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] 38.845718 35.624027 30.315206 25.951956 22.420452 19.594604 17.365943
#>   [8] 15.641241 14.340457 13.394945 12.745906 12.343041 12.143393 12.110334
#>  [15] 12.212689 12.393655 12.458722 12.472816 12.472816 12.444742 12.375167
#>  [22] 12.311606 12.249062 12.117945 11.967842 10.985618 10.440155  9.621111
#>  [29]  9.062488  8.891788  8.741900  8.613795  8.534606  8.496018  8.377482
#>  [36]  8.936309  9.186700 10.930083 11.114102 11.213140 11.608380 11.591664
#>  [43] 11.583357 11.581071 10.923517 10.826960 10.235431 10.156960 17.521848
#>  [50] 17.453736 17.440768 17.878493 16.269255 16.290827 16.794886 17.054973
#>  [57] 18.496647 18.499272 18.746192 20.146515 20.125799 20.127327 20.130340
#>  [64] 26.888714 26.854379 26.893088 26.843605 26.846402 26.830900 26.769023
#>  [71] 26.771333 27.364322 27.118453 27.291336 27.416901 27.417476 27.356811
#>  [78] 27.516726 27.517199 27.517640 27.518051 27.518432 27.415717 27.416110
#>  [85] 27.416478 27.424954 27.425262 27.456520 27.456744 27.456948 27.457131
#>  [92] 27.457296 27.457444 27.457646 27.478845 27.475007 27.398358 27.398655
#>  [99] 27.398955 27.399257
#> 
#> $cvse
#>   [1] 9.590540 9.317479 8.425885 7.631936 6.924062 6.287077 5.711328 5.191706
#>   [9] 4.726817 4.318266 3.969926 3.686986 3.474616 3.336223 3.271749 3.272759
#>  [17] 3.307020 3.337762 3.337762 3.322433 3.285573 3.253361 3.226031 3.202782
#>  [25] 3.174771 3.120967 3.075426 3.017984 2.999040 2.959466 2.924983 2.896100
#>  [33] 2.880197 2.866082 2.844906 2.802493 2.773002 3.318664 3.296616 3.283725
#>  [41] 3.527084 3.524863 3.508128 3.507501 3.511609 3.521312 3.191046 3.154685
#>  [49] 6.429709 6.420568 6.419338 6.377482 5.396497 5.393442 5.346174 5.408197
#>  [57] 6.236781 6.238179 6.290968 6.218565 6.215543 6.216393 6.218110 8.992511
#>  [65] 8.999307 9.012772 9.007910 9.009489 9.013230 9.021855 9.023275 9.145487
#>  [73] 9.165140 9.177709 9.311915 9.312455 9.320434 9.346993 9.347473 9.347933
#>  [81] 9.348374 9.348795 9.362121 9.362498 9.362859 9.362035 9.362366 9.360363
#>  [89] 9.360668 9.360959 9.361237 9.361501 9.361754 9.361999 9.363479 9.364654
#>  [97] 9.391230 9.391935 9.392629 9.393312
#> 
#> $fold
#>  [1]  3  8  6  5  5  4  1  7  6 10  4  2  9  9  1  2  1 10  3  8  7
#> 
#> $lambda
#>   [1] 5.297239285 4.940223087 4.607268585 4.296754103 4.007167257 3.737097595
#>   [7] 3.485229725 3.250336906 3.031275077 2.826977282 2.636448475 2.458760672
#>  [13] 2.293048432 2.138504642 1.994376586 1.859962279 1.734607047 1.617700337
#>  [19] 1.508672749 1.406993255 1.312166619 1.223730980 1.141255608 1.064338799
#>  [25] 0.992605927 0.925707609 0.863318015 0.805133270 0.750869982 0.700263858
#>  [31] 0.653068418 0.609053792 0.568005605 0.529723929 0.494022309 0.460726859
#>  [37] 0.429675410 0.400716726 0.373709760 0.348522972 0.325033691 0.303127508
#>  [43] 0.282697728 0.263644847 0.245876067 0.229304843 0.213850464 0.199437659
#>  [49] 0.185996228 0.173460705 0.161770034 0.150867275 0.140699325 0.131216662
#>  [55] 0.122373098 0.114125561 0.106433880 0.099260593 0.092570761 0.086331801
#>  [61] 0.080513327 0.075086998 0.070026386 0.065306842 0.060905379 0.056800561
#>  [67] 0.052972393 0.049402231 0.046072686 0.042967541 0.040071673 0.037370976
#>  [73] 0.034852297 0.032503369 0.030312751 0.028269773 0.026364485 0.024587607
#>  [79] 0.022930484 0.021385046 0.019943766 0.018599623 0.017346070 0.016177003
#>  [85] 0.015086727 0.014069933 0.013121666 0.012237310 0.011412556 0.010643388
#>  [91] 0.009926059 0.009257076 0.008633180 0.008051333 0.007508700 0.007002639
#>  [97] 0.006530684 0.006090538 0.005680056 0.005297239
#> 
#> $fit
#> $beta
#>               5.2972     4.9402     4.6073     4.2968    4.0072    3.7371
#> (Intercept) 20.77619 22.6167509 24.3332638 25.9340894 27.427025 28.819341
#> am           0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> carb         0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> cyl          0.00000 -0.3067601 -0.5928456 -0.8596498 -1.108472 -1.340525
#> disp         0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> drat         0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> gear         0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> hp           0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> qsec         0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> vs           0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#> wt           0.00000  0.0000000  0.0000000  0.0000000  0.000000  0.000000
#>                3.4852    3.2503    3.0313   2.8270    2.6364    2.4588   2.2930
#> (Intercept) 30.117820 31.328786 32.458137 33.51137 34.493625 35.409676 36.26399
#> am           0.000000  0.000000  0.000000  0.00000  0.000000  0.000000  0.00000
#> carb         0.000000  0.000000  0.000000  0.00000  0.000000  0.000000  0.00000
#> cyl         -1.556938 -1.758766 -1.946991 -2.12253 -2.286239 -2.438914 -2.58130
#> disp         0.000000  0.000000  0.000000  0.00000  0.000000  0.000000  0.00000
#> drat         0.000000  0.000000  0.000000  0.00000  0.000000  0.000000  0.00000
#> gear         0.000000  0.000000  0.000000  0.00000  0.000000  0.000000  0.00000
#> hp           0.000000  0.000000  0.000000  0.00000  0.000000  0.000000  0.00000
#> qsec         0.000000  0.000000  0.000000  0.00000  0.000000  0.000000  0.00000
#> vs           0.000000  0.000000  0.000000  0.00000  0.000000  0.000000  0.00000
#> wt           0.000000  0.000000  0.000000  0.00000  0.000000  0.000000  0.00000
#>                2.1385    1.9944    1.8600    1.7346    1.6177    1.5087
#> (Intercept) 37.060724 37.803761 38.496720 38.982440 38.982440 38.982440
#> 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         -2.714089 -2.837928 -2.953422 -3.034375 -3.034375 -3.034375
