Chapter 6 Model Selection
dim(Hitters)
[1] 263 20sum(is.na(Hitters))
[1] 0So now we have zero rows with missing data in Hitters. We’re going to start building a set of models First we’ll find the best model by number of variables
summary(regfit.full)
Subset selection object
Call: regsubsets.formula(Salary ~ ., Hitters)
19 Variables (and intercept)
Forced in Forced out
AtBat FALSE FALSE
Hits FALSE FALSE
HmRun FALSE FALSE
Runs FALSE FALSE
RBI FALSE FALSE
Walks FALSE FALSE
Years FALSE FALSE
CAtBat FALSE FALSE
CHits FALSE FALSE
CHmRun FALSE FALSE
CRuns FALSE FALSE
CRBI FALSE FALSE
CWalks FALSE FALSE
LeagueN FALSE FALSE
DivisionW FALSE FALSE
PutOuts FALSE FALSE
Assists FALSE FALSE
Errors FALSE FALSE
NewLeagueN FALSE FALSE
1 subsets of each size up to 8
Selection Algorithm: exhaustive
AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks LeagueN DivisionW PutOuts Assists Errors NewLeagueN
1 ( 1 ) " " " " " " " " " " " " " " " " " " " " " " "*" " " " " " " " " " " " " " "
2 ( 1 ) " " "*" " " " " " " " " " " " " " " " " " " "*" " " " " " " " " " " " " " "
3 ( 1 ) " " "*" " " " " " " " " " " " " " " " " " " "*" " " " " " " "*" " " " " " "
4 ( 1 ) " " "*" " " " " " " " " " " " " " " " " " " "*" " " " " "*" "*" " " " " " "
5 ( 1 ) "*" "*" " " " " " " " " " " " " " " " " " " "*" " " " " "*" "*" " " " " " "
6 ( 1 ) "*" "*" " " " " " " "*" " " " " " " " " " " "*" " " " " "*" "*" " " " " " "
7 ( 1 ) " " "*" " " " " " " "*" " " "*" "*" "*" " " " " " " " " "*" "*" " " " " " "
8 ( 1 ) "*" "*" " " " " " " "*" " " " " " " "*" "*" " " "*" " " "*" "*" " " " " " " Note that regsubsets only lists up to 8 models, we will modify that to show all 19 variables
reg.summary
Subset selection object
Call: regsubsets.formula(Salary ~ ., data = Hitters, nvmax = 19)
19 Variables (and intercept)
Forced in Forced out
AtBat FALSE FALSE
Hits FALSE FALSE
HmRun FALSE FALSE
Runs FALSE FALSE
RBI FALSE FALSE
Walks FALSE FALSE
Years FALSE FALSE
CAtBat FALSE FALSE
CHits FALSE FALSE
CHmRun FALSE FALSE
CRuns FALSE FALSE
CRBI FALSE FALSE
CWalks FALSE FALSE
LeagueN FALSE FALSE
DivisionW FALSE FALSE
PutOuts FALSE FALSE
Assists FALSE FALSE
Errors FALSE FALSE
NewLeagueN FALSE FALSE
1 subsets of each size up to 19
Selection Algorithm: exhaustive
AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks LeagueN DivisionW PutOuts Assists Errors NewLeagueN
1 ( 1 ) " " " " " " " " " " " " " " " " " " " " " " "*" " " " " " " " " " " " " " "
2 ( 1 ) " " "*" " " " " " " " " " " " " " " " " " " "*" " " " " " " " " " " " " " "
3 ( 1 ) " " "*" " " " " " " " " " " " " " " " " " " "*" " " " " " " "*" " " " " " "
4 ( 1 ) " " "*" " " " " " " " " " " " " " " " " " " "*" " " " " "*" "*" " " " " " "
5 ( 1 ) "*" "*" " " " " " " " " " " " " " " " " " " "*" " " " " "*" "*" " " " " " "
6 ( 1 ) "*" "*" " " " " " " "*" " " " " " " " " " " "*" " " " " "*" "*" " " " " " "
7 ( 1 ) " " "*" " " " " " " "*" " " "*" "*" "*" " " " " " " " " "*" "*" " " " " " "
8 ( 1 ) "*" "*" " " " " " " "*" " " " " " " "*" "*" " " "*" " " "*" "*" " " " " " "
9 ( 1 ) "*" "*" " " " " " " "*" " " "*" " " " " "*" "*" "*" " " "*" "*" " " " " " "
10 ( 1 ) "*" "*" " " " " " " "*" " " "*" " " " " "*" "*" "*" " " "*" "*" "*" " " " "
11 ( 1 ) "*" "*" " " " " " " "*" " " "*" " " " " "*" "*" "*" "*" "*" "*" "*" " " " "
12 ( 1 ) "*" "*" " " "*" " " "*" " " "*" " " " " "*" "*" "*" "*" "*" "*" "*" " " " "
13 ( 1 ) "*" "*" " " "*" " " "*" " " "*" " " " " "*" "*" "*" "*" "*" "*" "*" "*" " "
14 ( 1 ) "*" "*" "*" "*" " " "*" " " "*" " " " " "*" "*" "*" "*" "*" "*" "*" "*" " "
15 ( 1 ) "*" "*" "*" "*" " " "*" " " "*" "*" " " "*" "*" "*" "*" "*" "*" "*" "*" " "
16 ( 1 ) "*" "*" "*" "*" "*" "*" " " "*" "*" " " "*" "*" "*" "*" "*" "*" "*" "*" " "
17 ( 1 ) "*" "*" "*" "*" "*" "*" " " "*" "*" " " "*" "*" "*" "*" "*" "*" "*" "*" "*"
18 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*" " " "*" "*" "*" "*" "*" "*" "*" "*" "*"
19 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" Next we’ll look at the r-squared value for each of the 19 models. Note the r-squared value goes up as the number of variables goes up
reg.summary$rsq
[1] 0.3214501 0.4252237 0.4514294 0.4754067 0.4908036 0.5087146 0.5141227 0.5285569 0.5346124 0.5404950 0.5426153 0.5436302 0.5444570 0.5452164 0.5454692 0.5457656 0.5459518
[18] 0.5460945 0.5461159Let’s plot the RSS, adjusted R2, Cp and BIC for all the models, to help us decide which to select. RSS goes first
Next we’ll look at r-squared
plot(reg.summary$adjr2, xlab="Number of variables", ylab="Adj R2", type="l")
which.max(reg.summary$adjr2)
[1] 11points(11,reg.summary$adjr2[11], col="red",cex=2,pch=20)
The red dot shows the maximum value for adjusted R2 In a similar manner, plot Mallow’s Cp, and the BIC statistics, and determine which have the smallest using which.min()
Third we’ll look at Mallow’s Cp
Fourth let’s do the analysis using BIC
Now let’s plot to display the selected variables. Our goal is to find the best model. First we’ll look at r-squared.
Now let’s look at adjusted r-squared
Third we’ll look at Mallow’s Cp
Fourth we’ll look at BIC
Clearly the lowest bic in the range of -150, but there are multiple possibilities as well. The minimum model has six variables. Let’s see the variables:
rr coef(regfit.full,6)
(Intercept) AtBat Hits Walks CRBI DivisionW PutOuts
91.5117981 -1.8685892 7.6043976 3.6976468 0.6430169 -122.9515338 0.2643076 6.5.2 Forward and backward stepwise selection
library(glmnet)
Warning messages:
1: In scan(file = file, what = what, sep = sep, quote = quote, dec = dec, :
EOF within quoted string
2: In scan(file = file, what = what, sep = sep, quote = quote, dec = dec, :
EOF within quoted string
3: In scan(file = file, what = what, sep = sep, quote = quote, dec = dec, :
EOF within quoted string
4: In scan(file = file, what = what, sep = sep, quote = quote, dec = dec, :
EOF within quoted string
5: In scan(file = file, what = what, sep = sep, quote = quote, dec = dec, :
EOF within quoted stringNow let’s do the same thing using backward stepwise selection
summary(regfit.bwd)
Subset selection object
Call: regsubsets.formula(Salary ~ ., data = Hitters, nvmax = 19, method = "backward")
19 Variables (and intercept)
Forced in Forced out
AtBat FALSE FALSE
Hits FALSE FALSE
HmRun FALSE FALSE
Runs FALSE FALSE
RBI FALSE FALSE
Walks FALSE FALSE
Years FALSE FALSE
CAtBat FALSE FALSE
CHits FALSE FALSE
CHmRun FALSE FALSE
CRuns FALSE FALSE
CRBI FALSE FALSE
CWalks FALSE FALSE
LeagueN FALSE FALSE
DivisionW FALSE FALSE
PutOuts FALSE FALSE
Assists FALSE FALSE
Errors FALSE FALSE
NewLeagueN FALSE FALSE
1 subsets of each size up to 19
Selection Algorithm: backward
AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks LeagueN DivisionW PutOuts Assists Errors NewLeagueN
1 ( 1 ) " " " " " " " " " " " " " " " " " " " " "*" " " " " " " " " " " " " " " " "
2 ( 1 ) " " "*" " " " " " " " " " " " " " " " " "*" " " " " " " " " " " " " " " " "
3 ( 1 ) " " "*" " " " " " " " " " " " " " " " " "*" " " " " " " " " "*" " " " " " "
4 ( 1 ) "*" "*" " " " " " " " " " " " " " " " " "*" " " " " " " " " "*" " " " " " "
