HW8
Antonio Ramirez
4/29/2021
5
a)
x1 = runif(500) -0.5
x2 = runif(500) -0.5
y = 1 * (x1^2 - x2^2 > 0)b)
plot(x1[y==1], x2[y==1], col = "blue", xlab = "x1", ylab = "x2")
points(x1[y==0], x2[y==0])
c)
log.model = glm(y ~ x1 + x2, family = binomial)d)
log.PredProb = predict.glm(log.model, type = "response")
log.PredSur = ifelse(log.PredProb >= .5,1,0)
plot(x1[log.PredSur == 1], x2[log.PredSur == 1], col = "blue", xlab = "x1", ylab = "x2")
points(x1[log.PredSur == 0], x2[log.PredSur == 0])
e)
log.model2 = glm(y ~ x1* x2, family = binomial)f)
log.PredProb = predict.glm(log.model2, type = "response")
log.PredSur = ifelse(log.PredProb >= .5,1,0)
plot(x1[log.PredSur == 1], x2[log.PredSur == 1], col = "blue", xlab = "x1", ylab = "x2")
points(x1[log.PredSur == 0], x2[log.PredSur == 0])
g)
library(e1071)
svm.lin = svm(as.factor(y)~ x1 + x2, kernel = "linear")
svm.PredSur = predict(svm.lin)
plot(x1[svm.PredSur == 1], x2[svm.PredSur == 1], col = "blue", xlab = "x1", ylab = "x2")
points(x1[svm.PredSur == 0], x2[svm.PredSur == 0])
h)
svm.rad = svm(as.factor(y)~ x1 + x2, kernel = "radial")
svm.PredSur = predict(svm.rad)
plot(x1[svm.PredSur == 1], x2[svm.PredSur == 1], col = "blue", xlab = "x1", ylab = "x2")
points(x1[svm.PredSur == 0], x2[svm.PredSur == 0])
i)
It is clear that the linear models are incapable of finding the pattern of this dataset. The right model will change depending on the data, for this case using a radial SVM model can almost perfectly classify the data.
7
a)
library(ISLR)
car = Auto
median.mil = median(car$mpg)
car$med = 1
car$med[car$mpg < median.mil] = 0
car = subset(car, select = -c(mpg, name))
car$med = as.factor(car$med)b)
library(caret)## Loading required package: lattice## Loading required package: ggplot2set.seed(42)
train_control = trainControl(method="repeatedcv", number=10, repeats=3)
svm.lin = train(med ~., data = car, method = "svmLinear", trControl = train_control, preProcess = c("center","scale"), tuneGrid = expand.grid(C = seq(0, 2, length = 20)))
svm.lin## Support Vector Machines with Linear Kernel
##
## 392 samples
## 7 predictor
## 2 classes: '0', '1'
##
## Pre-processing: centered (7), scaled (7)
## Resampling: Cross-Validated (10 fold, repeated 3 times)
## Summary of sample sizes: 353, 352, 354, 352, 352, 353, ...
## Resampling results across tuning parameters:
##
## C Accuracy Kappa
## 0.0000000 NaN NaN
## 0.1052632 0.9071041 0.8141414
## 0.2105263 0.9062494 0.8123786
## 0.3157895 0.9037494 0.8073741
## 0.4210526 0.9037281 0.8073010
## 0.5263158 0.9097368 0.8193231
## 0.6315789 0.9088821 0.8175923
## 0.7368421 0.9097368 0.8192960
## 0.8421053 0.9097368 0.8192960
## 0.9473684 0.9089035 0.8176294
## 1.0526316 0.9106129 0.8210459
## 1.1578947 0.9106129 0.8210459
## 1.2631579 0.9089024 0.8176249
## 1.3684211 0.9089238 0.8176846
## 1.4736842 0.9106118 0.8210685
## 1.5789474 0.9106556 0.8211562
## 1.6842105 0.9123662 0.8245773
## 1.7894737 0.9115115 0.8228509
## 1.8947368 0.9132220 0.8262720
## 2.0000000 0.9132220 0.8262720
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was C = 1.894737.svm.lin$bestTune## C
