523 0.029739343 0.027735011 0.025865764
#>  [73] 0.024122498 0.022496723 0.020980519 0.019566502 0.018247785 0.017017946
#>  [79] 0.015870993 0.014801341 0.013803780 0.012873452 0.012005824 0.011196672
#>  [85] 0.010442054 0.009738294 0.009081966 0.008469872 0.007899031 0.007366662
#>  [91] 0.006870174 0.006407147 0.005975327 0.005572610 0.005197035 0.004846772
#>  [97] 0.004520116 0.004215475 0.003931366 0.003666405
#> 
#> $penalty
#> [1] "MCP"
#> 
#> $family
#> [1] "gaussian"
#> 
#> $gamma
#> [1] 3
#> 
#> $alpha
#> [1] 1
#> 
#> $convex.min
#> [1] 28
#> 
#> $loss
#>   [1] 385.86952 331.67779 286.33834 248.57728 217.29475 191.54178 170.50008
#>   [8] 153.46454 139.82808 129.06841 120.73666 114.44741 109.87009 106.72157
#>  [15] 104.75963 103.77737 103.57645  99.39309  94.46331  90.35273  86.94272
#>  [22]  84.13091  81.82899  78.41860  71.97446  66.94457  63.09531  60.24315
#>  [29]  41.34167  41.29837  41.29837  41.29837  41.29837  41.29837  41.29837
#>  [36]  41.29837  41.29837  41.29837  41.29837  35.84840  34.84687  34.19438
#>  [43]  33.82729  33.69710  33.69509  33.69509  33.69508  31.06423  26.47981
#>  [50]  26.47981  26.47980  26.47980  26.47980  26.47979  26.47753  22.73506
#>  [57]  22.73505  22.73504  22.73504  22.73504  18.45302  18.45301  18.45300
#>  [64]  18.45299  18.45298  18.45297  18.45297  18.45296  18.45295  18.45294
#>  [71]  18.45294  18.45293  18.45293  18.45292  18.45291  18.45291  18.45290
#>  [78]  18.45290  18.45289  18.45289  18.45289  18.45288  18.45288  18.43585
#>  [85]  18.43583  18.43582  18.43581  18.43579  18.43578  18.43577  18.43576
#>  [92]  18.43575  18.43574  18.43573  18.43572  18.43571  18.43570  18.43569
#>  [99]  18.43569  18.43568
#> 
#> $linear.predictors
#>      3.6664   3.4193   3.1889   2.9739   2.7735   2.5866   2.4122   2.2497
#> 1  17.79524 18.21037 18.59752 18.95857 19.29530 19.60933 19.90219 20.17532
#> 2  17.79524 18.10216 18.38839 18.65534 18.90429 19.13647 19.35299 19.55493
#> 3  17.79524 17.95788 18.10957 18.25102 18.38295 18.50599 18.62073 18.72774
#> 4  17.79524 17.86241 17.92505 17.98346 18.03795 18.08876 18.13614 18.18033
#> 5  17.79524 17.85392 17.90864 17.95968 18.00728 18.05167 18.09307 18.13167
#> 6  17.79524 17.80724 17.81843 17.82887 17.83861 17.84769 17.85616 17.86405
#> 7  17.79524 17.98546 18.16287 18.32832 18.48262 18.62652 18.76072 18.88588
#> 8  17.79524 17.86241 17.92505 17.98346 18.03795 18.08876 18.13614 18.18033
#> 9  17.79524 17.86241 17.92505 17.98346 18.03795 18.08876 18.13614 18.18033
#> 10 17.79524 17.59507 17.40839 17.23430 17.07193 16.92051 16.77930 16.64760
#> 11 17.79524 17.73935 17.68722 17.63861 17.59327 17.55099 17.51156 17.47479
#> 12 17.79524 17.71813 17.64622 17.57915 17.51661 17.45828 17.40388 17.35314
#> 13 17.79524 17.09435 16.44069 15.83109 15.26258 14.73238 14.23791 13.77677
#> 14 17.79524 17.02051 16.29800 15.62418 14.99577 14.40972 13.86316 13.35344
#> 15 17.79524 17.05403 16.36278 15.71812 15.11691 14.55621 14.03331 13.54564
#> 16 17.79524 18.63683 19.42170 20.15368 20.83632 21.47295 22.06668 22.62039
#> 17 17.79524 17.82846 17.85944 17.88833 17.91528 17.94041 17.96384 17.98570
#> 18 17.79524 17.86453 17.92915 17.98941 18.04561 18.09803 18.14691 18.19250
#> 19 17.79524 17.69055 17.59291 17.50186 17.41694 17.33774 17.26388 17.19501
#> 20 17.79524 18.14671 18.47450 18.78020 19.06529 19.33117 19.57913 19.81038