5 ( 1 ) "*" "*" " " " " " " "*" " " " " " " " " "*" " " " " " " " " "*" " " " " " "
6 ( 1 ) "*" "*" " " " " " " "*" " " " " " " " " "*" " " " " " " "*" "*" " " " " " "
7 ( 1 ) "*" "*" " " " " " " "*" " " " " " " " " "*" " " "*" " " "*" "*" " " " " " "
8 ( 1 ) "*" "*" " " " " " " "*" " " " " " " " " "*" "*" "*" " " "*" "*" " " " " " "
9 ( 1 ) "*" "*" " " " " " " "*" " " "*" " " " " "*" "*" "*" " " "*" "*" " " " " " "
10 ( 1 ) "*" "*" " " " " " " "*" " " "*" " " " " "*" "*" "*" " " "*" "*" "*" " " " "
11 ( 1 ) "*" "*" " " " " " " "*" " " "*" " " " " "*" "*" "*" "*" "*" "*" "*" " " " "
12 ( 1 ) "*" "*" " " "*" " " "*" " " "*" " " " " "*" "*" "*" "*" "*" "*" "*" " " " "
13 ( 1 ) "*" "*" " " "*" " " "*" " " "*" " " " " "*" "*" "*" "*" "*" "*" "*" "*" " "
14 ( 1 ) "*" "*" "*" "*" " " "*" " " "*" " " " " "*" "*" "*" "*" "*" "*" "*" "*" " "
15 ( 1 ) "*" "*" "*" "*" " " "*" " " "*" "*" " " "*" "*" "*" "*" "*" "*" "*" "*" " "
16 ( 1 ) "*" "*" "*" "*" "*" "*" " " "*" "*" " " "*" "*" "*" "*" "*" "*" "*" "*" " "
17 ( 1 ) "*" "*" "*" "*" "*" "*" " " "*" "*" " " "*" "*" "*" "*" "*" "*" "*" "*" "*"
18 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*" " " "*" "*" "*" "*" "*" "*" "*" "*" "*"
19 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" "*" Note the one-variable through six-variable models are identical. Let’s look at the seven variable models:
coef(regfit.full, 7)
(Intercept) Hits Walks CAtBat CHits CHmRun DivisionW PutOuts
79.4509472 1.2833513 3.2274264 -0.3752350 1.4957073 1.4420538 -129.9866432 0.2366813 coef(regfit.bwd, 7)
(Intercept) AtBat Hits Walks CRuns CWalks DivisionW PutOuts
105.6487488 -1.9762838 6.7574914 6.0558691 1.1293095 -0.7163346 -116.1692169 0.3028847 6.5.3 Choosing Among Models Using the Validation Set Approach and Cross-Validation
We will begin by splitting the data into a test set and a training set.
train
[1] TRUE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE TRUE FALSE TRUE FALSE FALSE TRUE FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
[29] FALSE TRUE TRUE FALSE TRUE TRUE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
[57] TRUE FALSE FALSE TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE FALSE TRUE FALSE TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE FALSE TRUE TRUE
[85] FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE TRUE TRUE FALSE FALSE TRUE TRUE TRUE FALSE FALSE FALSE FALSE
[113] TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[141] FALSE FALSE TRUE TRUE FALSE TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE TRUE TRUE TRUE
[169] FALSE TRUE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE TRUE FALSE
[197] TRUE FALSE TRUE FALSE TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE TRUE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE FALSE
[225] FALSE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE
[253] TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUEtest
[1] FALSE FALSE TRUE TRUE FALSE TRUE TRUE TRUE TRUE FALSE FALSE FALSE TRUE FALSE TRUE FALSE TRUE TRUE FALSE TRUE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
[29] TRUE FALSE FALSE TRUE FALSE FALSE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
[57] FALSE TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE TRUE FALSE TRUE FALSE FALSE FALSE TRUE TRUE FALSE TRUE TRUE FALSE TRUE FALSE FALSE
[85] TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE FALSE FALSE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
[113] FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE TRUE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[141] TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE FALSE TRUE TRUE TRUE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE FALSE FALSE FALSE
[169] TRUE FALSE TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE FALSE TRUE
[197] FALSE TRUE FALSE TRUE FALSE FALSE TRUE FALSE FALSE TRUE TRUE FALSE FALSE TRUE TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE FALSE FALSE FALSE FALSE TRUE
[225] TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE TRUE
[253] FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSENow we apply regsubsets to the training set in order to perform best subset selection.
regfit.best
Subset selection object
Call: regsubsets.formula(Salary ~ ., data = Hitters[train, ], nvmax = 19)
19 Variables (and intercept)
Forced in Forced out
AtBat FALSE FALSE
Hits FALSE FALSE
HmRun FALSE FALSE
Runs FALSE FALSE
RBI FALSE FALSE
Walks FALSE FALSE
Years FALSE FALSE
CAtBat FALSE FALSE
CHits FALSE FALSE
CHmRun FALSE FALSE
CRuns FALSE FALSE
CRBI FALSE FALSE
CWalks FALSE FALSE
LeagueN FALSE FALSE
DivisionW FALSE FALSE
PutOuts FALSE FALSE
Assists FALSE FALSE
Errors FALSE FALSE
NewLeagueN FALSE FALSE
1 subsets of each size up to 19
Selection Algorithm: exhaustivetest.mat
(Intercept) AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI CWalks LeagueN DivisionW PutOuts Assists Errors NewLeagueN
-Andre Dawson 1 496 141 20 65 78 37 11 5628 1575 225 828 838 354 1 0 200 11 3 1
-Andres Galarraga 1 321 87 10 39 42 30 2 396 101 12 48 46 33 1 0 805 40 4 1
-Al Newman 1 185 37 1 23 8 21 2 214 42 1 30 9 24 1 0 76 127 7 0
-Argenis Salazar 1 298 73 0 24 24 7 3 509 108 0 41 37 12 0 1 121 283 9 0
-Andres Thomas 1 323 81 6 26 32 8 2 341 86 6 32 34 8 1 1 143 290 19 1
-Andre Thornton 1 401 92 17 49 66 65 13 5206 1332 253 784 890 866 0 0 0 0 0 0
-Alan Wiggins 1 239 60 0 30 11 22 6 1941 510 4 309 103 207 0 0 121 151 6 0
-Buddy Bell 1 568 158 20 89 75 73 15 8068 2273 177 1045 993 732 1 1 105 290 10 1
-Bruce Bochy 1 127 32 8 16 22 14 8 727 180 24 67 82 56 1 1 202 22 2 1
-Barry Bonds 1 413 92 16 72 48 65 1 413 92 16 72 48 65 1 0 280 9 5 1
-Bob Brenly 1 472 116 16 60 62 74 6 1924 489 67 242 251 240 1 1 518 55 3 1
-Bill Buckner 1 629 168 18 73 102 40 18 8424 2464 164 1008 1072 402 0 0 1067 157 14 0
-Bob Dernier 1 324 73 4 32 18 22 7 1931 491 13 291 108 180 1 0 222 3 3 1
-Bob Kearney 1 204 49 6 23 25 12 7 1309 308 27 126 132 66 0 1 419 46 5 0
-BillyJo Robidoux 1 181 41 1 15 21 33 2 232 50 4 20 29 45 0 0 326 29 5 0
-Chris Brown 1 416 132 7 57 49 33 3 932 273 24 113 121 80 1 1 73 177 18 1
-Carmen Castillo 1 205 57 8 34 32 9 5 756 192 32 117 107 51 0 0 58 4 4 0
-Chili Davis 1 526 146 13 71 70 84 6 2648 715 77 352 342 289 1 1 303 9 9 1
-Curt Ford 1 214 53 2 30 29 23 2 226 59 2 32 32 27 1 0 109 7 3 1
-Chet Lemon 1 403 101 12 45 53 39 12 5150 1429 166 747 666 526 0 0 316 6 5 0
-Candy Maldonado 1 405 102 18 49 85 20 6 950 231 29 99 138 64 1 1 161 10 3 1
-Carmelo Martinez 1 244 58 9 28 25 35 4 1335 333 49 164 179 194 1 1 142 14 2 1
-Craig Reynolds 1 313 78 6 32 41 12 12 3742 968 35 409 321 170 1 1 106 206 7 1
-Cal Ripken 1 627 177 25 98 81 70 6 3210 927 133 529 472 313 0 0 240 482 13 0
-Cory Snyder 1 416 113 24 58 69 16 1 416 113 24 58 69 16 0 0 203 70 10 0
-Dave Anderson 1 216 53 1 31 15 22 4 926 210 9 118 69 114 1 1 73 152 11 1
-Don Baylor 1 585 139 31 93 94 62 17 7546 1982 315 1141 1179 727 0 0 0 0 0 0
-Darnell Coles 1 521 142 20 67 86 45 4 815 205 22 99 103 78 0 0 107 242 23 0