#> disp         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> drat         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> gear         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> hp           0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> qsec         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> vs           0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> wt           0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#>                1.4070    1.3122    1.2237    1.1413    1.0643    0.9926
#> (Intercept) 38.982440 38.982440 38.982440 38.982440 38.982440 39.533346
#> 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         -3.034375 -3.034375 -3.034375 -3.034375 -3.034375 -2.515036
#> disp         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> drat         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> gear         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> hp           0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> qsec         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> vs           0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> wt           0.000000  0.000000  0.000000  0.000000  0.000000 -1.167515
#>                0.9257    0.8633    0.8051    0.7509    0.7003    0.6531
#> (Intercept) 40.049107 40.254681 40.254459 40.254324 40.254243 40.254193
#> 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         -2.027375 -1.832173 -1.832045 -1.831967 -1.831920 -1.831891
#> 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          -2.263323 -2.701676 -2.701851 -2.701957 -2.702021 -2.702060
#>                0.6091    0.5680    0.5297    0.4940    0.4607    0.4297
#> (Intercept) 40.254163 40.254145 40.254134 40.254128 40.254124 40.254121
#> am           0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> carb         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
#> cyl         -1.831874 -1.831863 -1.831857 -1.831853 -1.831851 -1.831849
#> 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          -2.702084 -2.702098 -2.702107 -2.702112 -2.702115 -2.702117
#>                  0.4007     0.3737     0.3485     0.3250    0.3031     0.2827
#> (Intercept) 40.26664742 40.2790000 40.2905214 40.3012663 40.311287 40.3206323
#> am           0.00000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> carb        -0.08163198 -0.1583014 -0.2297962 -0.2964725 -0.358655 -0.4166466
#> cyl         -1.81698544 -1.8033657 -1.7906667 -1.7788236 -1.767779 -1.7574781
#> disp         0.00000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> drat         0.00000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> gear         0.00000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> hp           0.00000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> qsec         0.00000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> vs           0.00000000  0.0000000  0.0000000  0.0000000  0.000000  0.0000000
#> wt          -2.66642921 -2.6324475 -2.6007573 -2.5712030 -2.543640 -2.5179356
#>                 0.2636     0.2459     0.2293     0.2139     0.1994     0.1860
#> (Intercept) 40.3290427 37.8063353 37.8065985 37.8068812 37.8071409 37.8073597
#> am           0.0000000  1.5507506  1.5508417  1.5508382  1.5507891  1.5507236
#> carb        -0.4708643 -0.7200068 -0.7200077 -0.7199891 -0.7199632 -0.7199366
#> cyl         -1.7476586 -1.6269749 -1.6272099 -1.6273754 -1.6274883 -1.6275628
#> disp         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> drat         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> gear         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> hp           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> qsec         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> vs           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> wt          -2.4941610 -1.9018427 -1.9014879 -1.9012767 -1.9011594 -1.9011011
#>                 0.1735     0.1618     0.1509     0.1407     0.1312     0.1224
#> (Intercept) 37.8075337 34.2027263 34.2001452 34.1980194 34.1962687 34.1948269
#> am           1.5506576  2.3410560  2.3419561  2.3426976  2.3433083  2.3438114
#> carb        -0.7199128 -0.6977098 -0.6978156 -0.6979027 -0.6979745 -0.6980336
#> cyl         -1.6276100 -1.2447041 -1.2444607 -1.2442604 -1.2440956 -1.2439599
#> disp         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> drat         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> gear         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> hp           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> qsec         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> vs           0.0000000  1.3186199  1.3192420  1.3197545  1.3201765  1.3205240
#> wt          -1.9010780 -1.7991288 -1.7988873 -1.7986881 -1.7985238 -1.7983884
#>                 0.1141     0.1064     0.0993     0.0926     0.0863     0.0805
#> (Intercept) 28.9983589 28.9948933 28.9918990 28.9893120 28.9870772 28.9851468
#> am           2.2334386  2.2340258  2.2345308  2.2349653  2.2353396  2.2356621
#> carb        -0.9189347 -0.9190788 -0.9192033 -0.9193108 -0.9194037 -0.9194839
#> cyl         -1.0117942 -1.0115095 -1.0112634 -1.0110507 -1.0108668 -1.0107078
#> disp         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> drat         1.0472749  1.0475800  1.0478447  1.0480739  1.0482724  1.0484440
#> 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           1.3578789  1.3583902  1.3588312  1.3592118  1.3595404  1.3598241
#> wt          -1.6144404 -1.6142647 -1.6141137 -1.6139840 -1.6138725 -1.6137766
#>                 0.0751     0.0700     0.0653     0.0609     0.0568     0.0530