#> 21 17.79524 17.80724 17.81843 17.82887 17.83861 17.84769 17.85616 17.86405
#>      2.0981   1.9567   1.8248   1.7018   1.5871   1.4801   1.3804   1.2873
#> 1  20.43004 20.66759 20.88913 21.09574 21.28842 21.46812 21.63571 21.79200
#> 2  19.74325 19.91888 20.08267 20.23543 20.37789 20.51075 20.63465 20.75021
#> 3  18.82753 18.92060 19.00740 19.08835 19.16384 19.23425 19.29991 19.36114
#> 4  18.22155 18.25998 18.29583 18.32926 18.36043 18.38951 18.41662 18.44191
#> 5  18.16768 18.20126 18.23258 18.26178 18.28902 18.31442 18.33811 18.36020
#> 6  17.87142 17.87829 17.88469 17.89067 17.89624 17.90143 17.90628 17.91080
#> 7  19.00260 19.11145 19.21297 19.30765 19.39594 19.47829 19.55508 19.62670
#> 8  18.22155 18.25998 18.29583 18.32926 18.36043 18.38951 18.41662 18.44191
#> 9  18.22155 18.25998 18.29583 18.32926 18.36043 18.38951 18.41662 18.44191
#> 10 16.52478 16.41024 16.30341 16.20379 16.11088 16.02423 15.94342 15.86806
#> 11 17.44049 17.40851 17.37868 17.35087 17.32492 17.30073 17.27817 17.25712
#> 12 17.30583 17.26171 17.22056 17.18218 17.14639 17.11301 17.08188 17.05285
#> 13 13.34671 12.94563 12.57159 12.22275 11.89743 11.59403 11.31108 11.04719
#> 14 12.87808 12.43475 12.02130 11.63572 11.27612 10.94076 10.62800 10.33632
#> 15 13.09085 12.66670 12.27114 11.90224 11.55821 11.23736 10.93813 10.65907
#> 16 23.13678 23.61837 24.06750 24.48637 24.87700 25.24130 25.58106 25.89791
#> 17 18.00608 18.02509 18.04282 18.05936 18.07477 18.08915 18.10257 18.11507
#> 18 18.23501 18.27466 18.31164 18.34612 18.37829 18.40828 18.43625 18.46234
#> 19 17.13077 17.07086 17.01499 16.96288 16.91429 16.86897 16.82671 16.78729
#> 20 20.02604 20.22717 20.41474 20.58967 20.75282 20.90496 21.04685 21.17918
#> 21 17.87142 17.87829 17.88469 17.89067 17.89624 17.90143 17.90628 17.91080
#>      1.2006   1.1197   1.0442   0.9738   0.9082   0.8470   0.7899   0.7367
#> 1  21.90156 21.83200 21.74207 21.65820 21.57998 21.50703 21.43900 21.39450
#> 2  20.83120 20.79170 20.74061 20.69297 20.64855 20.60711 20.56847 20.55957
#> 3  19.40407 19.49092 19.60323 19.70796 19.80564 19.89673 19.98169 20.00516
#> 4  18.45964 18.42271 18.37497 18.33045 18.28892 18.25020 18.21408 18.15122
#> 5  18.37569 18.50389 18.66966 18.82425 18.96843 19.10289 19.22828 19.26241
#> 6  17.91397 17.81678 17.69112 17.57393 17.46463 17.36271 17.26765 17.16635
#> 7  19.67690 19.94191 20.28455 20.60411 20.90213 21.18006 21.43926 21.69747
#> 8  18.45964 18.48873 18.52634 18.56142 18.59414 18.62465 18.65310 18.72686
#> 9  18.45964 18.51967 18.59730 18.66969 18.73720 18.80017 18.85889 18.95842
#> 10 15.81524 15.80079 15.78211 15.76469 15.74845 15.73330 15.71917 15.69266
#> 11 17.24237 17.23669 17.22934 17.22248 17.21609 17.21013 17.20457 17.17126
#> 12 17.03250 17.04767 17.06729 17.08559 17.10265 17.11856 17.13341 17.11954
#> 13 10.86223 10.88309 10.91007 10.93522 10.95869 10.98057 11.00097 11.03794
#> 14 10.13187 10.14528 10.16261 10.17878 10.19385 10.20791 10.22103 10.26642
#> 15 10.46347 10.45589 10.44608 10.43693 10.42840 10.42045 10.41303 10.46206
#> 16 26.12001 26.15210 26.19359 26.23229 26.26839 26.30204 26.33343 26.44114
#> 17 18.12384 18.07954 18.02227 17.96886 17.91905 17.87260 17.82927 17.72223
#> 18 18.48062 18.45812 18.42902 18.40188 18.37657 18.35297 18.33095 18.27989
#> 19 16.75966 16.72614 16.68279 16.64237 16.60467 16.56951 16.53672 16.48605