-Dan Gladden 1 351 97 4 55 29 39 4 1258 353 16 196 110 117 1 1 226 7 3 0
-Dave Henderson 1 388 103 15 59 47 39 6 2174 555 80 285 274 186 0 1 182 9 4 0
-Davey Lopes 1 255 70 7 49 35 43 15 6311 1661 154 1019 608 820 1 0 51 54 8 1
-Dave Parker 1 637 174 31 89 116 56 14 6727 2024 247 978 1093 495 1 1 278 9 9 1
-Dick Schofield 1 458 114 13 67 57 48 4 1350 298 28 160 123 122 0 1 246 389 18 0
-Darryl Strawberry 1 475 123 27 76 93 72 4 1810 471 108 292 343 267 1 0 226 10 6 1
-Danny Tartabull 1 511 138 25 76 96 61 3 592 164 28 87 110 71 0 1 157 7 8 0
-Eddie Milner 1 424 110 15 70 47 36 7 2130 544 38 335 174 258 1 1 292 6 3 1
-Eddie Murray 1 495 151 17 61 84 78 10 5624 1679 275 884 1015 709 0 0 1045 88 13 0
-Frank White 1 566 154 22 76 84 43 14 6100 1583 131 743 693 300 0 1 316 439 10 0
-George Bell 1 641 198 31 101 108 41 5 2129 610 92 297 319 117 0 0 269 17 10 0
-George Brett 1 441 128 16 70 73 80 14 6675 2095 209 1072 1050 695 0 1 97 218 16 0
-Glenn Davis 1 574 152 31 91 101 64 3 985 260 53 148 173 95 1 1 1253 111 11 1
-Greg Gagne 1 472 118 12 63 54 30 4 793 187 14 102 80 50 0 1 228 377 26 0
-Gary Pettis 1 539 139 5 93 58 69 5 1469 369 12 247 126 198 0 1 462 9 7 0
-Gary Redus 1 340 84 11 62 33 47 5 1516 376 42 284 141 219 1 0 185 8 4 0
-Garry Templeton 1 510 126 2 42 44 35 11 5562 1578 44 703 519 256 1 1 207 358 20 1
-Greg Walker 1 282 78 13 37 51 29 5 1649 453 73 211 280 138 0 1 670 57 5 0
-Harold Baines 1 570 169 21 72 88 38 7 3754 1077 140 492 589 263 0 1 295 15 5 0
-Hubie Brooks 1 306 104 14 50 58 25 7 2954 822 55 313 377 187 1 0 116 222 15 1
-Howard Johnson 1 220 54 10 30 39 31 5 1185 299 40 145 154 128 1 0 50 136 20 1
-Harry Spilman 1 143 39 5 18 30 15 9 639 151 16 80 97 61 1 1 138 15 1 1
[ reached getOption("max.print") -- omitted 79 rows ]
attr(,"assign")
[1] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
attr(,"contrasts")
attr(,"contrasts")$League
[1] "contr.treatment"
attr(,"contrasts")$Division
[1] "contr.treatment"
attr(,"contrasts")$NewLeague
[1] "contr.treatment"val.errors
[1] -349656.2 -399578.0 -423796.6 -458003.5 -465179.9 -479617.1 -476801.7 -461133.8 -474254.5 -477127.3 -484379.6 -488721.9 -490440.3 -488990.6 -492407.4 -495777.8 -495932.4
[18] -496521.5 -496502.3which.min(val.errors)
[1] 18Create a function to do what we did above
predict.regsubsets=function(object, newdata, id...){
form=as.formula(object$call[2])
mat=model.matrix(form, newdata)
coefi=coef(object, id=id)
xvars=names(coefi)
mat[,xvars]%*%coefi
}Let’s look at the full 10-variable set. Note that these 10 variables are different from the results from the training set
coef(regfit.best,10)
(Intercept) AtBat Hits Walks CAtBat CRuns CRBI CWalks DivisionW PutOuts Assists
162.5354420 -2.1686501 6.9180175 5.7732246 -0.1300798 1.4082490 0.7743122 -0.8308264 -112.3800575 0.2973726 0.2831680 mean.cv.errors
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
-372757.8 -394983.0 -417675.6 -429044.2 -420025.2 -427329.5 -432711.9 -427515.5 -433256.4 -423672.7 -420272.3 -424385.0 -432931.9 -432409.7 -429792.3 -429673.3 -431672.6
18 19
-431249.2 -431678.3 
reg.best=regsubsets(Salary~., data=Hitters, nvmax=19)
coef(reg.best, 9)
(Intercept) AtBat Hits Walks CAtBat CRuns CRBI CWalks DivisionW PutOuts
146.24960033 -1.93676754 6.65672102 5.55204413 -0.09953904 1.25067124 0.66176849 -0.77798498 -115.34950146 0.27773062 6.6 Lab 2: Ridge Regression and the Lasso
y
[1] 475.000 480.000 500.000 91.500 750.000 70.000 100.000 75.000 1100.000 517.143 512.500 550.000 700.000 240.000 775.000 175.000 135.000 100.000 115.000
[20] 600.000 776.667 765.000 708.333 750.000 625.000 900.000 110.000 612.500 300.000 850.000 90.000 67.500 180.000 305.000 215.000 247.500 815.000 875.000
[39] 70.000 1200.000 675.000 415.000 340.000 416.667 1350.000 90.000 275.000 230.000 225.000 950.000 75.000 105.000 320.000 850.000 535.000 933.333 850.000
[58] 210.000 325.000 275.000 450.000 1975.000 1900.000 600.000 1041.667 110.000 260.000 475.000 431.500 1220.000 70.000 145.000 595.000 1861.460 300.000 490.000
[77] 2460.000 375.000 750.000 1175.000 70.000 1500.000 385.000 1925.571 215.000 900.000 155.000 700.000 535.000 362.500 733.333 200.000 400.000 400.000 737.500
[96] 500.000 600.000 662.500 950.000 750.000 297.500 325.000 87.500 175.000 90.000 1237.500 430.000 100.000 165.000 250.000 1300.000 773.333 1008.333 275.000
[115] 775.000 850.000 365.000 95.000 110.000 100.000 277.500 80.000 600.000 200.000 657.000 75.000 2412.500 250.000 155.000 640.000 300.000 110.000 825.000
[134] 195.000 450.000 630.000 86.500 1300.000 1000.000 1800.000 1310.000 737.500 625.000 125.000 1043.333 725.000 300.000 365.000 75.000 1183.333 202.500 225.000
[153] 525.000 265.000 787.500 800.000 587.500 145.000 420.000 75.000 575.000 780.000 90.000 150.000 700.000 550.000 650.000 68.000 100.000 670.000 175.000
[172] 137.000 2127.333 875.000 120.000 140.000 210.000 800.000 240.000 350.000 175.000 200.000 1940.000 700.000 750.000 450.000 172.000 1260.000 750.000 190.000
[191] 580.000 130.000 450.000 300.000 250.000 1050.000 215.000 400.000 560.000 1670.000 487.500 425.000 500.000 250.000 400.000 450.000 750.000 70.000 875.000
[210] 190.000 191.000 740.000 250.000 140.000 97.500 740.000 140.000 341.667 1000.000 100.000 90.000 200.000 135.000 155.000 475.000 1450.000 150.000 105.000
[229] 350.000 90.000 530.000 341.667 940.000 350.000 326.667 250.000 740.000 425.000 925.000 185.000 920.000 286.667 245.000 235.000 1150.000 160.000 425.000
[248] 900.000 500.000 277.500 750.000 160.000 1300.000 525.000 550.000 1600.000 120.000 165.000 700.000 875.000 385.000 960.000 1000.0006.6.1 Ridge Regression
ridge.mod
Call: glmnet(x = x, y = y, alpha = 0, lambda = grid)
Df %Dev Lambda
[1,] 19 2.757e-07 1.000e+10
[2,] 19 3.645e-07 7.565e+09
[3,] 19 4.818e-07 5.722e+09
[4,] 19 6.369e-07 4.329e+09
[5,] 19 8.420e-07 3.275e+09
[6,] 19 1.113e-06 2.477e+09
[7,] 19 1.471e-06 1.874e+09
[8,] 19 1.945e-06 1.417e+09
[9,] 19 2.571e-06 1.072e+09
[10,] 19 3.399e-06 8.111e+08
[11,] 19 4.493e-06 6.136e+08
[12,] 19 5.940e-06 4.642e+08
[13,] 19 7.852e-06 3.511e+08
[14,] 19 1.038e-05 2.656e+08
[15,] 19 1.372e-05 2.009e+08
[16,] 19 1.814e-05 1.520e+08
[17,] 19 2.398e-05 1.150e+08
[18,] 19 3.170e-05 8.697e+07
[19,] 19 4.190e-05 6.579e+07
[20,] 19 5.539e-05 4.977e+07
[21,] 19 7.322e-05 3.765e+07
[22,] 19 9.679e-05 2.848e+07
[23,] 19 1.279e-04 2.154e+07
[24,] 19 1.691e-04 1.630e+07
[25,] 19 2.236e-04 1.233e+07
[26,] 19 2.955e-04 9.326e+06
[27,] 19 3.906e-04 7.055e+06
[28,] 19 5.162e-04 5.337e+06
[29,] 19 6.822e-04 4.037e+06
[30,] 19 9.015e-04 3.054e+06
[31,] 19 1.191e-03 2.310e+06
[32,] 19 1.574e-03 1.748e+06
[33,] 19 2.079e-03 1.322e+06
[34,] 19 2.745e-03 1.000e+06
[35,] 19 3.623e-03 7.565e+05
[36,] 19 4.781e-03 5.722e+05
[37,] 19 6.304e-03 4.329e+05
[38,] 19 8.306e-03 3.275e+05
[39,] 19 1.093e-02 2.477e+05
[40,] 19 1.435e-02 1.874e+05
[41,] 19 1.881e-02 1.417e+05
[42,] 19 2.461e-02 1.072e+05
[43,] 19 3.208e-02 8.111e+04
[44,] 19 4.165e-02 6.136e+04
[45,] 19 5.378e-02 4.642e+04
[46,] 19 6.897e-02 3.511e+04
[47,] 19 8.769e-02 2.656e+04