#> (Intercept) 28.9834793 28.9820390 28.9807949 13.0454412 13.0403046 13.0353833
#> am           2.2359402  2.2361802  2.2363873  2.7458796  2.7461645  2.7464375
#> carb        -0.9195531 -0.9196129 -0.9196645 -1.1447046 -1.1448047 -1.1449006
#> cyl         -1.0105704 -1.0104515 -1.0103488 -0.1821045 -0.1817873 -0.1814835
#> disp         0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> drat         1.0485924  1.0487206  1.0488313  1.3492296  1.3493630  1.3494907
#> gear         0.0000000  0.0000000  0.0000000  1.2593356  1.2597049  1.2600588
#> hp           0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#> qsec         0.0000000  0.0000000  0.0000000  0.2999756  0.3000471  0.3001156
#> vs           1.3600691  1.3602808  1.3604636  1.5852939  1.5855375  1.5857709
#> wt          -1.6136941 -1.6136231 -1.6135620 -1.5666314 -1.5665855 -1.5665415
#>                  0.0494      0.0461      0.0430      0.0401      0.0374
#> (Intercept)  5.46628854  5.46408468  5.46198786  5.45999309  5.45809564
#> am           3.09464627  3.09494510  3.09522949  3.09550011  3.09575759
#> carb        -0.82571519 -0.82554454 -0.82538236 -0.82522824 -0.82508180
#> cyl          0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> disp         0.01638434  0.01638896  0.01639335  0.01639752  0.01640148
#> drat         1.50066833  1.50051852  1.50037599  1.50024040  1.50011143
#> gear         1.83513826  1.83515788  1.83517644  1.83519400  1.83521060
#> hp          -0.01240298 -0.01240340 -0.01240380 -0.01240416 -0.01240450
#> qsec         0.51302741  0.51317130  0.51330821  0.51343846  0.51356236
#> vs           2.13041126  2.13051113  2.13060589  2.13069580  2.13078109
#> wt          -2.58156090 -2.58203103 -2.58247794 -2.58290274 -2.58330650
#>                  0.0349      0.0325      0.0303      0.0283      0.0264
#> (Intercept)  5.45629096  5.45457468  5.45294266  5.45139092  5.44991565
#> am           3.09600254  3.09623555  3.09645717  3.09666794  3.09686836
#> carb        -0.82494266 -0.82481048 -0.82468490 -0.82456562 -0.82445233
#> cyl          0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> disp         0.01640525  0.01640882  0.01641221  0.01641544  0.01641849
#> drat         1.49998877  1.49987212  1.49976120  1.49965573  1.49955547
#> gear         1.83522631  1.83524116  1.83525521  1.83526849  1.83528106
#> hp          -0.01240482 -0.01240511 -0.01240539 -0.01240564 -0.01240588
#> qsec         0.51368021  0.51379229  0.51389888  0.51400022  0.51409658
#> vs           2.13086201  2.13093876  2.13101157  2.13108063  2.13114614
#> wt          -2.58369021 -2.58405484 -2.58440131 -2.58473050 -2.58504324
#>                 0.0246      0.0229      0.0214      0.0199      0.0186
#> (Intercept)  5.4485132  5.44718017  5.44591317  5.44470907  5.44356484
#> am           3.0970589  3.09724011  3.09741235  3.09757607  3.09773168
#> carb        -0.8243447 -0.82424254 -0.82414550 -0.82405336 -0.82396587
#> cyl          0.0000000  0.00000000  0.00000000  0.00000000  0.00000000
#> disp         0.0164214  0.01642415  0.01642677  0.01642925  0.01643161
#> drat         1.4994602  1.49936956  1.49928346  1.49920163  1.49912387
#> gear         1.8352929  1.83530418  1.83531482  1.83532487  1.83533438
#> hp          -0.0124061 -0.01240630 -0.01240649 -0.01240667 -0.01240684
#> qsec         0.5141882  0.51427525  0.51435802  0.51443667  0.51451142
#> vs           2.1312083  2.13126719  2.13132306  2.13137605  2.13142630
#> wt          -2.5853403 -2.58562253 -2.58589057 -2.58614514 -2.58638689
#>                  0.0173      0.0162      0.0151      0.0141      0.0131
#> (Intercept)  5.44247760  5.44144461  5.44046322  5.43953095  5.43864540
#> am           3.09787957  3.09802011  3.09815364  3.09828052  3.09840106
#> carb        -0.82388281 -0.82380396 -0.82372910 -0.82365805 -0.82359060
#> cyl          0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
#> disp         0.01643385  0.01643597  0.01643799  0.01643990  0.01644171
#> drat         1.49904999  1.49897979  1.49891310  1.49884975  1.49878957
#> gear         1.83534338  1.83535189  1.83535994  1.83536755  1.83537475
#> hp          -0.01240699 -0.01240713 -0.01240726 -0.01240739 -0.01240750
#> qsec         0.51458245  0.51464994  0.51471405  0.51477496  0.51483282
#> vs           2.13147395  2.13151913  2.13156196  2.13160258  2.13164108
#> wt          -2.58661646 -2.58683444 -2.58704141 -2.58723791 -2.58742445
#>                  0.0122      0.0114      0.0106      0.0099      0.0093
#> (Intercept)  5.43780429  5.43700546  5.43624684  9.06023246  9.06175331
#> am           3.09851558  3.09862435  3.09872766  2.95626796  2.95607426
#> carb        -0.82352659 -0.82346584 -0.82340819 -0.74916304 -0.74930007
#> cyl          0.00000000  0.00000000  0.00000000 -0.21760735 -0.21759963
#> disp         0.01644344  0.01644507  0.01644662  0.01666993  0.01666524
#> drat         1.49873242  1.49867814  1.49862659  1.36202902  1.36212755
#> gear         1.83538156  1.83538800  1.83539409  1.58439736  1.58433382
#> hp          -0.01240761 -0.01240771 -0.01240780 -0.01257549 -0.01257353
#> qsec         0.51488778  0.51493998  0.51498955  0.46586625  0.46577662
#> vs           2.13167759  2.13171219  2.13174500  1.99879386  1.99866061
#> wt          -2.58760154 -2.58776963 -2.58792917 -2.62597913 -2.62560188
#>                  0.0086      0.0081      0.0075      0.0070      0.0065
#> (Intercept)  9.06312735  9.06436032  9.06545785  9.06642540  9.06726832
#> am           2.95588928  2.95571277  2.95554452  2.95538427  2.95523181
#> carb        -0.74943612 -0.74957111 -0.74970495 -0.74983757 -0.74996889
#> cyl         -0.21758558 -0.21756551 -0.21753975 -0.21750860 -0.21747234
#> disp         0.01666067  0.01665622  0.01665190  0.01664769  0.01664360