## 19 1.894737The tuning functions found that using a cost of 1.894737 would be best and return to lowest error.
c)
svm.rad = train(med ~., data = car, method = "svmRadial", trControl = train_control, preProcess = c("center","scale"), tuneGrid = expand.grid(C = seq(0, 2, length = 20), sigma = seq(0, 1, length = 5)))
svm.rad$bestTune## sigma C
## 64 0.75 1.263158svm.poly = train(med ~., data = car, method = "svmPoly", trControl = train_control, preProcess = c("center","scale"), tuneGrid = expand.grid(C = seq(0, 2, length = 20), scale = seq(0, 1, length = 5), degree = seq(0,1, length = 5)))
svm.poly$bestTune ## degree scale C
## 275 1 1 1.052632The radial model chooses a sigma of .75 and a cost of 1.263158. The polynomial model decides to go with degree =1, scale =1 and cost = 1.052632
d)
plot(svm.lin)
plot(svm.rad)
plot(svm.poly)
8
a)
OJ = OJ
train = sample(nrow(OJ), 800)
OJ.train = OJ[train,]
OJ.test = OJ[-train,]b)
set.seed(42)
OJ.lin = svm(Purchase ~., OJ.train, kernel = "linear", cost = .01)
summary(OJ.lin)##
## Call:
## svm(formula = Purchase ~ ., data = OJ.train, kernel = "linear", cost = 0.01)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: linear
## cost: 0.01
##
## Number of Support Vectors: 442
##
## ( 222 220 )
##
##
## Number of Classes: 2
##
## Levels:
## CH MMc)
set.seed(42)
OJ.train.pred = predict(OJ.lin, OJ.train)
OJ.test.pred = predict(OJ.lin, OJ.test)
table(OJ.train$Purchase, OJ.train.pred)## OJ.train.pred
## CH MM
## CH 415 64
## MM 73 248table(OJ.test$Purchase, OJ.test.pred)## OJ.test.pred
## CH MM
## CH 154 20
## MM 25 71train.error = 1 - (428 + 241)/800
train.error## [1] 0.16375test.error = 1 - (143 + 76)/270
test.error## [1] 0.1888889The training error is .1637 and the testing error is .1889
d)
set.seed(42)
OJ.tune = tune(svm, Purchase ~ ., data = OJ.train, kernel = "linear", ranges=list(cost=seq(.01, 10, by = .1)))
summary(OJ.tune)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## cost
## 0.71
##
## - best performance: 0.1675
##
## - Detailed performance results:
## cost error dispersion
## 1 0.01 0.17500 0.03584302
## 2 0.11 0.16875 0.03076005
## 3 0.21 0.17000 0.03291403
## 4 0.31 0.17000 0.03291403
## 5 0.41 0.17000 0.03291403
## 6 0.51 0.17000 0.03291403
## 7 0.61 0.16875 0.03498512
## 8 0.71 0.16750 0.03496029
## 9 0.81 0.17000 0.03917553
## 10 0.91 0.17000 0.03917553
## 11 1.01 0.17000 0.03917553
## 12 1.11 0.17000 0.03917553
## 13 1.21 0.17000 0.03917553
## 14 1.31 0.17125 0.03729108
## 15 1.41 0.17125 0.03729108
## 16 1.51 0.17125 0.03729108
## 17 1.61 0.17125 0.03729108
## 18 1.71 0.17125 0.03729108
## 19 1.81 0.17125 0.03729108
## 20 1.91 0.17125 0.03729108
## 21 2.01 0.17000 0.03872983
## 22 2.11 0.17000 0.03872983
## 23 2.21 0.17000 0.03872983
## 24 2.31 0.17000 0.03872983
## 25 2.41 0.17000 0.03872983
## 26 2.51 0.17000 0.03872983
## 27 2.61 0.17000 0.03872983
## 28 2.71 0.17000 0.03872983
## 29 2.81 0.17000 0.03872983
## 30 2.91 0.16875 0.03830162
## 31 3.01 0.16875 0.03830162
## 