[48,] 19 1.103e-01 2.009e+04
[49,] 19 1.370e-01 1.520e+04
[50,] 19 1.675e-01 1.150e+04
[51,] 19 2.011e-01 8.697e+03
[52,] 19 2.369e-01 6.579e+03
[53,] 19 2.731e-01 4.977e+03
[54,] 19 3.081e-01 3.765e+03
[55,] 19 3.404e-01 2.848e+03
[56,] 19 3.688e-01 2.154e+03
[57,] 19 3.928e-01 1.630e+03
[58,] 19 4.125e-01 1.233e+03
[59,] 19 4.284e-01 9.326e+02
[60,] 19 4.412e-01 7.055e+02
[61,] 19 4.516e-01 5.337e+02
[62,] 19 4.601e-01 4.037e+02
[63,] 19 4.673e-01 3.054e+02
[64,] 19 4.737e-01 2.310e+02
[65,] 19 4.795e-01 1.748e+02
[66,] 19 4.850e-01 1.322e+02
[67,] 19 4.904e-01 1.000e+02
[68,] 19 4.957e-01 7.565e+01
[69,] 19 5.011e-01 5.722e+01
[70,] 19 5.066e-01 4.329e+01
[71,] 19 5.119e-01 3.275e+01
[72,] 19 5.171e-01 2.477e+01
[73,] 19 5.219e-01 1.874e+01
[74,] 19 5.263e-01 1.417e+01
[75,] 19 5.303e-01 1.072e+01
[76,] 19 5.336e-01 8.111e+00
[77,] 19 5.365e-01 6.136e+00
[78,] 19 5.388e-01 4.642e+00
[79,] 19 5.407e-01 3.511e+00
[80,] 19 5.421e-01 2.656e+00
[81,] 19 5.432e-01 2.009e+00
[82,] 19 5.441e-01 1.520e+00
[83,] 19 5.447e-01 1.150e+00
[84,] 19 5.451e-01 8.697e-01
[85,] 19 5.455e-01 6.579e-01
[86,] 19 5.457e-01 4.977e-01
[87,] 19 5.458e-01 3.765e-01
[88,] 19 5.459e-01 2.848e-01
[89,] 19 5.460e-01 2.154e-01
[90,] 19 5.460e-01 1.630e-01
[91,] 19 5.460e-01 1.233e-01
[92,] 19 5.460e-01 9.326e-02
[93,] 19 5.461e-01 7.055e-02
[94,] 19 5.461e-01 5.337e-02
[95,] 19 5.461e-01 4.037e-02
[96,] 19 5.461e-01 3.054e-02
[97,] 19 5.461e-01 2.310e-02
[98,] 19 5.461e-01 1.748e-02
[99,] 19 5.461e-01 1.322e-02
[100,] 19 5.461e-01 1.000e-02coef(ridge.mod)
20 x 100 sparse Matrix of class "dgCMatrix" [[ suppressing 81 column names ‘s0’, ‘s1’, ‘s2’ ... ]]
[[ suppressing 81 column names ‘s0’, ‘s1’, ‘s2’ ... ]]
(Intercept) 5.359257e+02 5.359256e+02 5.359256e+02 5.359254e+02 5.359253e+02 5.359251e+02 5.359249e+02 5.359246e+02 5.359241e+02 5.359236e+02 5.359228e+02 5.359218e+02
AtBat 5.443467e-08 7.195940e-08 9.512609e-08 1.257511e-07 1.662355e-07 2.197535e-07 2.905011e-07 3.840251e-07 5.076583e-07 6.710939e-07 8.871458e-07 1.172753e-06
Hits 1.974589e-07 2.610289e-07 3.450649e-07 4.561554e-07 6.030105e-07 7.971441e-07 1.053777e-06 1.393031e-06 1.841504e-06 2.434358e-06 3.218075e-06 4.254101e-06
HmRun 7.956523e-07 1.051805e-06 1.390424e-06 1.838059e-06 2.429805e-06 3.212059e-06 4.246151e-06 5.613159e-06 7.420260e-06 9.809139e-06 1.296709e-05 1.714170e-05
Runs 3.339178e-07 4.414196e-07 5.835307e-07 7.713931e-07 1.019736e-06 1.348031e-06 1.782017e-06 2.355720e-06 3.114121e-06 4.116682e-06 5.442006e-06 7.194001e-06
RBI 3.527222e-07 4.662778e-07 6.163918e-07 8.148335e-07 1.077162e-06 1.423944e-06 1.882370e-06 2.488380e-06 3.289490e-06 4.348509e-06 5.748467e-06 7.599123e-06
(Intercept) 5.359205e+02 5.359188e+02 5.359165e+02 5.359135e+02 5.359095e+02 5.359042e+02 5.358972e+02 5.358880e+02 5.358758e+02 5.358597e+02 5.358383e+02 5.358102e+02
AtBat 1.550308e-06 2.049411e-06 2.709192e-06 3.581378e-06 4.734346e-06 6.258482e-06 8.273267e-06 1.093664e-05 1.445735e-05 1.911136e-05 2.526337e-05 3.339542e-05
Hits 5.623662e-06 7.434134e-06 9.827459e-06 1.299127e-05 1.717361e-05 2.270236e-05 3.001092e-05 3.967221e-05 5.244352e-05 6.932585e-05 9.164225e-05 1.211414e-04
HmRun 2.266028e-05 2.995547e-05 3.959923e-05 5.234760e-05 6.920001e-05 9.147759e-05 1.209267e-04 1.598556e-04 2.113157e-04 2.793399e-04 3.692586e-04 4.881167e-04
Runs 9.510029e-06 1.257167e-05 1.661895e-05 2.196918e-05 2.904181e-05 3.839128e-05 5.075051e-05 6.708833e-05 8.868531e-05 1.172341e-04 1.549720e-04 2.048558e-04
RBI 1.004557e-05 1.327962e-05 1.755482e-05 2.320633e-05 3.067722e-05 4.055316e-05 5.360832e-05 7.086606e-05 9.367905e-05 1.238352e-04 1.636976e-04 2.163893e-04
(Intercept) 5.357729e+02 5.357237e+02 5.356586e+02 5.355726e+02 5.354590e+02 5.353088e+02 5.351104e+02 5.348483e+02 5.345021e+02 5.340450e+02 5.334417e+02 5.326458e+02
AtBat 4.414457e-05 5.835267e-05 7.713205e-05 1.019523e-04 1.347543e-04 1.781013e-04 2.353767e-04 3.110444e-04 4.109909e-04 5.429714e-04 7.171926e-04 9.470681e-04
Hits 1.601343e-04 2.116751e-04 2.797992e-04 3.698382e-04 4.888348e-04 6.460892e-04 8.538795e-04 1.128408e-03 1.491040e-03 1.969937e-03 2.602166e-03 3.436467e-03
HmRun 6.452240e-04 8.528825e-04 1.127346e-03 1.490084e-03 1.969454e-03 2.602891e-03 3.439801e-03 4.545349e-03 6.005426e-03 7.933134e-03 1.047721e-02 1.383295e-02
Runs 2.707932e-04 3.579481e-04 4.731433e-04 6.253924e-04 8.266006e-04 1.092488e-03 1.443804e-03 1.907924e-03 2.520942e-03 3.330403e-03 4.398874e-03 5.808559e-03
RBI 2.860379e-04 3.780973e-04 4.997733e-04 6.605853e-04 8.731052e-04 1.153932e-03 1.524974e-03 2.015129e-03 2.662489e-03 3.517224e-03 4.645322e-03 6.133445e-03
(Intercept) 5.315966e+02 5.302145e+02 5.283962e+02 5.260283e+02 522.91172696 5.188425e+02 5.135499e+02 5.067007e+02 497.89432739 486.66538760 472.49837844 454.86126015
AtBat 1.250193e-03 1.649587e-03 2.175269e-03 2.856183e-03 0.00375537 4.929271e-03 6.455825e-03 8.430885e-03 0.01096941 0.01420455 0.01828293 0.02335416
Hits 4.536802e-03 5.986922e-03 7.896145e-03 1.038009e-02 0.01365619 1.793929e-02 2.351966e-02 3.075783e-02 0.04009239 0.05204227 0.06719837 0.08619852
HmRun 1.825616e-02 2.408100e-02 3.174215e-02 4.166863e-02 0.05475351 7.181148e-02 9.395171e-02 1.225246e-01 0.15912611 0.20556391 0.26375808 0.33554396
Runs 7.667251e-03 1.011593e-02 1.333834e-02 1.753936e-02 0.02306905 3.029402e-02 3.969965e-02 5.188629e-02 0.06757994 0.08763193 0.11299845 0.14468833
RBI 8.095158e-03 1.067886e-02 1.407774e-02 1.850770e-02 0.02433453 3.194175e-02 4.183469e-02 5.463507e-02 0.07108903 0.09206175 0.11850817 0.15140705
(Intercept) 433.26825885 407.35605020 377.00656988 342.45146856 304.36285975 263.84665456 222.37830885 181.62066405 143.2209084 108.6007107 78.7760218 54.3251995 35.4632735
AtBat 0.02954756 0.03695718 0.04558973 0.05533408 0.06592341 0.07692026 0.08772909 0.09763889 0.1058832 0.1115181 0.1139551 0.1121111 0.1052545
Hits 0.10967001 0.13818034 0.17210886 0.21156280 0.25628237 0.30566272 0.35881027 0.41475429 0.4726795 0.5318660 0.5929157 0.6562241 0.7236362
HmRun 0.42231272 0.52462998 0.64153683 0.77000823 0.90440096 1.03656335 1.15605327 1.25121946 1.3103300 1.3223521 1.2805113 1.1798091 1.0201569
Runs 0.18366163 0.23070152 0.28620519 0.34999568 0.42114043 0.49795797 0.57807538 0.65873313 0.7371023 0.8107935 0.8778978 0.9376971 0.9897020
RBI 0.19164195 0.23984146 0.29614905 0.36000544 0.42995694 0.50367426 0.57804567 0.64954348 0.7146205 0.7705096 0.8147962 0.8471855 0.8675975
(Intercept) 22.07163454 13.69965470 10.08979010 10.368086610 14.26002563 21.2474898 30.6934829 42.0855152 54.9738422 68.6872524 82.6164012 96.3405543 109.2829120 121.0394128
AtBat 0.09238344 0.07214526 0.04333856 0.003859899 -0.04801371 -0.1143526 -0.1969965 -0.2970743 -0.4148060 -0.5489118 -0.6964360 -0.8532130 -1.0135354 -1.1712169
Hits 0.79744297 0.88059238 0.97661396 1.090128700 1.22574333 1.3888568 1.5858862 1.8230585 2.1053049 2.4364278 2.8163931 3.2390939 3.6940734 4.1655533