#> drat         1.36222814  1.36233061  1.36243476  1.36254039  1.36264734
#> gear         1.58428043  1.58423673  1.58420231  1.58417675  1.58415963
#> hp          -0.01257164 -0.01256981 -0.01256804 -0.01256633 -0.01256467
#> qsec         0.46569036  0.46560740  0.46552767  0.46545107  0.46537755
#> vs           1.99853552  1.99841832  1.99830873  1.99820650  1.99811138
#> wt          -2.62523268 -2.62487149 -2.62451831 -2.62417308 -2.62383577
#>                  0.0061      0.0057      0.0053
#> (Intercept)  9.06799181  9.06860096  9.06910069
#> am           2.95508691  2.95494934  2.95481889
#> carb        -0.75009884 -0.75022736 -0.75035439
#> cyl         -0.21743126 -0.21738565 -0.21733575
#> disp         0.01663963  0.01663577  0.01663202
#> drat         1.36275544  1.36286451  1.36297440
#> gear         1.58415058  1.58414920  1.58415513
#> hp          -0.01256307 -0.01256152 -0.01256002
#> qsec         0.46530701  0.46523940  0.46517463
#> vs           1.99802311  1.99794145  1.99786617
#> wt          -2.62350634 -2.62318473 -2.62287088
#> 
#> $iter
#>   [1]   0   2   2   2   2   2   2   2   2   2   2   2   2   2   2   2   2   1
#>  [19]   1   1   1   1   1   1  56  55  15   1   1   1   1   1   1   1   1   1
#>  [37]   1  11  10  10  10  10  10   9  67   1   1   1   1   1  44   1   1   1
#>  [55]   1  46   1   1   1   1   1   1   1   1 179   1   1 204   1   1   1   1
#>  [73]   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1
#>  [91] 123   1   1   1   1   1   1   1   1   1
#> 
#> $lambda
#>   [1] 5.297239285 4.940223087 4.607268585 4.296754103 4.007167257 3.737097595
#>   [7] 3.485229725 3.250336906 3.031275077 2.826977282 2.636448475 2.458760672
#>  [13] 2.293048432 2.138504642 1.994376586 1.859962279 1.734607047 1.617700337
#>  [19] 1.508672749 1.406993255 1.312166619 1.223730980 1.141255608 1.064338799
#>  [25] 0.992605927 0.925707609 0.863318015 0.805133270 0.750869982 0.700263858
#>  [31] 0.653068418 0.609053792 0.568005605 0.529723929 0.494022309 0.460726859
#>  [37] 0.429675410 0.400716726 0.373709760 0.348522972 0.325033691 0.303127508
#>  [43] 0.282697728 0.263644847 0.245876067 0.229304843 0.213850464 0.199437659
#>  [49] 0.185996228 0.173460705 0.161770034 0.150867275 0.140699325 0.131216662
#>  [55] 0.122373098 0.114125561 0.106433880 0.099260593 0.092570761 0.086331801
#>  [61] 0.080513327 0.075086998 0.070026386 0.065306842 0.060905379 0.056800561
#>  [67] 0.052972393 0.049402231 0.046072686 0.042967541 0.040071673 0.037370976
#>  [73] 0.034852297 0.032503369 0.030312751 0.028269773 0.026364485 0.024587607
#>  [79] 0.022930484 0.021385046 0.019943766 0.018599623 0.017346070 0.016177003
#>  [85] 0.015086727 0.014069933 0.013121666 0.012237310 0.011412556 0.010643388
#>  [91] 0.009926059 0.009257076 0.008633180 0.008051333 0.007508700 0.007002639
#>  [97] 0.006530684 0.006090538 0.005680056 0.005297239
#> 
#> $penalty
#> [1] "MCP"
#> 
#> $family
#> [1] "gaussian"
#> 
#> $gamma
#> [1] 3
#> 
#> $alpha
#> [1] 1
#> 
#> $convex.min
#> [1] 24
#> 
#> $loss
#>   [1] 741.09810 627.97499 533.33070 454.50596 389.20493 335.44662 291.52290
#>   [8] 255.96189 227.49631 205.03594 187.64374 174.51517 164.96021 158.38780
#>  [15] 154.29231 152.24189 151.82247 151.82247 151.82247 151.82247 151.82247
#>  [22] 151.82247 151.82247 151.82247 110.97803  93.12178  91.53189  91.53189
#>  [29]  91.53189  91.53189  91.53189  91.53189  91.53189  91.53189  91.53189
#>  [36]  91.53189  91.53189  89.92598  88.64020  87.63540  86.86722  86.29771
#>  [43]  85.89435  85.62878  81.21703  81.21703  81.21703  81.21702  81.21702
#>  [50]  81.21702  78.83510  78.83509  78.83508  78.83508  78.83507  77.47063
#>  [57]  77.47062  77.47061  77.47061  77.47060  77.47060  77.47060  77.47060
#>  [64]  77.47060  75.74620  75.74619  75.74618  73.41615  73.41613  73.41612
#>  [71]  73.41611  73.41610  73.41609  73.41608  73.41607  73.41607  73.41606
#>  [78]  73.41605  73.41605  73.41604  73.41604  73.41604  73.41603  73.41603
#>  [85]  73.41603  73.41603  73.41602  73.41602  73.41602  73.41602  73.33606
#>  [92]  73.33605  73.33604  73.33603  73.33602  73.33601  73.33600  73.33599
#>  [99]  73.33598  73.33598
#> 
#> $linear.predictors
#>      5.2972   4.9402   4.6073   4.2968   4.0072   3.7371   3.4852   3.2503
#> 1  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 2  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 3  20.77619 21.38971 21.96188 22.49549 22.99314 23.45724 23.89007 24.29372
#> 4  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 5  20.77619 20.16267 19.59050 19.05689 18.55925 18.09514 17.66231 17.25866
#> 6  20.77619 20.16267 19.59050 19.05689 18.55925 18.09514 17.66231 17.25866
#> 7  20.77619 21.38971 21.96188 22.49549 22.99314 23.45724 23.89007 24.29372
#> 8  20.77619 21.38971 21.96188 22.49549 22.99314 23.45724 23.89007 24.29372
#> 9  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 10 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 11 20.77619 20.16267 19.59050 19.05689 18.55925 18.09514 17.66231 17.25866
#> 12 20.77619 20.16267 19.59050 19.05689 18.55925 18.09514 17.66231 17.25866
#> 13 20.77619 20.16267 19.59050 19.05689 18.55925 18.09514 17.66231 17.25866
#> 14 20.77619 21.38971 21.96188 22.49549 22.99314 23.45724 23.89007 24.29372
#> 15 20.77619 21.38971 21.96188 22.49549 22.99314 23.45724 23.89007 24.29372
#> 16 20.77619 20.16267 19.59050 19.05689 18.55925 18.09514 17.66231 17.25866
#> 17 20.77619 20.16267 19.59050 19.05689 18.55925 18.09514 17.66231 17.25866
#> 18 20.77619 20.16267 19.59050 19.05689 18.55925 18.09514 17.66231 17.25866
#> 19 20.77619 21.38971 21.96188 22.49549 22.99314 23.45724 23.89007 24.29372
#> 20 20.77619 21.38971 21.96188 22.49549 22.99314 23.45724 23.89007 24.29372