32 3.11 0.16875 0.03830162
## 33 3.21 0.16875 0.03830162
## 34 3.31 0.16875 0.03830162
## 35 3.41 0.16875 0.03830162
## 36 3.51 0.16875 0.03830162
## 37 3.61 0.16875 0.03830162
## 38 3.71 0.16875 0.03830162
## 39 3.81 0.17000 0.04090979
## 40 3.91 0.17000 0.04090979
## 41 4.01 0.17000 0.04090979
## 42 4.11 0.17000 0.04090979
## 43 4.21 0.17000 0.04090979
## 44 4.31 0.17000 0.04090979
## 45 4.41 0.17000 0.04090979
## 46 4.51 0.17000 0.04090979
## 47 4.61 0.16875 0.03919768
## 48 4.71 0.16875 0.03919768
## 49 4.81 0.16875 0.03919768
## 50 4.91 0.16875 0.03919768
## 51 5.01 0.16875 0.03919768
## 52 5.11 0.16875 0.03919768
## 53 5.21 0.16875 0.03919768
## 54 5.31 0.16875 0.03919768
## 55 5.41 0.17000 0.03961621
## 56 5.51 0.17000 0.03961621
## 57 5.61 0.17000 0.03961621
## 58 5.71 0.17000 0.03961621
## 59 5.81 0.17000 0.03961621
## 60 5.91 0.17000 0.03961621
## 61 6.01 0.17000 0.03961621
## 62 6.11 0.17000 0.03961621
## 63 6.21 0.17000 0.03961621
## 64 6.31 0.17000 0.03961621
## 65 6.41 0.17000 0.03961621
## 66 6.51 0.17000 0.03961621
## 67 6.61 0.17000 0.03961621
## 68 6.71 0.17000 0.03961621
## 69 6.81 0.17000 0.03961621
## 70 6.91 0.17000 0.03961621
## 71 7.01 0.17000 0.03961621
## 72 7.11 0.17000 0.03961621
## 73 7.21 0.17000 0.03961621
## 74 7.31 0.17000 0.03961621
## 75 7.41 0.16875 0.03830162
## 76 7.51 0.16875 0.03830162
## 77 7.61 0.16875 0.03830162
## 78 7.71 0.16875 0.03830162
## 79 7.81 0.16875 0.03830162
## 80 7.91 0.16875 0.03830162
## 81 8.01 0.16875 0.03830162
## 82 8.11 0.16875 0.03830162
## 83 8.21 0.16750 0.03782269
## 84 8.31 0.16750 0.03782269
## 85 8.41 0.16750 0.03782269
## 86 8.51 0.16750 0.03782269
## 87 8.61 0.16750 0.03782269
## 88 8.71 0.16750 0.03782269
## 89 8.81 0.16750 0.03782269
## 90 8.91 0.16750 0.03782269
## 91 9.01 0.16750 0.03782269
## 92 9.11 0.16750 0.03782269
## 93 9.21 0.16750 0.03782269
## 94 9.31 0.16750 0.03782269
## 95 9.41 0.16750 0.03782269
## 96 9.51 0.16750 0.03782269
## 97 9.61 0.16750 0.03782269
## 98 9.71 0.16750 0.03782269
## 99 9.81 0.16750 0.03782269
## 100 9.91 0.16750 0.03782269e)
set.seed(42)
OJ.lin2 = svm(Purchase ~., OJ.train, kernel = "linear", cost = 6.31)
OJ.train.pred = predict(OJ.lin2, OJ.train)
OJ.test.pred = predict(OJ.lin2, OJ.test)
table(OJ.train$Purchase, OJ.train.pred)## OJ.train.pred
## CH MM
## CH 420 59
## MM 74 247table(OJ.test$Purchase, OJ.test.pred)## OJ.test.pred
## CH MM
## CH 154 20
## MM 24 72train.error = 1 - (433 + 250)/800
train.error## [1] 0.14625test.error = 1 - (140 + 78)/270
test.error## [1] 0.1925926f)
set.seed(42)
OJ.rad = svm(Purchase ~., OJ.train, kernel = "radial", cost = .01)
summary(OJ.rad)##
## Call:
## svm(formula = Purchase ~ ., data = OJ.train, kernel = "radial", cost = 0.01)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: radial
## cost: 0.01
##
## Number of Support Vectors: 645
##
## ( 324 321 )
##
##
## Number of Classes: 2
##
## Levels:
## CH MMOJ.train.pred = predict(OJ.rad, OJ.train)
OJ.test.pred = predict(OJ.rad, OJ.test)