HmRun 0.80505438 0.54367980 0.24336135 -0.074578917 -0.39844659 -0.7097177 -0.9847328 -1.2028780 -1.3482833 -1.4028069 -1.3562347 -1.2134681 -0.9796829 -0.6702762
Runs 1.03411394 1.07217873 1.10318741 1.129710071 1.15012799 1.1635394 1.1682319 1.1599670 1.1328125 1.0800738 0.9943610 0.8703921 0.7058863 0.5030149
RBI 0.87728221 0.87912033 0.87391232 0.866429174 0.85667724 0.8455760 0.8329787 0.8163507 0.7921941 0.7564450 0.7049849 0.6365634 0.5510051 0.4507415
(Intercept) 131.3383871 140.02704637 147.0439149 152.52893912 156.6073700 159.6160967 ......
AtBat -1.3203039 -1.45573912 -1.5737685 -1.67284639 -1.7526436 -1.8153438 ......
Hits 4.6348424 5.08339645 5.4958805 5.86106113 6.1739859 6.4337591 ......
HmRun -0.3059515 0.09220561 0.5084434 0.92327754 1.3285278 1.7038461 ......
Runs 0.2686396 0.01299834 -0.2529044 -0.51634440 -0.7689372 -0.9993212 ......
RBI 0.3400248 0.22342867 0.1039164 -0.01416825 -0.1297830 -0.2372834 ......
..............................
........suppressing columns and rows in show(); maybe adjust 'options(max.print= *, width = *)'
.............................. [[ suppressing 81 column names ‘s0’, ‘s1’, ‘s2’ ... ]]
LeagueN -5.800263e-07 -7.667601e-07 -1.013611e-06 -1.339933e-06 -1.771310e-06 -2.341563e-06 -3.095401e-06 -4.091926e-06 -5.409262e-06 -7.150687e-06 -9.452719e-06 -1.249582e-05
DivisionW -7.807263e-06 -1.032074e-05 -1.364341e-05 -1.803579e-05 -2.384225e-05 -3.151805e-05 -4.166500e-05 -5.507866e-05 -7.281073e-05 -9.625147e-05 -1.272387e-04 -1.682020e-04
PutOuts 2.180288e-08 2.882212e-08 3.810115e-08 5.036747e-08 6.658282e-08 8.801855e-08 1.163553e-07 1.538148e-07 2.033341e-07 2.687955e-07 3.553316e-07 4.697270e-07
Assists 3.561198e-09 4.707694e-09 6.223294e-09 8.226828e-09 1.087538e-08 1.437661e-08 1.900503e-08 2.512352e-08 3.321180e-08 4.390401e-08 5.803847e-08 7.672336e-08
Errors -1.660460e-08 -2.195031e-08 -2.901702e-08 -3.835881e-08 -5.070811e-08 -6.703317e-08 -8.861396e-08 -1.171425e-07 -1.548557e-07 -2.047105e-07 -2.706157e-07 -3.577390e-07
NewLeagueN -1.152288e-07 -1.523253e-07 -2.013646e-07 -2.661912e-07 -3.518874e-07 -4.651715e-07 -6.149243e-07 -8.128848e-07 -1.074570e-06 -1.420491e-06 -1.877758e-06 -2.482203e-06
LeagueN -1.651853e-05 -2.183616e-05 -2.886548e-05 -3.815735e-05 -5.043982e-05 -6.667507e-05 -8.813458e-05 -1.164983e-04 -1.539858e-04 -2.035284e-04 -2.689971e-04 -3.555015e-04
DivisionW -2.223530e-04 -2.939372e-04 -3.885671e-04 -5.136619e-04 -6.790292e-04 -8.976337e-04 -1.186614e-03 -1.568625e-03 -2.073614e-03 -2.741169e-03 -3.623616e-03 -4.790124e-03
PutOuts 6.209506e-07 8.208588e-07 1.085125e-06 1.434467e-06 1.896273e-06 2.506748e-06 3.313751e-06 4.380543e-06 5.790751e-06 7.654909e-06 1.011913e-05 1.337652e-05
Assists 1.014236e-07 1.340758e-07 1.772398e-07 2.342998e-07 3.097292e-07 4.094413e-07 5.412531e-07 7.154972e-07 9.458322e-07 1.250312e-06 1.652799e-06 2.184833e-06
Errors -4.729116e-07 -6.251642e-07 -8.264353e-07 -1.092508e-06 -1.444246e-06 -1.909236e-06 -2.523944e-06 -3.336588e-06 -4.410917e-06 -5.831225e-06 -7.708976e-06 -1.019158e-05
NewLeagueN -3.281181e-06 -4.337273e-06 -5.733176e-06 -7.578145e-06 -1.001651e-05 -1.323886e-05 -1.749685e-05 -2.312257e-05 -3.055403e-05 -4.036852e-05 -5.332619e-05 -7.042660e-05
LeagueN -4.697827e-04 -6.207293e-04 -8.200508e-04 -1.083156e-03 -1.430291e-03 -1.888006e-03 -2.491020e-03 -3.284581e-03 -4.327356e-03 -0.0056949163 -7.483703e-03 -9.815198e-03
DivisionW -6.332117e-03 -8.370433e-03 -1.106478e-02 -1.462621e-02 -1.933364e-02 -2.555557e-02 -3.377884e-02 -4.464643e-02 -5.900738e-02 -0.0779823252 -1.030497e-01 -1.361588e-01
PutOuts 1.768232e-05 2.337385e-05 3.089686e-05 4.084036e-05 5.398248e-05 7.135106e-05 9.430339e-05 1.246312e-04 1.646987e-04 0.0002176234 2.875133e-04 3.797757e-04
Assists 2.888099e-06 3.817685e-06 5.046383e-06 6.670373e-06 8.816708e-06 1.165319e-05 1.540137e-05 2.035366e-05 2.689578e-05 0.0000355362 4.694455e-05 6.200169e-05
Errors -1.347401e-05 -1.781420e-05 -2.355343e-05 -3.114342e-05 -4.118231e-05 -5.446250e-05 -7.203451e-05 -9.529233e-05 -1.260879e-04 -0.0001668854 -2.209705e-04 -2.927359e-04
NewLeagueN -9.298190e-05 -1.227106e-04 -1.618562e-04 -2.133355e-04 -2.809184e-04 -3.694389e-04 -4.850258e-04 -6.353256e-04 -8.296525e-04 -0.0010789371 -1.395226e-03 -1.790270e-03
LeagueN -0.0128395721 -0.0167373242 -0.0217159907 -0.0280180222 -0.0358218645 -0.0452607965 -0.0562455973 -0.0682475006 -0.0799080742 -0.0884029052 -0.088455415 -0.070900107
DivisionW -0.1798772840 -0.2375839591 -0.3137181754 -0.4140944699 -0.5463385944 -0.7203748178 -0.9490941869 -1.2491433121 -1.6418704123 -2.1544156505 -2.820910377 -3.683711643
PutOuts 0.0005015182 0.0006620666 0.0008736282 0.0011521526 0.0015183197 0.0019989047 0.0026282664 0.0034501145 0.0045194097 0.0059042365 0.007687359 0.009967040
Assists 0.0000818644 0.0001080486 0.0001425350 0.0001879291 0.0002475408 0.0003256905 0.0004278733 0.0005610195 0.0007337315 0.0009564578 0.001241514 0.001602813
Errors -0.0003880746 -0.0005149282 -0.0006840601 -0.0009099844 -0.0012130834 -0.0016213247 -0.0021741835 -0.0029279995 -0.0039644255 -0.0054036985 -0.007425602 -0.010302495
NewLeagueN -0.0022723780 -0.0028400432 -0.0034697857 -0.0040981520 -0.0045696803 -0.0045833369 -0.0035662636 -0.0004803376 0.0064935679 0.0204481161 0.046482957 0.092729187
LeagueN -0.020774094 0.085028114 0.279935865 0.60905693 1.128214010 1.899723621 2.983666664 4.426228883 6.24738811 8.43097213 10.9331798 13.68370191
DivisionW -4.794557569 -6.215440973 -8.019029703 -10.28826070 -13.114735551 -16.595066317 -20.824312663 -25.884977165 -31.83095172 -38.66712420 -46.3270024 -54.65877750
PutOuts 0.012856678 0.016482577 0.020980083 0.02648785 0.033141498 0.041066380 0.050370740 0.061135827 0.07340191 0.08715144 0.1022656 0.11852289
Assists 0.002055224 0.002612988 0.003287919 0.00408675 0.005009084 0.006047853 0.007193656 0.008446062 0.00983132 0.01145044 0.0134326 0.01606037
Errors -0.014448993 -0.020502690 -0.029430225 -0.04267625 -0.062329257 -0.091286854 -0.133333823 -0.193078245 -0.27563868 -0.38560521 -0.5276597 -0.70358655
NewLeagueN 0.171640916 0.301433531 0.507144682 0.82061611 1.278131419 1.914781859 2.754632704 3.798020915 5.00844788 6.30348942 7.5577690 8.61181213
LeagueN 16.61465820 19.67455371 22.84517646 26.12460529 29.54380999 33.09896528 3.676542e+01 40.47940462 44.1320135 47.5927880 50.7360881 53.4619888
DivisionW -63.42474502 -72.32155123 -81.01744688 -89.20563810 -96.63293786 -103.14119518 -1.086578e+02 -113.18373495 -116.7759307 -119.5254674 -121.5339873 -122.9054511
PutOuts 0.13556792 0.15293830 0.17009772 0.18653652 0.20176898 0.21549186 2.275307e-01 0.23784120 0.2465061 0.2536944 0.2595876 0.2643809
Assists 0.01962612 0.02448004 0.03096459 0.03934585 0.04976394 0.06229233 7.689081e-02 0.09336288 0.1114676 0.1309505 0.1513785 0.1722917
Errors -0.91405980 -1.15688766 -1.42769526 -1.71914339 -2.02403835 -2.33138423 -2.630586e+00 -2.91182205 -3.1655027 -3.3836914 -3.5612567 -3.6953814
NewLeagueN 9.29582644 9.45368575 8.96604057 7.76059860 5.82733116 3.20887052 6.796074e-03 -3.62280233 -7.4842126 -11.3667064 -15.0581359 -18.3782371