#> 21 20.77619 21.38971 21.96188 22.49549 22.99314 23.45724 23.89007 24.29372
#>      3.0313   2.8270   2.6364   2.4588   2.2930   2.1385   1.9944   1.8600
#> 1  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 2  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 3  24.67017 25.02125 25.34867 25.65402 25.93879 26.20437 26.45205 26.68303
#> 4  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 5  16.88221 16.53113 16.20371 15.89836 15.61359 15.34801 15.10033 14.86935
#> 6  16.88221 16.53113 16.20371 15.89836 15.61359 15.34801 15.10033 14.86935
#> 7  24.67017 25.02125 25.34867 25.65402 25.93879 26.20437 26.45205 26.68303
#> 8  24.67017 25.02125 25.34867 25.65402 25.93879 26.20437 26.45205 26.68303
#> 9  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 10 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 11 16.88221 16.53113 16.20371 15.89836 15.61359 15.34801 15.10033 14.86935
#> 12 16.88221 16.53113 16.20371 15.89836 15.61359 15.34801 15.10033 14.86935
#> 13 16.88221 16.53113 16.20371 15.89836 15.61359 15.34801 15.10033 14.86935
#> 14 24.67017 25.02125 25.34867 25.65402 25.93879 26.20437 26.45205 26.68303
#> 15 24.67017 25.02125 25.34867 25.65402 25.93879 26.20437 26.45205 26.68303
#> 16 16.88221 16.53113 16.20371 15.89836 15.61359 15.34801 15.10033 14.86935
#> 17 16.88221 16.53113 16.20371 15.89836 15.61359 15.34801 15.10033 14.86935
#> 18 16.88221 16.53113 16.20371 15.89836 15.61359 15.34801 15.10033 14.86935
#> 19 24.67017 25.02125 25.34867 25.65402 25.93879 26.20437 26.45205 26.68303
#> 20 24.67017 25.02125 25.34867 25.65402 25.93879 26.20437 26.45205 26.68303
#> 21 24.67017 25.02125 25.34867 25.65402 25.93879 26.20437 26.45205 26.68303
#>      1.7346   1.6177   1.5087   1.4070   1.3122   1.2237   1.1413   1.0643
#> 1  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 2  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 3  26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494
#> 4  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 5  14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744
#> 6  14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744
#> 7  26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494
#> 8  26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494
#> 9  20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 10 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619 20.77619
#> 11 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744
#> 12 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744
#> 13 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744
#> 14 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494
#> 15 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494
#> 16 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744
#> 17 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744
#> 18 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744 14.70744
#> 19 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494
#> 20 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494
#> 21 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494 26.84494
#>      0.9926   0.9257   0.8633   0.8051   0.7509   0.7003   0.6531   0.6091
#> 1  21.38424 21.95495 22.18325 22.18334 22.18340 22.18343 22.18345 22.18346
#> 2  21.08653 21.37780 21.49432 21.49437 21.49440 21.49441 21.49442 21.49443
#> 3  26.76457 26.68870 26.65810 26.65799 26.65792 26.65787 26.65785 26.65783
#> 4  20.68957 20.60827 20.57575 20.57574 20.57573 20.57573 20.57572 20.57572
#> 5  15.39681 16.04428 16.30353 16.30373 16.30386 16.30393 16.30398 16.30401
#> 6  15.24503 15.75004 15.95231 15.95249 15.95260 15.95267 15.95271 15.95273
#> 7  25.74883 24.71961 24.30764 24.30737 24.30721 24.30712 24.30706 24.30702
#> 8  25.79553 24.81014 24.41571 24.41545 24.41529 24.41520 24.41514 24.41510
#> 9  20.42688 20.09903 19.96787 19.96782 19.96779 19.96777 19.96776 19.96775
#> 10 20.42688 20.09903 19.96787 19.96782 19.96779 19.96777 19.96776 19.96775
#> 11 15.05823 15.38791 15.52004 15.52020 15.52029 15.52035 15.52038 15.52040
#> 12 13.08046 11.55384 10.94340 10.94326 10.94317 10.94312 10.94309 10.94307
#> 13 13.17269 11.73264 11.15683 11.15671 11.15663 11.15658 11.15655 11.15654
#> 14 26.90467 26.96030 26.98230 26.98221 26.98215 26.98212 26.98210 26.98208
#> 15 27.58767 28.28434 28.56278 28.56279 28.56280 28.56280 28.56280 28.56280
#> 16 15.30341 15.86321 16.08739 16.08758 16.08770 16.08777 16.08781 16.08784
#> 17 15.40265 16.05559 16.31704 16.31724 16.31737 16.31744 16.31749 16.31752
#> 18 14.92980 15.13895 15.22286 15.22299 15.22307 15.22312 15.22315 15.22317
#> 19 27.21406 27.56008 27.69824 27.69820 27.69817 27.69815 27.69814 27.69814
#> 20 26.97472 27.09610 27.14440 27.14432 27.14427 27.14424 27.14422 27.14421
#> 21 27.70675 28.51520 28.83835 28.83838 28.83840 28.83841 28.83841 28.83842
#>      0.5680   0.5297   0.4940   0.4607   0.4297   0.4007   0.3737   0.3485
#> 1  22.18347 22.18347 22.18348 22.18348 22.18348 22.05216 21.92859 21.81335
#> 2  21.49443 21.49444 21.49444 21.49444 21.49444 21.37222 21.25731 21.15016
#> 3  26.65782 26.65782 26.65782 26.65781 26.65781 26.73096 26.79996 26.86430
#> 4  20.57572 20.57572 20.57572 20.57572 20.57572 20.71053 20.83719 20.95529
#> 5  16.30402 16.30403 16.30404 16.30404 16.30404 16.39498 16.47985 16.55899
#> 6  15.95275 15.95276 15.95276 15.95277 15.95277 15.88508 15.82103 15.76130
#> 7  24.30700 24.30699 24.30698 24.30697 24.30697 24.32953 24.35143 24.37185
#> 8  24.41508 24.41507 24.41506 24.41506 24.41506 24.43619 24.45672 24.47588
#> 9  19.96775 19.96775 19.96774 19.96774 19.96774 19.86569 19.76998 19.68073
#> 10 19.96775 19.96775 19.96774 19.96774 19.96774 19.86569 19.76998 19.68073
#> 11 15.52041 15.52042 15.52043 15.52043 15.52043 15.54009 15.55814 15.57497
#> 12 10.94306 10.94305 10.94305 10.94305 10.94304 10.94152 10.94047 10.93950