table(OJ.train$Purchase, OJ.train.pred)## OJ.train.pred
## CH MM
## CH 479 0
## MM 321 0table(OJ.test$Purchase, OJ.test.pred)## OJ.test.pred
## CH MM
## CH 174 0
## MM 96 0train.error = 1 - (490 + 0)/800
train.error## [1] 0.3875test.error = 1 - (163 + 0)/270
test.error## [1] 0.3962963OJ.tune = tune(svm, Purchase ~ ., data = OJ.train, kernel = "radial", ranges=list(cost=seq(.01, 10, by = .1)))
summary(OJ.tune)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## cost
## 0.91
##
## - best performance: 0.1725
##
## - Detailed performance results:
## cost error dispersion
## 1 0.01 0.40125 0.04348132
## 2 0.11 0.17875 0.03634805
## 3 0.21 0.17375 0.03251602
## 4 0.31 0.17875 0.03866254
## 5 0.41 0.18250 0.03961621
## 6 0.51 0.17625 0.04466309
## 7 0.61 0.17750 0.04362084
## 8 0.71 0.17625 0.04348132
## 9 0.81 0.17500 0.04526159
## 10 0.91 0.17250 0.04594683
## 11 1.01 0.17375 0.04656611
## 12 1.11 0.17375 0.04656611
## 13 1.21 0.17625 0.04619178
## 14 1.31 0.17625 0.04875178
## 15 1.41 0.17875 0.04528076
## 16 1.51 0.17875 0.04528076
## 17 1.61 0.18000 0.04647281
## 18 1.71 0.18125 0.04868051
## 19 1.81 0.18125 0.04973890
## 20 1.91 0.18250 0.04972145
## 21 2.01 0.18250 0.04972145
## 22 2.11 0.18250 0.04972145
## 23 2.21 0.18250 0.04972145
## 24 2.31 0.18500 0.04958158
## 25 2.41 0.18625 0.05152197
## 26 2.51 0.18625 0.05478810
## 27 2.61 0.18625 0.05478810
## 28 2.71 0.18625 0.05478810
## 29 2.81 0.18750 0.05368374
## 30 2.91 0.18625 0.05604128
## 31 3.01 0.18750 0.05368374
## 32 3.11 0.18750 0.05368374
## 33 3.21 0.18750 0.05368374
## 34 3.31 0.18750 0.05368374
## 35 3.41 0.18625 0.05185785
## 36 3.51 0.18625 0.05185785
## 37 3.61 0.18500 0.05197489
## 38 3.71 0.18500 0.05197489
## 39 3.81 0.18500 0.05197489
## 40 3.91 0.18625 0.05152197
## 41 4.01 0.18625 0.05152197
## 42 4.11 0.18625 0.05152197
## 43 4.21 0.18625 0.05152197
## 44 4.31 0.18500 0.05394184
## 45 4.41 0.18500 0.05394184
## 46 4.51 0.18500 0.05394184
## 47 4.61 0.18375 0.05434266
## 48 4.71 0.18375 0.05434266
## 49 4.81 0.18500 0.05394184
## 50 4.91 0.18625 0.05415064
## 51 5.01 0.18500 0.05552777
## 52 5.11 0.18625 0.05318012
## 53 5.21 0.18625 0.05318012
## 54 5.31 0.18625 0.05318012
## 55 5.41 0.18625 0.05318012
## 56 5.51 0.18750 0.05103104
## 57 5.61 0.18750 0.05103104
## 58 5.71 0.18750 0.05103104
## 59 5.81 0.18750 0.05103104
## 60 5.91 0.18750 0.05103104
## 61 6.01 0.18750 0.05103104
## 62 6.11 0.18750 0.05103104
## 63 6.21 0.18625 0.05219155
## 64 6.31 0.18750 0.05034602
## 65 6.41 0.18625 0.04875178
## 66 6.51 0.18750 0.04714045
## 67 6.61 0.18750 0.04714045
## 68 6.71 0.18750 0.04714045
## 69 6.81 0.18750 0.04714045
## 70 6.91 0.18625 0.04910660
## 71 7.01 0.18625 0.04910660
## 72 7.11 0.18750 0.04930066
## 73 7.21 0.18750 0.04930066
## 74 7.31 0.18625 0.04910660
## 75 7.41 0.18625 0.04910660
## 76 7.51 0.18625 0.04910660
## 77 7.61 0.18750 0.05068969
## 78 7.71 0.18750 0.05068969
## 79 7.81 0.18875 0.05050096
## 80 7.91 0.18875 0.05050096
## 81 8.01 