LeagueN 55.7235091 57.5193908 58.8944048 59.9223467 60.6853879 61.2550034 61.6945220 62.0427219 62.3317136 ......
DivisionW -123.7434565 -124.1385803 -124.1754513 -123.9329566 -123.4841070 -122.8933487 -122.2263138 -121.5286522 -120.8579562 ......
PutOuts 0.2682829 0.2714489 0.2740185 0.2761046 0.2777901 0.2791275 0.2801691 0.2809457 0.2815135 ......
Assists 0.1933099 0.2139257 0.2337346 0.2524191 0.2697458 0.2855605 0.2997947 0.3124435 0.3234769 ......
Errors -3.7865596 -3.8379446 -3.8551650 -3.8455713 -3.8170608 -3.7767606 -3.7313945 -3.6852362 -3.6425729 ......
NewLeagueN -21.2158131 -23.5048569 -25.2442911 -26.4819571 -27.2930738 -27.7553037 -27.9647155 -27.9849755 -27.9076182 ......ridge.mod$lambda[50]
[1] 11497.57coef(ridge.mod)[,50]
(Intercept) AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns
407.356050200 0.036957182 0.138180344 0.524629976 0.230701523 0.239841459 0.289618741 1.107702929 0.003131815 0.011653637 0.087545670 0.023379882
CRBI CWalks LeagueN DivisionW PutOuts Assists Errors NewLeagueN
0.024138320 0.025015421 0.085028114 -6.215440973 0.016482577 0.002612988 -0.020502690 0.301433531 sqrt(sum(coef(ridge.mod)[-1,50]^2))
[1] 6.360612ridge.mod$lambda[60]
[1] 705.4802sqrt(sum(coef(ridge.mod)[-1,60]^2))
[1] 57.11001predict(ridge.mod, s=50, type="coefficients")[1:20,]
(Intercept) AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns
4.876610e+01 -3.580999e-01 1.969359e+00 -1.278248e+00 1.145892e+00 8.038292e-01 2.716186e+00 -6.218319e+00 5.447837e-03 1.064895e-01 6.244860e-01 2.214985e-01
CRBI CWalks LeagueN DivisionW PutOuts Assists Errors NewLeagueN
2.186914e-01 -1.500245e-01 4.592589e+01 -1.182011e+02 2.502322e-01 1.215665e-01 -3.278600e+00 -9.496680e+00 train
[1] 208 185 44 17 196 161 261 16 28 97 43 76 49 65 46 119 191 7 130 215 91 12 34 78 38 32 53 54 31 230 77 118 158 23 255 242 211 153 22 111 103 84
[43] 220 39 179 15 87 235 42 181 154 57 105 18 74 202 245 137 250 83 203 173 192 163 156 236 151 194 58 240 157 218 70 85 30 110 182 262 33 100 71 124 251 190
[85] 216 66 129 86 228 206 73 169 214 145 14 149 79 19 55 138 249 96 135 175 112 224 263 69 88 143 36 241 64 51 177 27 193 63 82 95 140 186 152 159 116 256
[127] 132 21 20 187 68y.test
[1] 475.000 480.000 500.000 91.500 750.000 70.000 75.000 1100.000 517.143 512.500 700.000 750.000 625.000 900.000 300.000 215.000 815.000 1200.000 675.000
[20] 1350.000 275.000 230.000 950.000 105.000 933.333 325.000 275.000 450.000 1975.000 260.000 145.000 300.000 1175.000 70.000 535.000 362.500 200.000 400.000
[39] 400.000 662.500 950.000 297.500 325.000 175.000 1237.500 430.000 100.000 165.000 1008.333 275.000 775.000 365.000 100.000 277.500 80.000 600.000 657.000
[58] 75.000 2412.500 250.000 300.000 825.000 195.000 630.000 1000.000 1310.000 737.500 125.000 725.000 300.000 365.000 1183.333 787.500 75.000 780.000 150.000
[77] 700.000 550.000 650.000 68.000 670.000 175.000 137.000 875.000 140.000 800.000 350.000 1940.000 700.000 1260.000 750.000 250.000 215.000 400.000 560.000
[96] 1670.000 487.500 250.000 400.000 750.000 875.000 190.000 740.000 250.000 140.000 1000.000 90.000 200.000 135.000 475.000 1450.000 150.000 350.000 530.000
[115] 341.667 940.000 350.000 740.000 425.000 925.000 245.000 235.000 160.000 425.000 900.000 160.000 1300.000 525.000 120.000 165.000 700.000 875.000ridge.mod
Call: glmnet(x = x[train, ], y = y[train], alpha = 0, lambda = grid, thresh = 1e-12)
Df %Dev Lambda
[1,] 19 3.189e-07 1.000e+10
[2,] 19 4.216e-07 7.565e+09
[3,] 19 5.573e-07 5.722e+09
[4,] 19 7.368e-07 4.329e+09
[5,] 19 9.740e-07 3.275e+09
[6,] 19 1.288e-06 2.477e+09
[7,] 19 1.702e-06 1.874e+09
[8,] 19 2.250e-06 1.417e+09
[9,] 19 2.974e-06 1.072e+09
[10,] 19 3.932e-06 8.111e+08
[11,] 19 5.198e-06 6.136e+08
[12,] 19 6.871e-06 4.642e+08
[13,] 19 9.083e-06 3.511e+08
[14,] 19 1.201e-05 2.656e+08
[15,] 19 1.587e-05 2.009e+08
[16,] 19 2.098e-05 1.520e+08
[17,] 19 2.774e-05 1.150e+08
[18,] 19 3.667e-05 8.697e+07
[19,] 19 4.847e-05 6.579e+07
[20,] 19 6.407e-05 4.977e+07
[21,] 19 8.470e-05 3.765e+07
[22,] 19 1.120e-04 2.848e+07
[23,] 19 1.480e-04 2.154e+07
[24,] 19 1.956e-04 1.630e+07
[25,] 19 2.586e-04 1.233e+07
[26,] 19 3.418e-04 9.326e+06
[27,] 19 4.517e-04 7.055e+06
[28,] 19 5.970e-04 5.337e+06
[29,] 19 7.889e-04 4.037e+06
[30,] 19 1.042e-03 3.054e+06
[31,] 19 1.377e-03 2.310e+06
[32,] 19 1.819e-03 1.748e+06
[33,] 19 2.402e-03 1.322e+06
[34,] 19 3.172e-03 1.000e+06
[35,] 19 4.185e-03 7.565e+05
[36,] 19 5.520e-03 5.722e+05
[37,] 19 7.274e-03 4.329e+05
[38,] 19 9.577e-03 3.275e+05
[39,] 19 1.259e-02 2.477e+05
[40,] 19 1.653e-02 1.874e+05
[41,] 19 2.165e-02 1.417e+05
[42,] 19 2.827e-02 1.072e+05
[43,] 19 3.679e-02 8.111e+04
[44,] 19 4.763e-02 6.136e+04
[45,] 19 6.130e-02 4.642e+04
[46,] 19 7.828e-02 3.511e+04
[47,] 19 9.901e-02 2.656e+04
[48,] 19 1.237e-01 2.009e+04
[49,] 19 1.525e-01 1.520e+04
[50,] 19 1.848e-01 1.150e+04
[51,] 19 2.198e-01 8.697e+03
[52,] 19 2.561e-01 6.579e+03
[53,] 19 2.922e-01 4.977e+03
[54,] 19 3.262e-01 3.765e+03
[55,] 19 3.570e-01 2.848e+03
[56,] 19 3.838e-01 2.154e+03
[57,] 19 4.064e-01 1.630e+03
[58,] 19 4.251e-01 1.233e+03
[59,] 19 4.405e-01 9.326e+02
[60,] 19 4.533e-01 7.055e+02
[61,] 19 4.642e-01 5.337e+02
[62,] 19 4.737e-01 4.037e+02
[63,] 19 4.822e-01 3.054e+02
[64,] 19 4.901e-01 2.310e+02
[65,] 19 4.978e-01 1.748e+02
[66,] 19 5.054e-01 1.322e+02
[67,] 19 5.132e-01 1.000e+02
[68,] 19 5.212e-01 7.565e+01
[69,] 19 5.294e-01 5.722e+01
[70,] 19 5.378e-01 4.329e+01
[71,] 19 5.463e-01 3.275e+01
[72,] 19 5.548e-01 2.477e+01
[73,] 19 5.633e-01 1.874e+01
[74,] 19 5.716e-01 1.417e+01
[75,] 19 5.796e-01 1.072e+01
[76,] 19 5.873e-01 8.111e+00
[77,] 19 5.944e-01 6.136e+00
[78,] 19 6.008e-01 4.642e+00
[79,] 19 6.064e-01 3.511e+00
[80,] 19 6.111e-01 2.656e+00
[81,] 19 6.149e-01 2.009e+00
[82,] 19 6.179e-01 1.520e+00
[83,] 19 6.201e-01 1.150e+00
[84,] 19 6.217e-01 8.697e-01
[85,] 19 6.228e-01 6.579e-01
[86,] 19 6.235e-01 4.977e-01
[87,] 19 6.240e-01 3.765e-01
[88,] 19 6.243e-01 2.848e-01
[89,] 19 6.246e-01 2.154e-01
[90,] 19 6.247e-01 1.630e-01
[91,] 19 6.248e-01 1.233e-01
[92,] 19 6.248e-01 9.326e-02
[93,] 19 6.248e-01 7.055e-02
[94,] 19 6.249e-01 5.337e-02
[95,] 19 6.249e-01 4.037e-02
[96,] 19 6.249e-01 3.054e-02
[97,] 19 6.249e-01 2.310e-02
[98,] 19 6.249e-01 1.748e-02
[99,] 19 6.249e-01 1.322e-02
[100,] 19 6.249e-01 1.000e-02ridge.pred
1
-Alan Ashby 336.53551
-Andre Dawson 1059.21367
-Alfredo Griffin 425.89084
-Argenis Salazar 33.84849
-Andres Thomas 157.92724
-Andre Thornton 655.28160
-Alan Trammell 913.86802
-Andy VanSlyke 610.52244
-Alan Wiggins 434.28132
-Bill Almon 423.26981
-Barry Bonds 570.36543
-Bobby Bonilla 410.94536
-Bob Brenly 671.37930
-Bo Diaz 436.37279
-Brian Downing 794.39888
-Billy Hatcher 116.88686
-Brook Jacoby 567.72532
-Bill Madlock 787.45952
-BillyJo Robidoux 434.00991
-Bill Schroeder 217.64094
-Chris Brown 328.17030
-Carmen Castillo 231.08101
-Carlton Fisk 633.98649
-Curt Ford 327.65834
-Carney Lansford 645.13196
-Chet Lemon 796.40031
-Cory Snyder 399.74235
-Chris Speier 404.01744
-Curt Wilkerson 84.00033