#> 20 21.27194 21.15356 21.00049 20.85775 20.72462 20.60047 20.48468 20.37605
#> 21 17.91397 17.75283 17.54448 17.35017 17.16896 16.99996 16.84235 16.72279
#>      0.6870   0.6407   0.5975   0.5573   0.5197   0.4847   0.4520   0.4215
#> 1  21.40270 21.41025 21.41739 21.42404 21.56696 21.54333 21.54331 21.54329
#> 2  20.62245 20.68097 20.73569 20.78671 20.97433 20.95775 20.95778 20.95779
#> 3  19.88075 19.76498 19.65674 19.55580 19.42261 19.46710 19.46708 19.46706
#> 4  18.01599 17.89001 17.77237 17.66266 18.30031 18.32361 18.32358 18.32356
#> 5  19.07694 18.90436 18.74300 18.59251 17.51043 17.54565 17.54553 17.54546
#> 6  17.03864 16.91961 16.80852 16.70493 16.46371 16.43176 16.43162 16.43155
#> 7  21.98166 22.24661 22.49380 22.72433 22.20538 22.25929 22.25953 22.25966
#> 8  18.91963 19.09918 19.26687 19.42326 19.74516 19.74523 19.74537 19.74544
#> 9  19.16879 19.36477 19.54776 19.71843 19.74516 19.74523 19.74537 19.74544
#> 10 15.63294 15.57731 15.52536 15.47690 15.60734 15.61313 15.61310 15.61309
#> 11 17.06638 16.96871 16.87747 16.79239 16.39752 16.39390 16.39381 16.39376
#> 12 17.03390 16.95417 16.87966 16.81018 16.28131 16.27908 16.27900 16.27895
#> 13 11.11950 11.19547 11.26642 11.33259 11.38436 11.38486 11.38492 11.38495
#> 14 10.39580 10.51630 10.62885 10.73382 11.27371 11.28254 11.28266 11.28272
#> 15 10.65461 10.83391 11.00142 11.15764 12.42244 12.44062 12.44082 12.44093
#> 16 26.74748 27.03279 27.29928 27.54780 30.01099 30.07308 30.07346 30.07367
#> 17 17.44749 17.19159 16.95259 16.72970 16.47786 16.48381 16.48362 16.48352
#> 18 18.15212 18.03311 17.92196 17.81831 18.31193 18.33509 18.33506 18.33504
#> 19 16.38607 16.29292 16.20595 16.12484 17.06534 17.09633 17.09635 17.09635
#> 20 20.27297 20.17685 20.08719 20.00358 18.25716 18.16177 18.16150 18.16136
#> 21 16.68319 16.64613 16.61169 16.57958 14.27597 14.13685 14.13655 14.13638
#>      0.3931   0.3666   0.3419   0.3189   0.2974   0.2774   0.2587   0.2412
#> 1  21.54329 21.54328 21.54328 21.54328 21.54328 21.54328 21.54328 22.19593
#> 2  20.95780 20.95780 20.95781 20.95781 20.95781 20.95781 20.95781 21.76818
#> 3  19.46705 19.46705 19.46704 19.46704 19.46704 19.46704 19.46704 19.64902
#> 4  18.32355 18.32355 18.32354 18.32354 18.32354 18.32354 18.32354 18.14132
#> 5  17.54543 17.54541 17.54540 17.54539 17.54539 17.54539 17.54538 17.98636
#> 6  16.43151 16.43148 16.43147 16.43146 16.43146 16.43146 16.43146 15.66787
#> 7  22.25973 22.25977 22.25979 22.25980 22.25981 22.25981 22.25981 21.79869
#> 8  19.74549 19.74551 19.74552 19.74553 19.74553 19.74554 19.74554 18.82216
#> 9  19.74549 19.74551 19.74552 19.74553 19.74553 19.74554 19.74554 18.82216
#> 10 15.61308 15.61308 15.61307 15.61307 15.61307 15.61307 15.61307 15.52656
#> 11 16.39373 16.39372 16.39371 16.39370 16.39370 16.39370 16.39370 16.09690
#> 12 16.27893 16.27892 16.27891 16.27891 16.27890 16.27890 16.27890 16.01303
#> 13 11.38496 11.38497 11.38498 11.38498 11.38498 11.38498 11.38498 11.75450
#> 14 11.28276 11.28278 11.28279 11.28279 11.28280 11.28280 11.28280 11.73643
#> 15 12.44100 12.44103 12.44105 12.44106 12.44106 12.44107 12.44107 12.76860
#> 16 30.07379 30.07385 30.07389 30.07390 30.07391 30.07392 30.07392 30.55975
#> 17 16.48347 16.48344 16.48342 16.48341 16.48341 16.48340 16.48340 16.48163
#> 18 18.33503 18.33503 18.33502 18.33502 18.33502 18.33502 18.33502 18.14971