#> 13 11.15653 11.15652 11.15651 11.15651 11.15651 11.15217 11.14844 11.14495
#> 14 26.98208 26.98207 26.98207 26.98207 26.98207 27.05093 27.11585 27.17639
#> 15 28.56280 28.56280 28.56280 28.56280 28.56281 28.52916 28.49753 28.46804
#> 16 16.08785 16.08786 16.08787 16.08787 16.08787 16.18167 16.26926 16.35093
#> 17 16.31753 16.31754 16.31755 16.31755 16.31755 16.40832 16.49301 16.57199
#> 18 15.22318 15.22319 15.22319 15.22320 15.22320 15.16515 15.11027 15.05909
#> 19 27.69813 27.69813 27.69813 27.69813 27.69813 27.75753 27.81345 27.86559
#> 20 27.14420 27.14420 27.14420 27.14419 27.14419 27.12928 27.11550 27.10264
#> 21 28.83842 28.83842 28.83842 28.83842 28.83842 28.80113 28.76604 28.73332
#>      0.3250   0.3031   0.2827   0.2636   0.2459   0.2293   0.2139   0.1994
#> 1  21.70588 21.60566 21.51219 21.42493 21.73238 21.73225 21.73217 21.73211
#> 2  21.05023 20.95703 20.87011 20.78892 21.24741 21.24737 21.24734 21.24731
#> 3  26.92431 26.98027 27.03246 27.08109 27.71690 27.71714 27.71727 27.71732
#> 4  21.06543 21.16816 21.26395 21.35350 21.21005 21.21005 21.21004 21.21002
#> 5  16.63279 16.70162 16.76582 16.82613 16.80818 16.80779 16.80751 16.80732
#> 6  15.70559 15.65364 15.60519 15.56016 15.12093 15.12058 15.12036 15.12024
#> 7  24.39089 24.40865 24.42521 24.44031 23.79154 23.79200 23.79233 23.79256
#> 8  24.49374 24.51039 24.52593 24.54007 23.86762 23.86806 23.86838 23.86861
#> 9  19.59750 19.51987 19.44748 19.37972 18.62212 18.62219 18.62228 18.62237
#> 10 19.59750 19.51987 19.44748 19.37972 18.62212 18.62219 18.62228 18.62237
#> 11 15.59067 15.60531 15.61897 15.63196 15.53664 15.53635 15.53615 15.53602
#> 12 10.93858 10.93773 10.93694 10.93599 11.59491 11.59522 11.59540 11.59549
#> 13 11.14171 11.13868 11.13586 11.13303 11.74516 11.74544 11.74560 11.74568
#> 14 27.23285 27.28551 27.33462 27.38039 27.94513 27.94532 27.94542 27.94546
#> 15 28.44053 28.41488 28.39096 28.36861 28.33770 28.33768 28.33768 28.33768
#> 16 16.42710 16.49813 16.56438 16.62660 16.65604 16.65567 16.65541 16.65523
#> 17 16.64565 16.71434 16.77841 16.83860 16.81769 16.81729 16.81701 16.81683
#> 18 15.01137 14.96686 14.92535 14.88674 14.60743 14.60718 14.60702 14.60693
#> 19 27.91422 27.95957 28.00187 28.04134 28.44911 28.44921 28.44926 28.44927
#> 20 27.09065 27.07947 27.06904 27.05918 27.33923 27.33940 27.33951 27.33957
#> 21 28.70280 28.67433 28.64779 28.62301 28.53168 28.53163 28.53161 28.53160
#>      0.1860   0.1735   0.1618   0.1509   0.1407   0.1312   0.1224   0.1141
#> 1  21.73208 21.73206 21.57100 21.57099 21.57098 21.57097 21.57097 21.33983
#> 2  21.24729 21.24728 21.11222 21.11227 21.11232 21.11235 21.11238 20.92815
#> 3  27.71734 27.71734 28.01190 28.01227 28.01257 28.01282 28.01303 27.91007
#> 4  21.21001 21.21000 21.57121 21.57138 21.57153 21.57164 21.57174 21.40172
#> 5  16.80720 16.80712 16.66067 16.66066 16.66064 16.66063 16.66062 16.81138
#> 6  15.12018 15.12015 15.03136 15.03117 15.03101 15.03088 15.03077 14.82647
#> 7  23.79272 23.79283 23.40789 23.40746 23.40711 23.40682 23.40659 23.18557
#> 8  23.86877 23.86887 23.47985 23.47942 23.47906 23.47876 23.47852 23.49102
#> 9  18.62245 18.62251 19.07328 19.07319 19.07311 19.07305 19.07300 19.16138
#> 10 18.62245 18.62251 19.07328 19.07319 19.07311 19.07305 19.07300 19.16138
#> 11 15.53594 15.53589 15.44121 15.44116 15.44112 15.44109 15.44106 15.34047
#> 12 11.59554 11.59556 11.69578 11.69603 11.69624 11.69641 11.69655 11.61337
#> 13 11.74573 11.74574 11.83791 11.83814 11.83834 11.83850 11.83863 11.98178
#> 14 27.94547 27.94547 28.22779 28.22813 28.22841 28.22864 28.22883 28.34468
#> 15 28.33768 28.33768 28.58257 28.58267 28.58274 28.58281 28.58286 29.26037
#> 16 16.65511 16.65503 16.51674 16.51674 16.51675 16.51675 16.51675 16.27378
#> 17 16.81670 16.81662 16.66967 16.66965 16.66964 16.66963 16.66962 16.81945
#> 18 14.60688 14.60686 14.54560 14.54547 14.54536 14.54527 14.54520 14.93515
#> 19 28.44927 28.44925 28.70456 28.70484 28.70507 28.70525 28.70541 28.77250
#> 20 27.33960 27.33962 26.31941 26.31901 26.31868 26.31840 26.31818 26.53128
#> 21 28.53159 28.53159 28.76608 28.76615 28.76621 28.76626 28.76629 28.21021
#>      0.1064   0.0993   0.0926   0.0863   0.0805   0.0751   0.0700   0.0653
#> 1  21.33974 21.33965 21.33958 21.33952 21.33946 21.33942 21.33938 21.33934
#> 2  20.92810 20.92805 20.92801 20.92798 20.92795 20.92792 20.92790 20.92788
#> 3  27.91028 27.91046 27.91062 27.91075 27.91087 27.91096 27.91105 27.91112
#> 4  21.40183 21.40193 21.40202 21.40209 21.40216 21.40221 21.40226 21.40230
#> 5  16.81147 16.81154 16.81161 16.81167 16.81172 16.81177 16.81181 16.81184
#> 6  14.82631 14.82617 14.82606 14.82596 14.82587 14.82580 14.82573 14.82568
#> 7  23.18515 23.18479 23.18448 23.18421 23.18398 23.18378 23.18361 23.18346
#> 8  23.49067 23.49036 23.49010 23.48987 23.48968 23.48951 23.48936 23.48923
#> 9  19.16135 19.16134 19.16132 19.16131 19.16130 19.16129 19.16128 19.16127
#> 10 19.16135 19.16134 19.16132 19.16131 19.16130 19.16129 19.16128 19.16127
#> 11 15.34044 15.34042 15.34040 15.34038 15.34037 15.34036 15.34035 15.34034
#> 12 11.61347 11.61356 11.61364 11.61370 11.61376 11.61380 11.61384 11.61388
#> 13 11.98194 11.98208 11.98220 11.98230 11.98239 11.98246 11.98253 11.98258
#> 14 28.34494 28.34516 28.34535 28.34552 28.34566 28.34578 28.34589 28.34598
#> 15 29.26065 29.26088 29.26108 29.26126 29.26141 29.26155 29.26166 29.26176
#> 16 16.27377 16.27376 16.27374 16.27374 16.27373 16.27372 16.27372 16.27371
#> 17 16.81954 16.81962 16.81968 16.81974 16.81979 16.81984 16.81988 16.81991
#> 18 14.93520 14.93524 14.93528 14.93531 14.93534 14.93537 14.93539 14.93541
#> 19 28.77272 28.77290 28.77306 28.77319 28.77331 28.77341 28.77350 28.77358
#> 20 26.53098 26.53072 26.53049 26.53030 26.53013 26.52999 26.52987 26.52976