-Dave Anderson 173.55689
-Don Baylor 954.85178
-Daryl Boston 183.80043
-Darrell Evans 1207.15869
-Dwight Evans 1284.34990
-Damaso Garcia 571.38914
-Davey Lopes 984.13866
-Don Mattingly 1330.55823
-Dick Schofield 368.25201
-Danny Tartabull 481.32167
-Dave Winfield 1284.45009
-Eddie Milner 396.85512
-Ed Romero 110.91895
-Frank White 839.56290
-Glenn Braggs 213.22657
-George Brett 1292.64861
-Gary Carter 1175.66167
-Glenn Davis 963.01302
-Gary Gaetti 665.60382
-Greg Gagne 177.69003
-George Hendrick 642.96866
-Glenn Hubbard 617.24628
-Garth Iorg 305.28398
-Greg Walker 565.99678
-Harold Baines 652.25495
-Harold Reynolds 55.98904
-John Cangelosi 293.37588
-Jose Canseco 536.48392
-Jack Clark 910.21443
-Jim Dwyer 243.98296
-Jim Gantner 476.46424
-Jack Howell 190.74086
-John Kruk 460.41761
-Jeffrey Leonard 252.81864
-Jim Morrison 616.28985
-Jerry Mumphrey 656.69934
-Johnny Ray 937.54471
-Jim Rice 1391.50937
-Jerry Royster 409.81846
-John Russell 521.94946
-John Shelby 206.84447
-Jim Sundberg 504.25006
-Joel Youngblood 332.01159
-Kal Daniels 311.81177
-Kirk Gibson 842.97983
-Ken Griffey 1068.73624
-Kent Hrbek 1073.02311
-Keith Moreland 499.70502
-Ken Oberkfell 608.48368
-Ken Phelps 533.03409
-Kirby Puckett 599.91797
-Larry Herndon 582.55908
-Lloyd Moseby 784.41130
-Lance Parrish 846.70527
-Larry Parrish 759.54613
-Mike Aldrete 386.49208
-Mariano Duncan 248.00900
-Mike Easler 539.70223
-Mike LaValliere 483.13137
-Mike Pagliarulo 548.66076
-Mark Salas 245.70700
-Mickey Tettleton 417.35298
-Milt Thompson 348.81624
-Marvell Wynne 315.95582
-Mike Young 451.29494
-Oddibe McDowell 388.43780
-Pete Incaviglia 412.74710
-Pete Rose 1975.63578
-Pat Tabler 645.18825
-Rick Burleson 585.48615
-Randy Bush 262.29037
-Rick Cerone 250.12064
-Ron Cey 715.76119
-Rob Deer 707.07058
-Rick Dempsey 355.96389
-Ron Kittle 291.87275
-Rick Leach 207.61161
-Rafael Ramirez 239.76641
-Rafael Santana 325.48295
-Ruben Sierra 240.30953
-Roy Smalley 580.17050
-Robby Thompson 341.36676
-Rob Wilfong 165.81407
-Robin Yount 1286.55844
-Steve Balboni 701.73628
-Steve Buechele 255.59910
-Scott Fletcher 291.94484
-Steve Jeltz 453.42790
-Spike Owen 223.91880
-Tony Bernazard 791.59388
-Tom Brunansky 475.47776
-Terry Harper 211.88225
-Terry Pendleton 281.48929
-Tony Phillips 490.45950
-Terry Puhl 513.66793
-Tim Teufel 463.16100
-Vince Coleman 302.79695
-Von Hayes 1209.48512
-Wally Backman 493.92569
-Wally Joyner 874.89298
-Willie Randolph 1221.01325
-Willie Upshaw 1036.08429
-Willie Wilson 743.22265mean((ridge.pred-y.test)^2)
[1] 101036.8mean((ridge.pred-y.test)^2)
[1] 193253.1ridge.pred
1
-Alan Ashby 235.63818
-Andre Dawson 1201.14455
-Alfredo Griffin 424.70452
-Argenis Salazar 43.91310
-Andres Thomas 212.42390
-Andre Thornton 570.09883
-Alan Trammell 896.40889
-Andy VanSlyke 623.03648
-Alan Wiggins 498.82999
-Bill Almon 406.52579
-Barry Bonds 466.17981
-Bobby Bonilla 373.48436
-Bob Brenly 631.93056
-Bo Diaz 432.10907
-Brian Downing 712.98638
-Billy Hatcher 68.42194
-Brook Jacoby 573.17053
-Bill Madlock 884.57812
-BillyJo Robidoux 452.73010
-Bill Schroeder 143.76679
-Chris Brown 365.47945
-Carmen Castillo 244.60545
-Carlton Fisk 755.42706
-Curt Ford 312.84071
-Carney Lansford 690.96741
-Chet Lemon 818.19405
-Cory Snyder 380.02113
-Chris Speier 96.16379
-Curt Wilkerson 67.00053
-Dave Anderson 172.24260
-Don Baylor 984.16456
-Daryl Boston 194.01637
-Darrell Evans 1016.35792
-Dwight Evans 1306.65751
-Damaso Garcia 572.71185
-Davey Lopes 1109.86743
-Don Mattingly 1411.46999
-Dick Schofield 321.62810
-Danny Tartabull 493.60568
-Dave Winfield 1351.07626
-Eddie Milner 376.17031
-Ed Romero 34.03658
-Frank White 883.46905
-Glenn Braggs 212.22902
-George Brett 1556.84427
-Gary Carter 1051.71050
-Glenn Davis 956.21852
-Gary Gaetti 675.16823
-Greg Gagne 169.47098
-George Hendrick 642.28258
-Glenn Hubbard 600.48620
-Garth Iorg 295.53586
-Greg Walker 598.71886
-Harold Baines 668.10910
-Harold Reynolds 14.17725
-John Cangelosi 213.79200
-Jose Canseco 507.42094
-Jack Clark 959.16559
-Jim Dwyer 305.04379
-Jim Gantner 410.46689
-Jack Howell 221.01240
-John Kruk 537.90210
-Jeffrey Leonard 246.36762
-Jim Morrison 621.48108
-Jerry Mumphrey 706.13227
-Johnny Ray 968.99215
-Jim Rice 1548.58531
-Jerry Royster 520.07312
-John Russell 520.45394
-John Shelby 146.32708
-Jim Sundberg 200.83746
-Joel Youngblood 350.64455
-Kal Daniels 353.62629
-Kirk Gibson 836.31788
-Ken Griffey 1292.55358
-Kent Hrbek 1059.37186
-Keith Moreland 377.57472
-Ken Oberkfell 546.96602
-Ken Phelps 531.28401
-Kirby Puckett 565.87775
-Larry Herndon 554.61809
-Lloyd Moseby 723.91380
-Lance Parrish 818.11686
-Larry Parrish 740.20328
-Mike Aldrete 410.92263
-Mariano Duncan 237.91611
-Mike Easler 526.73999
-Mike LaValliere 508.06510
-Mike Pagliarulo 515.51065
-Mark Salas 266.16238
-Mickey Tettleton 438.40079
-Milt Thompson 306.13339
-Marvell Wynne 320.46602
-Mike Young 449.64916
-Oddibe McDowell 263.22719
-Pete Incaviglia 374.29057
-Pete Rose 2290.18341
-Pat Tabler 657.56305
-Rick Burleson 624.15442
-Randy Bush 243.51696
-Rick Cerone 171.05247
-Ron Cey 556.39043
-Rob Deer 666.16574
-Rick Dempsey 172.33219
-Ron Kittle 271.61996
-Rick Leach 193.82457
-Rafael Ramirez 142.64372
-Rafael Santana 240.69143
-Ruben Sierra 232.13735
-Roy Smalley 460.97883
-Robby Thompson 313.26347
-Rob Wilfong 164.63301
-Robin Yount 1445.27061
-Steve Balboni 675.98907
-Steve Buechele 233.60031
-Scott Fletcher 272.89817
-Steve Jeltz 421.40294
-Spike Owen 130.33139
-Tony Bernazard 791.48509
-Tom Brunansky 399.09881
-Terry Harper 222.99446
-Terry Pendleton 204.86587
-Tony Phillips 461.06113
-Terry Puhl 585.07449
-Tim Teufel 443.77564
-Vince Coleman 115.59456
-Von Hayes 1197.33277
-Wally Backman 520.84748
-Wally Joyner 907.19053
-Willie Randolph 1341.06580
-Willie Upshaw 976.36746
-Willie Wilson 941.79263mean((ridge.pred-y.test)^2)
[1] 114783.1predict(ridge.mod, s=0, exact=T, type="coefficients")[1:20]
[1] 299.42883596 -2.54014665 8.36611719 11.64400720 -9.09877719 2.44152119 9.23403909 -22.93584442 -0.18160843 -0.11561496 -1.33836534 3.32817777 0.07511771
[14] -1.07828647 59.76529059 -98.85996590 0.34086400 0.34165605 -0.64205839 -0.67606314Find the best lambda by using cross-validation
set.seed(1)
cv.out=cv.glmnet(x[train,], y[train],alpha=0)
plot(cv.out)
bestlam=cv.out$lambda.min
bestlam
[1] 211.7416ridge.pred=predict(ridge.mod, s=bestlam, newx=x[test,])
mean((ridge.pred-y.test)^2)
[1] 96015.51out=glmnet(x,y,alpha=0)
predict(out,type="coefficients", s=bestlam)[1:20,]
(Intercept) AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI
9.88487157 0.03143991 1.00882875 0.13927624 1.11320781 0.87318990 1.80410229 0.13074381 0.01113978 0.06489843 0.45158546 0.12900049 0.13737712
CWalks LeagueN DivisionW PutOuts Assists Errors NewLeagueN
0.02908572 27.18227535 -91.63411299 0.19149252 0.04254536 -1.81244470 7.21208390 ---
title: "Chapter 6 Model Selection"
output: html_notebook
---


```{r}
library(ISLR)
names(Hitters)
Hitters
```
```{r}
dim(Hitters)
```
```{r}
sum(is.na(Hitters))
Hitters=na.omit(Hitters)
dim(Hitters)
sum(is.na(Hitters))
    
```