#> 19 17.09636 17.09636 17.09636 17.09636 17.09636 17.09636 17.09636 17.18814
#> 20 18.16128 18.16124 18.16121 18.16120 18.16119 18.16119 18.16119 18.35902
#> 21 14.13629 14.13624 14.13621 14.13620 14.13619 14.13618 14.13618 14.21406
#>      0.2250   0.2098   0.1957   0.1825   0.1702   0.1587   0.1480   0.1380
#> 1  22.14151 22.09081 22.04347 21.99938 21.99349 21.99360 21.99368 21.55778
#> 2  21.72492 21.68459 21.64696 21.61189 21.60718 21.60732 21.60743 21.16815
#> 3  19.81478 19.96895 20.11318 20.24724 20.26529 20.26549 20.26563 20.49535
#> 4  18.03552 17.93715 17.84509 17.75955 17.74802 17.74785 17.74772 18.06182
#> 5  18.21589 18.42932 18.62905 18.81464 18.83972 18.84007 18.84033 18.83624
#> 6  15.57854 15.49550 15.41776 15.34557 15.33595 15.33573 15.33555 15.81963
#> 7  21.83272 21.86447 21.89407 21.92168 21.92515 21.92500 21.92490 21.95966
#> 8  18.88960 18.95244 19.01111 19.06576 19.07299 19.07283 19.07272 18.66503
#> 9  18.88960 18.95244 19.01111 19.06576 19.07299 19.07283 19.07272 18.66503
#> 10 15.47196 15.42118 15.37367 15.32952 15.32358 15.32350 15.32344 15.24523
#> 11 16.02741 15.96281 15.90235 15.84617 15.83867 15.83854 15.83844 15.76474
#> 12 15.94573 15.88316 15.82460 15.77020 15.76292 15.76280 15.76271 15.68834
#> 13 11.78512 11.81355 11.84019 11.86492 11.86821 11.86832 11.86841 11.63651
#> 14 11.76305 11.78778 11.81095 11.83245 11.83526 11.83537 11.83545 11.77467
#> 15 12.75364 12.73971 12.72670 12.71459 12.71280 12.71280 12.71282 12.97632
#> 16 30.55004 30.54103 30.53258 30.52475 30.52335 30.52333 30.52334 31.07787
#> 17 16.44399 16.40896 16.37620 16.34574 16.34177 16.34176 16.34174 16.11270
#> 18 18.04369 17.94511 17.85286 17.76715 17.75560 17.75542 17.75529 17.72422
#> 19 17.11167 17.04056 16.97402 16.91218 16.90381 16.90372 16.90365 17.17706
#> 20 18.37830 18.39614 18.41293 18.42843 18.43082 18.43101 18.43113 17.92429
#> 21 14.30233 14.38433 14.46116 14.53245 14.54243 14.54271 14.54290 15.36937
#>      0.1287   0.1201   0.1120   0.1044   0.0974   0.0908   0.0847   0.0790
#> 1  21.21924 21.21915 21.21906 21.21899 21.21891 21.21885 21.21843 21.03866
#> 2  21.00414 21.00410 21.00406 21.00402 21.00399 21.00395 21.00361 20.85816
#> 3  19.93965 19.93974 19.93982 19.93989 19.93996 19.94002 19.94025 20.16237
#> 4  18.62025 18.62032 18.62038 18.62043 18.62049 18.62053 18.62038 18.36163
#> 5  18.30996 18.31006 18.31016 18.31024 18.31033 18.31040 18.31104 18.72926
#> 6  14.75030 14.75010 14.74991 14.74974 14.74958 14.74943 14.74927 14.83407
#> 7  23.44829 23.44850 23.44870 23.44888 23.44904 23.44920 23.44966 22.87325
#> 8  18.37606 18.37591 18.37578 18.37565 18.37553 18.37542 18.37554 18.68711
#> 9  18.37606 18.37591 18.37578 18.37565 18.37553 18.37542 18.37554 18.49372
#> 10 15.16819 15.16814 15.16809 15.16804 15.16800 15.16796 15.16831 15.73435
#> 11 15.45498 15.45487 15.45476 15.45466 15.45457 15.45449 15.45475 15.66988
#> 12 15.41281 15.41270 15.41260 15.41251 15.41243 15.41235 15.41263 15.54095
#> 13 11.39355 11.39353 11.39352 11.39350 11.39349 11.39348 11.39304 10.69944
#> 14 11.73169 11.73174 11.73178 11.73182 11.73185 11.73189 11.73159 11.45896
#> 15 13.04349 13.04358 13.04365 13.04372 13.04379 13.04385 13.04360 13.19586
#> 16 30.57638 30.57648 30.57657 30.57665 30.57673 30.57680 30.57607 30.75429
#> 17 16.44988 16.44987 16.44987 16.44986 16.44986 16.44985 16.45004 16.42358
