Update page 'Solutions to the questions concerning R language'

Solutions to the questions concerning R language.md

@@ -8,3 +8,211 @@ train = sample(dim(OJ)[1], 800)
 OJ.train = OJ[train, ]
 OJ.test = OJ[-train, ]
 ```
+
+**ii.**
+```
+library(e1071)
+```
+```
+## Warning: package 'e1071' was built under R version 3.0.2
+```
+```
+## Loading required package: class
+```
+```
+svm.linear = svm(Purchase ~ ., kernel = "linear", data = OJ.train, cost = 0.01)
+summary(svm.linear)
+```
+
+```
+## 
+## Call:
+## svm(formula = Purchase ~ ., data = OJ.train, kernel = "linear", 
+##     cost = 0.01)
+## 
+## 
+## Parameters:
+##    SVM-Type:  C-classification 
+##  SVM-Kernel:  linear 
+##        cost:  0.01 
+##       gamma:  0.05556 
+## 
+## Number of Support Vectors:  432
+## 
+##  ( 217 215 )
+## 
+## 
+## Number of Classes:  2 
+## 
+## Levels: 
+##  CH MM
+```
+Support vector classifier creates 432 support vectors out of 800 training points. Out of these, 217 belong to level 𝙲𝙷 and remaining 215 belong to level 𝙼𝙼.
+
+**iii.**
+```
+train.pred = predict(svm.linear, OJ.train)
+table(OJ.train$Purchase, train.pred)
+```
+```
+##     train.pred
+##       CH  MM
+##   CH 439  53
+##   MM  82 226
+```
+```
+(82 + 53)/(439 + 53 + 82 + 226)
+```
+```
+## [1] 0.1688
+```
+```
+test.pred = predict(svm.linear, OJ.test)
+table(OJ.test$Purchase, test.pred)
+```
+```
+##     test.pred
+##       CH  MM
+##   CH 142  19
+##   MM  29  80
+```
+```
+(19 + 29)/(142 + 19 + 29 + 80)
+```
+```
+## [1] 0.1778
+```
+The training error rate is 16.9% and test error rate is about 17.8%.
+
+**iv.**
+```
+set.seed(1554)
+tune.out = tune(svm, Purchase ~ ., data = OJ.train, kernel = "linear", ranges = list(cost = 10^seq(-2, 1, by = 0.25)))
+summary(tune.out)
+```
+```
+## 
+## Parameter tuning of 'svm':
+## 
+## - sampling method: 10-fold cross validation 
+## 
+## - best parameters:
+##    cost
+##  0.3162
+## 
+## - best performance: 0.1687 
+## 
+## - Detailed performance results:
+##        cost  error dispersion
+## 1   0.01000 0.1688    0.03692
+## 2   0.01778 0.1688    0.03398
+## 3   0.03162 0.1713    0.03230
+## 4   0.05623 0.1725    0.03162
+## 5   0.10000 0.1700    0.03291
+## 6   0.17783 0.1712    0.03336
+## 7   0.31623 0.1687    0.03499
+## 8   0.56234 0.1700    0.03129
+## 9   1.00000 0.1687    0.03398
+## 10  1.77828 0.1688    0.03241
+## 11  3.16228 0.1688    0.03294
+## 12  5.62341 0.1713    0.03121
+## 13 10.00000 0.1713    0.03283
+```
+Tuning shows that optimal cost is 0.3162.
+
+**v.**
+```
+svm.linear = svm(Purchase ~ ., kernel = "linear", data = OJ.train, cost = tune.out$best.parameters$cost)
+train.pred = predict(svm.linear, OJ.train)
+table(OJ.train$Purchase, train.pred)
+```
+```
+##     train.pred
+##       CH  MM
+##   CH 435  57
+##   MM  71 237
+```
+```
+(57 + 71)/(435 + 57 + 71 + 237)
+```
+```
+## [1] 0.16
+```
+```
+test.pred = predict(svm.linear, OJ.test)
+table(OJ.test$Purchase, test.pred)
+```
+```
+##     test.pred
+##       CH  MM
+##   CH 141  20
+##   MM  29  80
+```
+```
+(29 + 20)/(141 + 20 + 29 + 80)
+```
+```
+## [1] 0.1815
+```
+The training error decreases to 16% but test error slightly increases to 18.1% by using best cost.
+
+**vi.**
+```
+set.seed(410)
+svm.radial = svm(Purchase ~ ., data = OJ.train, kernel = "radial")
+summary(svm.radial)
+```
+```
+## 
+## Call:
+## svm(formula = Purchase ~ ., data = OJ.train, kernel = "radial")
+## 
+## 
+## Parameters:
+##    SVM-Type:  C-classification 
+##  SVM-Kernel:  radial 
+##        cost:  1 
+##       gamma:  0.05556 
+## 
+## Number of Support Vectors:  367
+## 
+##  ( 184 183 )
+## 
+## 
+## Number of Classes:  2 
+## 
+## Levels: 
+##  CH MM
+```
+```
+train.pred = predict(svm.radial, OJ.train)
+table(OJ.train$Purchase, train.pred)
+```
+```
+##     train.pred
+##       CH  MM
+##   CH 452  40
+##   MM  78 230
+```
+```
+(40 + 78)/(452 + 40 + 78 + 230)
+```
+```
+## [1] 0.1475
+```
+```
+test.pred = predict(svm.radial, OJ.test)
+table(OJ.test$Purchase, test.pred)
+```
+```
+##     test.pred
+##       CH  MM
+##   CH 146  15
+##   MM  27  82
+```
+```
+(27 + 15)/(146 + 15 + 27 + 82)
+```
+```
+## [1] 0.1556
+```