So now we have zero rows with missing data in Hitters.
We're going to start building a set of models
First we'll find the best model by number of variables

```{r}
library(leaps)
regfit.full=regsubsets(Salary~., Hitters)
summary(regfit.full)

```

Note that regsubsets only lists up to 8 models, we will modify that to show all 19 variables

```{r}
regfit.full=regsubsets(Salary~., data=Hitters, nvmax = 19)
regfit.full
reg.summary=summary(regfit.full)
reg.summary
names(reg.summary)
```


Next we'll look at the r-squared value for each of the 19 models. Note the r-squared value goes up as the number of variables goes up
```{r}
reg.summary$rsq
```

Let's plot the RSS, adjusted R2, Cp and BIC for all the models, to help us decide which to select.
RSS goes first

```{r}
plot(reg.summary$rss, xlab="Number of Variables", ylab="RSS", type="l")

```


Next we'll look at r-squared
```{r}

#plot(reg.summary$adjr2,xlab="Number of Variables",ylab="Adjusted RSq",type="l")
#which.max(reg.summary$adjr2)
#points(11,reg.summary$adjr2[11], col="red",cex=2,pch=20)


plot(reg.summary$adjr2, xlab="Number of variables", ylab="Adj R2", type="l")
which.max(reg.summary$adjr2)
points(11,reg.summary$adjr2[11], col="red",cex=2,pch=20)
#points(x = 11, reg.summary$adjr2[11], col="red", cex=2, pch=20)
#points(11,reg.summary$adjr2[11], col="red",cex=2,pch=20)
#points(11, reg.summary$adjr2[11], col="red", cex=2, pch=20)
```

The red dot shows the maximum value for adjusted R2
In a similar manner, plot Mallow's Cp, and the BIC statistics, and determine which have the smallest using which.min()

Third we'll look at Mallow's Cp
```{r}
plot(reg.summary$cp, xlab="Number of Variables", ylab="Cp", type="l")
which.min(reg.summary$cp)
points(10, reg.summary$cp[10], col="red", cex=2, pch=20)
```

Fourth let's do the analysis using BIC
```{r}
which.min(reg.summary$bic) # it is 6
plot(reg.summary$bic, xlab="Number of variables", ylab="BIC", type="l")
points(6, reg.summary$bic[6], col="red", cex=2, pch=20)

```

Now let's plot to display the selected variables. Our goal is to find the best model. First we'll look at r-squared.

```{r}
plot(regfit.full, scale="r2")
```

Now let's look at adjusted r-squared
```{r}
plot(regfit.full, scale="adjr2")
```

Third we'll look at Mallow's Cp
```{r}
plot(regfit.full, scale = "Cp")
```

Fourth we'll look at BIC
```{r}
plot(regfit.full, scale = "bic")
```



Clearly the lowest bic in the range of -150, but there are multiple possibilities as well. The minimum model has six variables. Let's see the variables:

```{r}
coef(regfit.full,6)
```

# 6.5.2 Forward and backward stepwise selection

```{r}
library(glmnet)
regfit.fwd=regsubsets(Salary~., data=Hitters, nvmax=19, method="forward")
summary(regfit.fwd)
```

Now let's do the same thing using backward stepwise selection

```{r}
regfit.bwd=regsubsets(Salary~., data=Hitters, nvmax=19, method="backward")
summary(regfit.bwd)
```

Note the one-variable through six-variable models are identical. Let's look at the seven variable models:

```{r}
coef(regfit.full, 7)
```

```{r}
coef(regfit.bwd, 7)
```

#### 6.5.3 Choosing Among Models Using the Validation Set Approach and Cross-Validation ####

We will begin by splitting the data into a test set and a training set.
```{r}
set.seed(1)
train=sample(c(TRUE,FALSE),nrow(Hitters), rep=TRUE)
train
```

```{r}
test=(!train)
test
```

Now we apply regsubsets to the training set in order to perform best subset selection.

```{r}
regfit.best=regsubsets(Salary~.,data=Hitters[train,], nvmax=19)
regfit.best
```

```{r}
test.mat=model.matrix(Salary~., data=Hitters[test,])
test.mat
```

```{r}
val.errors=rep(NA,19)
for (i in 1:19){
  coefi=coef(regfit.best, id = i)
  pred=test.mat[,names(coefi)]%*%coefi
  val.errors[i]=mean((Hitters$Salary[test]-pred^2))
}
coefi
pred
val.errors
```

```{r}
which.min(val.errors) #it's supposed to be 10 - why is this wrong???
```

Create a function to do what we did above
```{r}
predict.regsubsets=function(object, newdata, id...){
  form=as.formula(object$call[2])
  mat=model.matrix(form, newdata)
  coefi=coef(object, id=id)
  xvars=names(coefi)
  mat[,xvars]%*%coefi
}
```


Let's look at the full 10-variable set. Note that these 10 variables are different from the results from the training set
```{r}
regfit.best=regsubsets(Salary~., data=Hitters, nvmax=19)
coef(regfit.best,10)
```

```{r}
k=10 #number of folds
set.seed(1)
folds=sample(1:k, nrow(Hitters),replace=TRUE)
cv.errors=matrix(NA,k,19, dimnames=list(NULL, paste(1:19)))
cv.errors
k=10
for(j in 1:k){
  best.fit = regsubsets(Salary~., data=Hitters[folds!=j,],nvmax=19)
  for (i in 1:19){
    pred=predict(best.fit, Hitters[folds==j,],id=i)
    cv.errors[j,i]=mean((Hitters$Salary[folds==j]-pred^2))
  }
}

cv.errors
mean.cv.errors=apply(cv.errors,2,mean)
mean.cv.errors
min(mean.cv.errors) #the minimum is a 9-variable model
```

```{r}
par(mfrow=c(1,1))
plot(mean.cv.errors, type="b")
```

```{r}
reg.best=regsubsets(Salary~., data=Hitters, nvmax=19)
coef(reg.best, 9)
```

#### 6.6 Lab 2: Ridge Regression and the Lasso ####

```{r}
x=model.matrix(Salary~., Hitters)[,-1]
y=Hitters$Salary
x
y
```

#### 6.6.1 Ridge Regression ####

```{r}
library(glmnet)
grid=10^seq(10,-2,length=100)
grid
ridge.mod=glmnet(x,y,alpha=0, lambda=grid)
ridge.mod
```

```{r}
coef(ridge.mod)
dim(coef(ridge.mod))
```

```{r}
ridge.mod$lambda[50]
```

```{r}
coef(ridge.mod)[,50]
```

```{r}
sqrt(sum(coef(ridge.mod)[-1,50]^2))
```

```{r}
ridge.mod$lambda[60]
```

```{r}
sqrt(sum(coef(ridge.mod)[-1,60]^2))
```

```{r}
predict(ridge.mod, s=50, type="coefficients")[1:20,]
```

```{r}
set.seed(1)
train=sample(1:nrow(x), nrow(x)/2)
train

```

```{r}
test=(-train)
test
y.test=y[test]
y.test
```

```{r}
ridge.mod=glmnet(x[train,], y[train],alpha=0, lambda=grid, thresh=1e-12)
ridge.mod
```

```{r}
ridge.pred=predict(ridge.mod, s=4, newx = x[test,])
ridge.pred
```

```{r}
mean((ridge.pred-y.test)^2)
```

```{r}
ridge.pred=predict(ridge.mod,s=1e10, newx=x[test,])
mean((ridge.pred-y.test)^2)
```

```{r}
ridge.pred=predict(ridge.mod, s=0, newx = x[test,], exact=T)
ridge.pred
```

```{r}
mean((ridge.pred-y.test)^2)
```

```{r}
lm(y~x, subset=train)
predict(ridge.mod, s=0, exact=T, type="coefficients")[1:20]
```
Find the best lambda by using cross-validation

```{r}
set.seed(1)
cv.out=cv.glmnet(x[train,], y[train],alpha=0)
plot(cv.out)
bestlam=cv.out$lambda.min
bestlam
```

```{r}
ridge.pred=predict(ridge.mod, s=bestlam, newx=x[test,])
mean((ridge.pred-y.test)^2)

```

```{r}
out=glmnet(x,y,alpha=0)
predict(out,type="coefficients", s=bestlam)[1:20,]
```