#> 18 18.13710 18.13710 18.13709 18.13709 18.13708 18.13708 18.13709 18.06302
#> 19 17.98866 17.98880 17.98893 17.98904 17.98915 17.98925 17.98902 17.67371
#> 20 18.77991 18.77991 18.77992 18.77992 18.77992 18.77993 18.78016 18.73439
#> 21 15.51939 15.51950 15.51959 15.51968 15.51976 15.51984 15.51999 15.71335
#>      0.0737   0.0687   0.0641   0.0598   0.0557   0.0520   0.0485   0.0452
#> 1  21.03865 21.03864 21.03864 21.03864 20.82897 20.82890 20.82884 20.82878
#> 2  20.85812 20.85809 20.85807 20.85805 20.66568 20.66565 20.66562 20.66559
#> 3  20.16267 20.16292 20.16314 20.16333 20.25988 20.25987 20.25986 20.25986
#> 4  18.36173 18.36181 18.36188 18.36193 18.04021 18.04022 18.04023 18.04024
#> 5  18.72956 18.72983 18.73006 18.73027 18.91781 18.91783 18.91784 18.91786
#> 6  14.83380 14.83358 14.83340 14.83326 14.98058 14.98044 14.98031 14.98018
#> 7  22.87308 22.87294 22.87280 22.87268 22.91862 22.91860 22.91858 22.91856
#> 8  18.68698 18.68686 18.68676 18.68667 18.81330 18.81333 18.81337 18.81340
#> 9  18.49356 18.49341 18.49329 18.49318 18.03096 18.03093 18.03090 18.03087
#> 10 15.73410 15.73390 15.73373 15.73359 16.42714 16.42726 16.42737 16.42749
#> 11 15.66963 15.66941 15.66924 15.66909 15.41050 15.41048 15.41045 15.41042
#> 12 15.54068 15.54045 15.54026 15.54010 15.00010 15.00005 15.00000 14.99995
#> 13 10.69964 10.69980 10.69994 10.70006 10.02578 10.02564 10.02550 10.02537
#> 14 11.45907 11.45916 11.45924 11.45930 11.72323 11.72323 11.72323 11.72324
#> 15 13.19579 13.19573 13.19568 13.19564 14.30713 14.30725 14.30738 14.30750
#> 16 30.75416 30.75404 30.75395 30.75388 30.86973 30.86978 30.86983 30.86988
#> 17 16.42380 16.42399 16.42414 16.42427 16.41035 16.41038 16.41040 16.41042
#> 18 18.06302 18.06301 18.06300 18.06299 17.66658 17.66661 17.66663 17.66665
#> 19 17.67397 17.67417 17.67434 17.67447 17.66793 17.66799 17.66805 17.66810
#> 20 18.73459 18.73475 18.73489 18.73500 19.50521 19.50526 19.50531 19.50536
#> 21 15.71343 15.71351 15.71357 15.71364 15.23030 15.23029 15.23029 15.23029
#>      0.0422   0.0393   0.0367   0.0342   0.0319   0.0297   0.0277   0.0259
#> 1  20.82872 20.82866 20.82860 20.82855 20.82849 20.82844 20.82838 20.82833
#> 2  20.66556 20.66553 20.66551 20.66548 20.66545 20.66542 20.66540 20.66537
#> 3  20.25985 20.25984 20.25983 20.25983 20.25982 20.25981 20.25981 20.25980
#> 4  18.04024 18.04025 18.04026 18.04027 18.04027 18.04028 18.04029 18.04029
#> 5  18.91787 18.91789 18.91790 18.91792 18.91793 18.91795 18.91796 18.91797
#> 6  14.98005 14.97992 14.97980 14.97968 14.97956 14.97945 14.97933 14.97922
#> 7  22.91854 22.91853 22.91851 22.91849 22.91848 22.91846 22.91845 22.91843
#> 8  18.81343 18.81346 18.81349 18.81352 18.81354 18.81357 18.81360 18.81363
#> 9  18.03085 18.03082 18.03079 18.03076 18.03074 18.03071 18.03068 18.03066
#> 10 16.42760 16.42770 16.42781 16.42791 16.42802 16.42812 16.42821 16.42831
#> 11 15.41040 15.41038 15.41035 15.41033 15.41030 15.41028 15.41026 15.41024
#> 12 14.99990 14.99986 14.99981 14.99977 14.99972 14.99968 14.99964 14.99960
#> 13 10.02523 10.02510 10.02498 10.02485 10.02473 10.02461 10.02449 10.02438
#> 14 11.72324 11.72324 11.72324 11.72324 11.72324 11.72324 11.72324 11.72325
#> 15 14.30762 14.30774 14.30785 14.30797 14.30808 14.30819 14.30829 14.30840
#> 16 30.86992 30.86997 30.87001 30.87006 30.87010 30.87014 30.87018 30.87022