#> 21 28.21011 28.21002 28.20995 28.20988 28.20982 28.20977 28.20973 28.20970
#>      0.0609   0.0568   0.0530   0.0494   0.0461   0.0430   0.0401   0.0374
#> 1  21.25224 21.25218 21.25213 21.38914 21.38924 21.38934 21.38943 21.38952
#> 2  21.02073 21.02073 21.02073 21.01814 21.01820 21.01826 21.01832 21.01837
#> 3  27.68333 27.68332 27.68331 27.15801 27.15792 27.15784 27.15776 27.15769
#> 4  21.12184 21.12181 21.12178 21.43482 21.43492 21.43501 21.43510 21.43518
#> 5  17.04365 17.04375 17.04385 17.62637 17.62652 17.62666 17.62679 17.62692
#> 6  14.27756 14.27739 14.27723 14.25580 14.25602 14.25623 14.25642 14.25661
#> 7  22.63087 22.63059 22.63032 22.48325 22.48305 22.48285 22.48266 22.48248
#> 8  23.87378 23.87374 23.87370 23.91348 23.91364 23.91378 23.91392 23.91406
#> 9  19.38595 19.38603 19.38610 19.24529 19.24510 19.24492 19.24475 19.24458
#> 10 19.56594 19.56606 19.56617 19.55311 19.55300 19.55290 19.55281 19.55272
#> 11 15.51067 15.51072 15.51076 14.78793 14.78782 14.78771 14.78761 14.78751
#> 12 11.68364 11.68367 11.68370 12.18076 12.18090 12.18103 12.18116 12.18128
#> 13 11.99774 11.99777 11.99779 12.01092 12.01090 12.01089 12.01087 12.01086
#> 14 28.43963 28.43970 28.43977 28.10897 28.10891 28.10885 28.10879 28.10873
#> 15 29.07327 29.07326 29.07326 29.70615 29.70626 29.70636 29.70646 29.70656
#> 16 16.34712 16.34717 16.34721 16.37957 16.37953 16.37949 16.37946 16.37943
#> 17 17.13548 17.13560 17.13572 17.17548 17.17542 17.17537 17.17531 17.17526
#> 18 14.42718 14.42706 14.42695 13.95468 13.95459 13.95450 13.95441 13.95433
#> 19 28.68380 28.68382 28.68384 28.50557 28.50555 28.50554 28.50552 28.50550
#> 20 26.70426 26.70421 26.70416 26.61854 26.61832 26.61812 26.61793 26.61774
#> 21 28.44134 28.44142 28.44151 28.79400 28.79418 28.79436 28.79452 28.79468
#>      0.0349   0.0325   0.0303   0.0283   0.0264   0.0246   0.0229   0.0214
#> 1  21.38960 21.38968 21.38976 21.38983 21.38989 21.38996 21.39002 21.39008
#> 2  21.01842 21.01847 21.01852 21.01856 21.01860 21.01864 21.01868 21.01872
#> 3  27.15762 27.15756 27.15749 27.15743 27.15738 27.15733 27.15728 27.15723
#> 4  21.43526 21.43533 21.43540 21.43547 21.43553 21.43559 21.43565 21.43570
#> 5  17.62704 17.62715 17.62726 17.62736 17.62746 17.62755 17.62764 17.62772
#> 6  14.25679 14.25696 14.25712 14.25728 14.25743 14.25756 14.25770 14.25782
#> 7  22.48231 22.48215 22.48200 22.48185 22.48171 22.48158 22.48145 22.48133
#> 8  23.91418 23.91430 23.91442 23.91453 23.91463 23.91473 23.91482 23.91491
#> 9  19.24442 19.24427 19.24413 19.24400 19.24387 19.24375 19.24363 19.24352
#> 10 19.55263 19.55255 19.55247 19.55240 19.55233 19.55226 19.55220 19.55214
#> 11 14.78741 14.78733 14.78724 14.78716 14.78709 14.78702 14.78695 14.78689
#> 12 12.18139 12.18150 12.18160 12.18169 12.18179 12.18187 12.18196 12.18203
#> 13 12.01085 12.01084 12.01083 12.01081 12.01081 12.01080 12.01079 12.01078
#> 14 28.10868 28.10863 28.10859 28.10854 28.10850 28.10846 28.10842 28.10839
#> 15 29.70664 29.70673 29.70681 29.70688 29.70696 29.70702 29.70709 29.70715
#> 16 16.37939 16.37937 16.37934 16.37931 16.37928 16.37926 16.37924 16.37921
#> 17 17.17521 17.17517 17.17512 17.17508 17.17504 17.17500 17.17497 17.17493
#> 18 13.95425 13.95418 13.95411 13.95405 13.95399 13.95393 13.95387 13.95382
#> 19 28.50548 28.50547 28.50545 28.50544 28.50543 28.50542 28.50540 28.50539
#> 20 26.61757 26.61740 26.61724 26.61709 26.61695 26.61681 26.61668 26.61656
#> 21 28.79483 28.79497 28.79510 28.79523 28.79535 28.79547 28.79558 28.79568
#>      0.0199   0.0186   0.0173   0.0162   0.0151   0.0141   0.0131   0.0122
#> 1  21.39013 21.39018 21.39023 21.39028 21.39033 21.39037 21.39041 21.39045
#> 2  21.01875 21.01878 21.01881 21.01884 21.01887 21.01890 21.01892 21.01894
#> 3  27.15718 27.15714 27.15710 27.15706 27.15702 27.15699 27.15696 27.15693
#> 4  21.43575 21.43580 21.43585 21.43589 21.43593 21.43597 21.43601 21.43604
#> 5  17.62780 17.62787 17.62794 17.62801 17.62808 17.62814 17.62819 17.62825
#> 6  14.25794 14.25806 14.25817 14.25827 14.25837 14.25846 14.25855 14.25863
#> 7  22.48122 22.48111 22.48101 22.48091 22.48082 22.48073 22.48064 22.48056
#> 8  23.91500 23.91508 23.91515 23.91523 23.91530 23.91536 23.91542 23.91548
#> 9  19.24342 19.24332 19.24322 19.24313 19.24305 19.24296 19.24289 19.24281
#> 10 19.55208 19.55202 19.55197 19.55192 19.55187 19.55183 19.55179 19.55175
#> 11 14.78682 14.78677 14.78671 14.78666 14.78661 14.78656 14.78652 14.78648
#> 12 12.18211 12.18218 12.18225 12.18231 12.18237 12.18243 12.18248 12.18253
#> 13 12.01077 12.01076 12.01076 12.01075 12.01074 12.01074 12.01073 12.01073
#> 14 28.10835 28.10832 28.10829 28.10826 28.10824 28.10821 28.10819 28.10816
#> 15 29.70721 29.70726 29.70732 29.70737 29.70741 29.70746 29.70750 29.70754
#> 16 16.37919 16.37917 16.37915 16.37913 16.37912 16.37910 16.37908 16.37907
#> 17 17.17490 17.17487 17.17484 17.17481 17.17479 17.17476 17.17474 17.17471
#> 18 13.95377 13.95372 13.95368 13.95363 13.95359 13.95355 13.95352 13.95348
#> 19 28.50538 28.50537 28.50536 28.50536 28.50535 28.50534 28.50533 28.50532
#> 20 26.61644 26.61633 26.61622 26.61612 26.61603 26.61594 26.61585 26.61577
#> 21 28.79578 28.79587 28.79596 28.79605 28.79613 28.79620 28.79628 28.79635
#>      0.0114   0.0106   0.0099   0.0093   0.0086   0.0081   0.0075   0.0070
#> 1  21.39048 21.39052 21.43568 21.43562 21.43555 21.43548 21.43542 21.43535
#> 2  21.01897 21.01899 21.02695 21.02692 21.02690 21.02688 21.02686 21.02684
#> 3  27.15690 27.15687 27.18543 27.18553 27.18562 27.18571 27.18579 27.18588
#> 4  21.43608 21.43611 21.48392 21.48380 21.48369 21.48358 21.48347 21.48336
#> 5  17.62830 17.62835 17.56077 17.56062 17.56048 17.56035 17.56022 17.56010
#> 6  14.25871 14.25879 14.37278 14.37266 14.37253 14.37241 14.37228 14.37216