0.18875 0.05050096
## 82 8.11 0.18875 0.05050096
## 83 8.21 0.18875 0.05050096
## 84 8.31 0.18875 0.05050096
## 85 8.41 0.18875 0.05050096
## 86 8.51 0.18875 0.05050096
## 87 8.61 0.18875 0.05050096
## 88 8.71 0.18875 0.05050096
## 89 8.81 0.18875 0.05050096
## 90 8.91 0.18750 0.04859127
## 91 9.01 0.18750 0.04859127
## 92 9.11 0.18750 0.04859127
## 93 9.21 0.18750 0.04859127
## 94 9.31 0.18750 0.04859127
## 95 9.41 0.18750 0.04859127
## 96 9.51 0.18750 0.04859127
## 97 9.61 0.18750 0.04859127
## 98 9.71 0.18750 0.04859127
## 99 9.81 0.18750 0.04859127
## 100 9.91 0.18500 0.05230785OJ.rad2 = svm(Purchase ~., OJ.train, kernel = "radial", cost = 7.61)
OJ.train.pred = predict(OJ.rad2, OJ.train)
OJ.test.pred = predict(OJ.rad2, OJ.test)
table(OJ.train$Purchase, OJ.train.pred)## OJ.train.pred
## CH MM
## CH 441 38
## MM 80 241table(OJ.test$Purchase, OJ.test.pred)## OJ.test.pred
## CH MM
## CH 152 22
## MM 25 71train.error = 1 - (446 + 246)/800
train.error## [1] 0.135test.error = 1 - (140 + 74)/270
test.error## [1] 0.2074074g)
set.seed(42)
OJ.poly = svm(Purchase ~., OJ.train, kernel = "polynomial", cost = .01, degree = 2)
summary(OJ.poly)##
## Call:
## svm(formula = Purchase ~ ., data = OJ.train, kernel = "polynomial",
## cost = 0.01, degree = 2)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: polynomial
## cost: 0.01
## degree: 2
## coef.0: 0
##
## Number of Support Vectors: 647
##
## ( 326 321 )
##
##
## Number of Classes: 2
##
## Levels:
## CH MMOJ.train.pred = predict(OJ.poly, OJ.train)
OJ.test.pred = predict(OJ.poly, OJ.test)
table(OJ.train$Purchase, OJ.train.pred)## OJ.train.pred
## CH MM
## CH 474 5
## MM 299 22table(OJ.test$Purchase, OJ.test.pred)## OJ.test.pred
## CH MM
## CH 172 2
## MM 89 7train.error = 1 - (488 + 12)/800
train.error## [1] 0.375test.error = 1 - (163 + 9)/270
test.error## [1] 0.362963OJ.tune = tune(svm, Purchase ~ ., data = OJ.train, kernel = "polynomial", ranges=list(cost=seq(.01, 10, by = .1)), degree = 2)
summary(OJ.tune)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## cost
## 7.71
##
## - best performance: 0.1875
##
## - Detailed performance results:
## cost error dispersion
## 1 0.01 0.39875 0.04581439
## 2 0.11 0.33000 0.04609772
## 3 0.21 0.22875 0.05036326
## 4 0.31 0.21500 0.05263871
## 5 0.41 0.21125 0.05050096
## 6 0.51 0.21125 0.05084358
## 7 0.61 0.21000 0.05489890
## 8 0.71 0.20750 0.05374838
## 9 0.81 0.20625 0.05145454
## 10 0.91 0.21000 0.05062114
## 11 1.01 0.20875 0.05434266
## 12 1.11 0.21000 0.06003471
## 13 1.21 0.21250 0.05682576
## 14 1.31 0.21125 0.05478810
## 15 1.41 0.21125 0.05510407
## 16 1.51 0.21125 0.05635022
## 17 1.61 0.20750 0.05719120
## 18 1.71 0.20750 0.05779514
## 19 1.81 0.20500 0.05596378
## 20 1.91 0.20250 0.05394184
## 21 2.01 0.20375 0.05529278
## 22 2.11 0.20250 0.05614960
## 23 2.21 0.20000 0.05464532
## 24 2.31 0.19750 0.05614960
## 25 2.41 0.19500 0.05957022
## 26 2.51 0.19625 0.05864500
## 27 2.61 0.19625 0.05864500
## 28 2.71 0.19500 0.05957022