#> 17 16.41045 16.41047 16.41049 16.41051 16.41053 16.41055 16.41057 16.41059
#> 18 17.66667 17.66670 17.66672 17.66674 17.66676 17.66678 17.66680 17.66682
#> 19 17.66816 17.66821 17.66827 17.66832 17.66837 17.66842 17.66847 17.66851
#> 20 19.50541 19.50546 19.50551 19.50555 19.50560 19.50564 19.50568 19.50573
#> 21 15.23028 15.23028 15.23027 15.23027 15.23027 15.23026 15.23026 15.23026
#>      0.0241   0.0225   0.0210   0.0196   0.0182   0.0170   0.0159   0.0148
#> 1  20.82828 20.82823 20.82818 20.82813 20.82808 20.82803 20.82799 20.82794
#> 2  20.66535 20.66532 20.66530 20.66528 20.66525 20.66523 20.66521 20.66519
#> 3  20.25979 20.25979 20.25978 20.25978 20.25977 20.25976 20.25976 20.25975
#> 4  18.04030 18.04031 18.04031 18.04032 18.04032 18.04033 18.04034 18.04034
#> 5  18.91799 18.91800 18.91801 18.91803 18.91804 18.91805 18.91806 18.91807
#> 6  14.97911 14.97900 14.97890 14.97880 14.97869 14.97859 14.97850 14.97840
#> 7  22.91841 22.91840 22.91839 22.91837 22.91836 22.91834 22.91833 22.91832
#> 8  18.81365 18.81368 18.81370 18.81373 18.81375 18.81377 18.81380 18.81382
#> 9  18.03063 18.03061 18.03059 18.03056 18.03054 18.03052 18.03050 18.03047
#> 10 16.42840 16.42850 16.42859 16.42868 16.42876 16.42885 16.42893 16.42901
#> 11 15.41022 15.41019 15.41017 15.41015 15.41013 15.41011 15.41010 15.41008
#> 12 14.99955 14.99951 14.99948 14.99944 14.99940 14.99936 14.99933 14.99929
#> 13 10.02426 10.02415 10.02404 10.02394 10.02383 10.02373 10.02363 10.02353
#> 14 11.72325 11.72325 11.72325 11.72325 11.72325 11.72325 11.72325 11.72326
#> 15 14.30850 14.30860 14.30870 14.30880 14.30889 14.30899 14.30908 14.30917
#> 16 30.87026 30.87030 30.87034 30.87038 30.87041 30.87045 30.87049 30.87052
#> 17 16.41061 16.41063 16.41065 16.41067 16.41069 16.41070 16.41072 16.41074
#> 18 17.66684 17.66685 17.66687 17.66689 17.66691 17.66693 17.66694 17.66696
#> 19 17.66856 17.66861 17.66865 17.66870 17.66874 17.66878 17.66882 17.66886
#> 20 19.50577 19.50581 19.50585 19.50589 19.50593 19.50597 19.50600 19.50604
#> 21 15.23025 15.23025 15.23025 15.23024 15.23024 15.23024 15.23023 15.23023
#>      0.0138   0.0129   0.0120   0.0112   0.0104   0.0097   0.0091   0.0085
#> 1  20.82790 20.82786 20.82781 20.84395 20.84393 20.84390 20.84387 20.84385
#> 2  20.66517 20.66514 20.66512 20.67770 20.67766 20.67763 20.67759 20.67755
#> 3  20.25975 20.25974 20.25974 20.21884 20.21881 20.21878 20.21875 20.21872
#> 4  18.04035 18.04035 18.04036 18.05131 18.05127 18.05122 18.05118 18.05114
#> 5  18.91809 18.91810 18.91811 18.87305 18.87302 18.87298 18.87295 18.87292
#> 6  14.97831 14.97822 14.97813 15.00627 15.00637 15.00646 15.00654 15.00661
#> 7  22.91830 22.91829 22.91828 22.98095 22.98103 22.98110 22.98116 22.98123
#> 8  18.81384 18.81387 18.81389 18.78423 18.78429 18.78434 18.78440 18.78445
#> 9  18.03045 18.03043 18.03041 17.99685 17.99679 17.99674 17.99669 17.99664
#> 10 16.42910 16.42917 16.42925 16.43994 16.44008 16.44022 16.44036 16.44050
#> 11 15.41006 15.41004 15.41002 15.41928 15.41927 15.41925 15.41924 15.41922
#> 12 14.99926 14.99922 14.99919 15.00586 15.00578 15.00571 15.00565 15.00558
#> 13 10.02343 10.02334 10.02324 10.01626 10.01610 10.01594 10.01579 10.01563
#> 14 11.72326 11.72326 11.72326 11.72154 11.72155 11.72155 11.72155 11.72156
#> 15 14.30925 14.30934 14.30943 14.31679 14.31696 14.31712 14.31729 14.31745
#> 16 30.87056 30.87059 30.87062 30.84490 30.84490 30.84490 30.84490 30.84491