#> 7  22.48049 22.48042 22.66000 22.66009 22.66019 22.66027 22.66035 22.66042
#> 8  23.91554 23.91559 23.91597 23.91591 23.91585 23.91579 23.91573 23.91567
#> 9  19.24274 19.24268 19.17255 19.17268 19.17281 19.17294 19.17306 19.17319
#> 10 19.55171 19.55167 19.45207 19.45215 19.45222 19.45230 19.45238 19.45246
#> 11 14.78644 14.78640 14.74483 14.74500 14.74517 14.74533 14.74549 14.74564
#> 12 12.18258 12.18263 12.18486 12.18471 12.18457 12.18443 12.18429 12.18416
#> 13 12.01072 12.01072 11.99720 11.99721 11.99721 11.99721 11.99722 11.99722
#> 14 28.10814 28.10812 28.06557 28.06565 28.06573 28.06581 28.06589 28.06596
#> 15 29.70758 29.70761 29.69381 29.69368 29.69357 29.69345 29.69334 29.69323
#> 16 16.37905 16.37904 16.36387 16.36388 16.36389 16.36389 16.36390 16.36391
#> 17 17.17469 17.17467 17.08521 17.08525 17.08530 17.08534 17.08539 17.08543
#> 18 13.95345 13.95342 14.00500 14.00512 14.00523 14.00533 14.00543 14.00553
#> 19 28.50532 28.50531 28.50091 28.50094 28.50097 28.50100 28.50103 28.50106
#> 20 26.61569 26.61562 26.62491 26.62504 26.62517 26.62529 26.62541 26.62552
#> 21 28.79641 28.79647 28.76769 28.76752 28.76736 28.76721 28.76706 28.76692
#>      0.0065   0.0061   0.0057   0.0053
#> 1  21.43528 21.43521 21.43515 21.43508
#> 2  21.02681 21.02679 21.02677 21.02675
#> 3  27.18596 27.18603 27.18611 27.18618
#> 4  21.48325 21.48315 21.48305 21.48295
#> 5  17.55998 17.55987 17.55976 17.55966
#> 6  14.37203 14.37190 14.37178 14.37165
#> 7  22.66048 22.66054 22.66059 22.66064
#> 8  23.91561 23.91555 23.91549 23.91544
#> 9  19.17331 19.17344 19.17356 19.17368
#> 10 19.45254 19.45262 19.45270 19.45278
#> 11 14.74579 14.74594 14.74608 14.74622
#> 12 12.18403 12.18391 12.18379 12.18367
#> 13 11.99723 11.99724 11.99724 11.99725
#> 14 28.06604 28.06611 28.06619 28.06626
#> 15 29.69313 29.69303 29.69293 29.69284
#> 16 16.36392 16.36393 16.36394 16.36395
#> 17 17.08548 17.08553 17.08558 17.08563
#> 18 14.00562 14.00571 14.00579 14.00587
#> 19 28.50108 28.50111 28.50113 28.50116
#> 20 26.62564 26.62575 26.62586 26.62596
#> 21 28.76678 28.76665 28.76652 28.76639
#> 
#> $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 18.7 14.3 24.4 22.8 19.2 17.8 17.3 10.4 14.7 32.4 30.4
#> [16] 15.5 15.2 13.3 27.3 26.0 30.4
#> 
#> $X
#>               am       carb       cyl       disp        drat       gear
#>  [1,]  1.2747549  1.1761053  0.000000 -0.4988096  0.46612062  0.5188745
#>  [2,]  1.2747549  1.1761053  0.000000 -0.4988096  0.46612062  0.5188745
#>  [3,]  1.2747549 -1.3788821 -1.145644 -0.9293004  0.37071582  0.5188745
#>  [4,] -0.7844645 -1.3788821  0.000000  0.3125001 -1.09851819 -1.0377490
#>  [5,] -0.7844645 -0.5272196  1.145644  1.1569244 -0.96495147 -1.0377490
#>  [6,] -0.7844645  1.1761053  1.145644  1.1569244 -0.85046570 -1.0377490
#>  [7,] -0.7844645 -0.5272196 -1.145644 -0.6089159  0.06542044  0.5188745
#>  [8,] -0.7844645 -0.5272196 -1.145644 -0.6577600  0.50428255  0.5188745
#>  [9,] -0.7844645  1.1761053  0.000000 -0.4358917  0.50428255  0.5188745
#> [10,] -0.7844645  1.1761053  0.000000 -0.4358917  0.50428255  0.5188745
#> [11,] -0.7844645  0.3244428  1.145644  0.4598604 -1.11759916 -1.0377490
#> [12,] -0.7844645  1.1761053  1.145644  1.9847914 -1.25116588 -1.0377490
#> [13,] -0.7844645  1.1761053  1.145644  1.8192180 -0.81230378 -1.0377490
#> [14,]  1.2747549 -1.3788821 -1.145644 -1.1718654  0.80957793  0.5188745
#> [15,]  1.2747549 -0.5272196 -1.145644 -1.1967014  2.43145963  0.5188745
#> [16,] -0.7844645 -0.5272196  1.145644  0.8092203 -1.70910895 -1.0377490
#> [17,] -0.7844645 -0.5272196  1.145644  0.6933189 -0.96495147 -1.0377490
#> [18,] -0.7844645  1.1761053  1.145644  1.0741377  0.14174428 -1.0377490
#> [19,]  1.2747549 -1.3788821 -1.145644 -1.1693818  0.80957793  0.5188745
#> [20,]  1.2747549 -0.5272196 -1.145644 -0.8274728  1.47741157  2.0754981
#> [21,]  1.2747549 -0.5272196 -1.145644 -1.0360953  0.21806813  2.0754981
#>               hp        qsec         vs           wt
#>  [1,] -0.3980551 -0.93020608 -0.9534626 -0.521645806
#>  [2,] -0.3980551 -0.58555506 -0.9534626 -0.266236343
#>  [3,] -0.6857184  0.39300767  1.0488088 -0.822127526
#>  [4,] -0.3980551  0.90382973  1.0488088  0.074309606
#>  [5,]  0.7018340 -0.58555506 -0.9534626  0.299670897
#>  [6,]  1.8863299 -1.31178400 -0.9534626  0.429879642
#>  [7,] -1.2102809  1.24848075  1.0488088  0.049269463
#>  [8,] -0.6518756  3.03328069  1.0488088  0.009205234
#>  [9,] -0.1780773  0.20221871  1.0488088  0.299670897
#> [10,] -0.1780773  0.57148767  1.0488088  0.299670897
#> [11,]  0.7864408 -0.22859507 -0.9534626  0.590136560
#> [12,]  1.3786888 -0.09319645 -0.9534626  2.286856674
#> [13,]  1.6325093 -0.33937575 -0.9534626  2.207729821
#> [14,] -1.1425954  0.92229317  1.0488088 -0.942320214
#> [15,] -1.3794946  0.33761733  1.0488088 -1.528259569
#> [16,]  0.2787997 -0.67787229 -0.9534626  0.379799355
#> [17,]  0.2787997 -0.41322954 -0.9534626  0.294662868
#> [18,]  1.8863299 -1.57642675 -0.9534626  0.700313191
#> [19,] -1.1425954  0.57148767  1.0488088 -1.207745734
#> [20,] -0.7195611 -0.78249850 -0.9534626 -1.002416558
#> [21,] -0.3472910 -0.65940885  1.0488088 -1.630423354
#> attr(,"center")
#>  [1]   0.3809524   2.6190476   6.0000000 220.2523810   3.6557143   3.6666667
#>  [7] 133.5238095  17.9714286   0.4761905   3.1408095
#> attr(,"scale")
#>  [1]   0.4856209   1.1741741   1.7457431 120.7923508   0.5240826   0.6424161
#>  [7]  59.0968689   1.6248320   0.4994328   0.9983968
#> attr(,"nonsingular")
#>  [1]  1  2  3  4  5  6  7  8  9 10
#> 
#> attr(,"class")
#> [1] "ncvreg"
#> 
#> $min
#> [1] 35
#> 
#> $lambda.min
#> [1] 0.4940223
#> 
#> $null.dev
#> [1] 35.29039
#> 
#> $Bias
#> [1] 3.270881
#> 
#> 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 
#> 9.479423