## 29 2.81 0.19625 0.05923412
## 30 2.91 0.19625 0.05923412
## 31 3.01 0.19750 0.05737305
## 32 3.11 0.19875 0.05573063
## 33 3.21 0.19875 0.05350558
## 34 3.31 0.20000 0.05464532
## 35 3.41 0.19875 0.05350558
## 36 3.51 0.19750 0.05361903
## 37 3.61 0.19750 0.05361903
## 38 3.71 0.19375 0.05566829
## 39 3.81 0.19375 0.05566829
## 40 3.91 0.19250 0.05719120
## 41 4.01 0.19125 0.05622685
## 42 4.11 0.19125 0.05622685
## 43 4.21 0.19250 0.05719120
## 44 4.31 0.19125 0.05952649
## 45 4.41 0.19250 0.05809475
## 46 4.51 0.19375 0.05690208
## 47 4.61 0.19500 0.05596378
## 48 4.71 0.19250 0.05596378
## 49 4.81 0.19250 0.05596378
## 50 4.91 0.19250 0.05596378
## 51 5.01 0.19375 0.05472469
## 52 5.11 0.19375 0.05472469
## 53 5.21 0.19375 0.05472469
## 54 5.31 0.19375 0.05472469
## 55 5.41 0.19375 0.05472469
## 56 5.51 0.19375 0.05472469
## 57 5.61 0.19375 0.05472469
## 58 5.71 0.19250 0.05342440
## 59 5.81 0.19125 0.05466120
## 60 5.91 0.19125 0.05466120
## 61 6.01 0.19125 0.05337563
## 62 6.11 0.19000 0.05361903
## 63 6.21 0.19000 0.05361903
## 64 6.31 0.19125 0.05337563
## 65 6.41 0.19125 0.05337563
## 66 6.51 0.19125 0.05337563
## 67 6.61 0.19125 0.05337563
## 68 6.71 0.19000 0.05130248
## 69 6.81 0.19000 0.05130248
## 70 6.91 0.19000 0.05130248
## 71 7.01 0.19000 0.05130248
## 72 7.11 0.19000 0.05130248
## 73 7.21 0.19125 0.05239076
## 74 7.31 0.18875 0.05382908
## 75 7.41 0.18875 0.05382908
## 76 7.51 0.18875 0.05382908
## 77 7.61 0.18875 0.05382908
## 78 7.71 0.18750 0.05204165
## 79 7.81 0.18875 0.05185785
## 80 7.91 0.18875 0.05185785
## 81 8.01 0.18875 0.05185785
## 82 8.11 0.18875 0.05185785
## 83 8.21 0.18875 0.05185785
## 84 8.31 0.18875 0.05185785
## 85 8.41 0.19000 0.05296750
## 86 8.51 0.19000 0.05296750
## 87 8.61 0.19000 0.05296750
## 88 8.71 0.19125 0.05304937
## 89 8.81 0.19125 0.05304937
## 90 8.91 0.19125 0.05304937
## 91 9.01 0.18875 0.05185785
## 92 9.11 0.18875 0.05185785
## 93 9.21 0.18875 0.05185785
## 94 9.31 0.18875 0.05185785
## 95 9.41 0.18875 0.05185785
## 96 9.51 0.19000 0.05361903
## 97 9.61 0.19125 0.05369991
## 98 9.71 0.18875 0.05185785
## 99 9.81 0.18875 0.05185785
## 100 9.91 0.18875 0.05185785OJ.poly2 = svm(Purchase ~., OJ.train, kernel = "radial", cost = 4.21, degree = 2)
OJ.train.pred = predict(OJ.poly2, OJ.train)
OJ.test.pred = predict(OJ.poly2, OJ.test)
table(OJ.train$Purchase, OJ.train.pred)## OJ.train.pred
## CH MM
## CH 439 40
## MM 79 242table(OJ.test$Purchase, OJ.test.pred)## OJ.test.pred
## CH MM
## CH 151 23
## MM 22 74train.error = 1 - (449 + 245)/800
train.error## [1] 0.1325test.error = 1 - (140 + 73)/270
test.error## [1] 0.2111111h)
Definitely the worst model was the radial svm. The testing error wasn’t too different from the other models, but it was not able to make any predictions on MM. Even though the linear model performed worst than the polynomial for making training predictions, it achieved a better error when making predictions on the testing dataset over the polynomial model.