#> 17 16.41076 16.41077 16.41079 16.41796 16.41797 16.41798 16.41799 16.41799
#> 18 17.66698 17.66699 17.66701 17.67278 17.67272 17.67267 17.67263 17.67258
#> 19 17.66890 17.66894 17.66898 17.67662 17.67660 17.67659 17.67658 17.67657
#> 20 19.50608 19.50611 19.50615 19.54803 19.54820 19.54837 19.54853 19.54868
#> 21 15.23023 15.23023 15.23022 15.18688 15.18671 15.18654 15.18638 15.18622
#>      0.0079   0.0074   0.0069   0.0064   0.0060   0.0056   0.0052   0.0048
#> 1  20.84382 20.84379 20.84376 20.84373 20.84370 20.84367 20.84364 20.84361
#> 2  20.67752 20.67749 20.67745 20.67742 20.67739 20.67736 20.67733 20.67730
#> 3  20.21869 20.21866 20.21863 20.21860 20.21857 20.21854 20.21851 20.21848
#> 4  18.05110 18.05106 18.05102 18.05098 18.05095 18.05091 18.05088 18.05085
#> 5  18.87289 18.87286 18.87283 18.87281 18.87278 18.87276 18.87274 18.87271
#> 6  15.00668 15.00674 15.00680 15.00684 15.00689 15.00692 15.00695 15.00698
#> 7  22.98129 22.98134 22.98140 22.98145 22.98150 22.98154 22.98159 22.98163
#> 8  18.78451 18.78456 18.78461 18.78466 18.78471 18.78476 18.78480 18.78485
#> 9  17.99659 17.99654 17.99649 17.99645 17.99641 17.99636 17.99632 17.99628
#> 10 16.44064 16.44078 16.44091 16.44105 16.44118 16.44131 16.44144 16.44157
#> 11 15.41921 15.41920 15.41918 15.41917 15.41916 15.41915 15.41914 15.41913
#> 12 15.00552 15.00545 15.00539 15.00534 15.00528 15.00522 15.00517 15.00512
#> 13 10.01548 10.01532 10.01517 10.01503 10.01488 10.01473 10.01459 10.01445
#> 14 11.72156 11.72156 11.72157 11.72157 11.72157 11.72158 11.72158 11.72158
#> 15 14.31761 14.31777 14.31792 14.31807 14.31823 14.31837 14.31852 14.31866
#> 16 30.84491 30.84492 30.84493 30.84494 30.84495 30.84496 30.84498 30.84499
#> 17 16.41800 16.41801 16.41801 16.41802 16.41803 16.41803 16.41804 16.41804
#> 18 17.67254 17.67250 17.67246 17.67243 17.67239 17.67236 17.67233 17.67230
#> 19 17.67656 17.67655 17.67655 17.67654 17.67654 17.67654 17.67654 17.67654
#> 20 19.54883 19.54898 19.54911 19.54925 19.54938 19.54950 19.54963 19.54974
#> 21 15.18607 15.18593 15.18579 15.18566 15.18553 15.18541 15.18530 15.18519
#>      0.0045   0.0042   0.0039   0.0037
#> 1  20.84358 20.84355 20.84352 20.84348
#> 2  20.67727 20.67725 20.67722 20.67719
#> 3  20.21845 20.21843 20.21840 20.21837
#> 4  18.05082 18.05079 18.05076 18.05074
#> 5  18.87269 18.87267 18.87266 18.87264
#> 6  15.00700 15.00702 15.00703 15.00704
#> 7  22.98167 22.98170 22.98174 22.98177
#> 8  18.78489 18.78494 18.78498 18.78502
#> 9  17.99624 17.99620 17.99616 17.99613
#> 10 16.44169 16.44182 16.44194 16.44206
#> 11 15.41912 15.41910 15.41909 15.41908
#> 12 15.00507 15.00502 15.00497 15.00492
#> 13 10.01431 10.01417 10.01403 10.01390
#> 14 11.72158 11.72158 11.72159 11.72159
#> 15 14.31880 14.31894 14.31908 14.31921
#> 16 30.84501 30.84502 30.84504 30.84506
#> 17 16.41805 16.41806 16.41806 16.41807
#> 18 17.67228 17.67226 17.67223 17.67221
#> 19 17.67654 17.67654 17.67654 17.67655
#> 20 19.54986 19.54997 19.55008 19.55018
#> 21 15.18508 15.18497 15.18488 15.18478
#> 
#> $penalty.factor
#>  [1] 1 1 1 1 1 1 1 1 1 1
#> 
#> $n
#> [1] 21
#> 
#> $y
#>  [1] 21.0 21.0 21.4 18.7 18.1 14.3 22.8 19.2 17.8 16.4 17.3 15.2 10.4 10.4 14.7
#> [16] 30.4 15.5 15.2 19.2 19.7 15.0
#> 
#> $X
#>              am       carb        cyl        disp       drat       gear
#>  [1,]  1.788854  0.4442617 -0.7179582 -1.01829188  0.9822663  0.7897540
#>  [2,]  1.788854  0.4442617 -0.7179582 -1.01829188  0.9822663  0.7897540
#>  [3,] -0.559017 -1.4216373 -0.7179582 -0.13854515 -0.6000186 -0.7179582
#>  [4,] -0.559017 -0.7996710  0.7897540  0.77710961 -0.4649455 -0.7179582
#>  [5,] -0.559017 -1.4216373 -0.7179582 -0.43478639 -1.2174956 -0.7179582
#>  [6,] -0.559017  0.4442617  0.7897540  0.77710961 -0.3491686 -0.7179582
#>  [7,] -0.559017 -0.7996710 -2.2256703 -1.19065042  1.0208586  0.7897540
#>  [8,] -0.559017  0.4442617 -0.7179582 -0.95006662  1.0208586  0.7897540
#>  [9,] -0.559017  0.4442617 -0.7179582 -0.95006662  1.0208586  0.7897540
#> [10,] -0.559017 -0.1777047  0.7897540  0.02124558 -0.6193148 -0.7179582
#> [11,] -0.559017 -0.1777047  0.7897540  0.02124558 -0.6193148 -0.7179582
#> [12,] -0.559017 -0.1777047  0.7897540  0.02124558 -0.6193148 -0.7179582
#> [13,] -0.559017  0.4442617  0.7897540  1.78253445 -0.8894610 -0.7179582
#> [14,] -0.559017  0.4442617  0.7897540  1.67481036 -0.7543879 -0.7179582
#> [15,] -0.559017  0.4442617  0.7897540  1.49527021 -0.3105762 -0.7179582
#> [16,]  1.788854 -0.7996710 -2.2256703 -1.77505361  2.9697705  0.7897540
#> [17,] -0.559017 -0.7996710  0.7897540  0.40007530 -1.2174956 -0.7179582
#> [18,] -0.559017 -0.7996710  0.7897540  0.27439719 -0.4649455 -0.7179582
#> [19,] -0.559017 -0.7996710  0.7897540  1.13618991 -0.6000186 -0.7179582
#> [20,]  1.788854  1.6881943 -0.7179582 -1.15294699  0.4419739  2.2974661
#> [21,]  1.788854  2.9321269  0.7897540  0.24746617  0.2876046  2.2974661
#>               hp        qsec         vs          wt
#>  [1,] -0.8650032 -0.74110773 -0.6324555 -1.11998462
#>  [2,] -0.8650032 -0.41222370 -0.6324555 -0.82804938
#>  [3,] -0.8650032  1.00902517  1.5811388 -0.43880238
#>  [4,]  0.1958498 -0.41222370 -0.6324555 -0.18121246
#>  [5,] -0.9466073  1.46711364  1.5811388 -0.15831558
#>  [6,]  1.3383068 -1.10522934 -0.6324555 -0.03238273
#>  [7,] -1.1098154  3.04105866  1.5811388 -0.51321725
#>  [8,] -0.6528326  0.33951124  1.5811388 -0.18121246
#>  [9,] -0.6528326  0.69188699  1.5811388 -0.18121246
#> [10,]  0.2774539 -0.18905239 -0.6324555  0.54003931
#> [11,]  0.2774539 -0.07159380 -0.6324555  0.15079232
#> [12,]  0.2774539  0.16332336 -0.6324555  0.20803453
#> [13,]  0.6854742  0.15157751 -0.6324555  1.89095534
#> [14,]  0.8486824  0.05761064 -0.6324555  2.09015821
#> [15,]  1.0934946 -0.17730653 -0.6324555  1.99971553
#> [16,] -1.8116105  0.46871568  1.5811388 -2.27055293
#> [17,] -0.2121706 -0.50031763 -0.6324555 -0.08962494
#> [18,] -0.2121706 -0.24778168 -0.6324555 -0.18693668
#> [19,]  0.1958498 -0.39460491 -0.6324555  0.28244939
#> [20,]  0.1958498 -1.30490893 -0.6324555 -0.94825800
#> [21,]  2.8071802 -1.83347256 -0.6324555 -0.03238273
#> attr(,"center")
#>  [1]   0.2380952   3.2857143   6.9523810 273.4333333   3.3909524   3.4761905
#>  [7] 163.0000000  17.7219048   0.2857143   3.5982857
#> attr(,"scale")
#>  [1]   0.4259177   1.6078041   1.3265132 111.3956968   0.5182379   0.6632566
#>  [7]  61.2714491   1.7027278   0.4517540   0.8734814
#> attr(,"nonsingular")
#>  [1]  1  2  3  4  5  6  7  8  9 10
#> 
#> attr(,"class")
#> [1] "ncvreg"
#> 
#> $min
#> [1] 40
#> 
#> $lambda.min
#> [1] 0.241225
#> 
#> $null.dev
#> [1] 18.37474
#> 
#> $Bias
#> [1] 2.461
#> 
#> 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 
#> 16.17156