diff --git a/Solutions to the questions concerning R language.md b/Solutions to the questions concerning R language.md
index 493a947..e09b9f4 100644
--- a/Solutions to the questions concerning R language.md	
+++ b/Solutions to the questions concerning R language.md	
@@ -217,4 +217,208 @@ table(OJ.test$Purchase, test.pred)
 ## [1] 0.1556
 ```
 The radial basis kernel with default gamma creates 367 support vectors, out of which, 184 belong to level `𝙲𝙷` and remaining 183 belong to level `𝙼𝙼`. The classifier has a training error of 14.7% and a test error of 15.6% which is a slight improvement over linear kernel. We now use cross validation to find optimal gamma.
- 
+```
+set.seed(755)
+tune.out = tune(svm, Purchase ~ ., data = OJ.train, kernel = "radial", ranges = list(cost = 10^seq(-2, 
+    1, by = 0.25)))
+summary(tune.out)
+```
+```
+## 
+## Parameter tuning of 'svm':
+## 
+## - sampling method: 10-fold cross validation 
+## 
+## - best parameters:
+##    cost
+##  0.5623
+## 
+## - best performance: 0.165 
+## 
+## - Detailed performance results:
+##        cost  error dispersion
+## 1   0.01000 0.3850    0.06258
+## 2   0.01778 0.3850    0.06258
+## 3   0.03162 0.3762    0.06908
+## 4   0.05623 0.2100    0.03855
+## 5   0.10000 0.1862    0.03143
+## 6   0.17783 0.1837    0.03230
+## 7   0.31623 0.1712    0.03438
+## 8   0.56234 0.1650    0.03764
+## 9   1.00000 0.1750    0.03584
+## 10  1.77828 0.1738    0.04059
+## 11  3.16228 0.1763    0.03748
+## 12  5.62341 0.1763    0.03839
+## 13 10.00000 0.1738    0.03459
+```
+```
+svm.radial = svm(Purchase ~ ., data = OJ.train, kernel = "radial", cost = tune.out$best.parameters$cost)
+train.pred = predict(svm.radial, OJ.train)
+table(OJ.train$Purchase, train.pred)
+```
+```
+##     train.pred
+##       CH  MM
+##   CH 452  40
+##   MM  77 231
+```
+```
+(77 + 40)/(452 + 40 + 77 + 231)
+```
+```
+## [1] 0.1462
+```
+```
+test.pred = predict(svm.radial, OJ.test)
+table(OJ.test$Purchase, test.pred)
+```
+```
+##     test.pred
+##       CH  MM
+##   CH 146  15
+##   MM  28  81
+```
+```
+(28 + 15)/(146 + 15 + 28 + 81)
+```
+```
+## [1] 0.1593
+```
+Tuning slightly decreases training error to 14.6% and slightly increases test error to 16% which is still better than linear kernel.
+
+**vii.**
+```
+set.seed(8112)
+svm.poly = svm(Purchase ~ ., data = OJ.train, kernel = "poly", degree = 2)
+summary(svm.poly)
+```
+```
+## 
+## Call:
+## svm(formula = Purchase ~ ., data = OJ.train, kernel = "poly", 
+##     degree = 2)
+## 
+## 
+## Parameters:
+##    SVM-Type:  C-classification 
+##  SVM-Kernel:  polynomial 
+##        cost:  1 
+##      degree:  2 
+##       gamma:  0.05556 
+##      coef.0:  0 
+## 
+## Number of Support Vectors:  452
+## 
+##  ( 232 220 )
+## 
+## 
+## Number of Classes:  2 
+## 
+## Levels: 
+##  CH MM
+```
+```
+train.pred = predict(svm.poly, OJ.train)
+table(OJ.train$Purchase, train.pred)
+```
+```
+##     train.pred
+##       CH  MM
+##   CH 460  32
+##   MM 105 203
+```
+```
+(32 + 105)/(460 + 32 + 105 + 203)
+```
+```
+## [1] 0.1713
+```
+```
+test.pred = predict(svm.poly, OJ.test)
+table(OJ.test$Purchase, test.pred)
+```
+```
+##     test.pred
+##       CH  MM
+##   CH 149  12
+##   MM  37  72
+```
+```
+(12 + 37)/(149 + 12 + 37 + 72)
+```
+```
+## [1] 0.1815
+```
+Summary shows that polynomial kernel produces 452 support vectors, out of which, 232 belong to level 𝙲𝙷
+ and remaining 220 belong to level 𝙼𝙼
+. This kernel produces a train error of 17.1
+% and a test error of 18.1
+% which are slightly higher than the errors produces by radial kernel but lower than the errors produced by linear kernel.
+
+```
+set.seed(322)
+tune.out = tune(svm, Purchase ~ ., data = OJ.train, kernel = "poly", degree = 2, ranges = list(cost = 10^seq(-2, 1, by = 0.25)))
+summary(tune.out)
+```
+```
+## 
+## Parameter tuning of 'svm':
+## 
+## - sampling method: 10-fold cross validation 
+## 
+## - best parameters:
+##   cost
+##  5.623
+## 
+## - best performance: 0.1837 
+## 
+## - Detailed performance results:
+##        cost  error dispersion
+## 1   0.01000 0.3850    0.05426
+## 2   0.01778 0.3675    0.05076
+## 3   0.03162 0.3575    0.05177
+## 4   0.05623 0.3425    0.04937
+## 5   0.10000 0.3150    0.05231
+## 6   0.17783 0.2487    0.03929
+## 7   0.31623 0.2088    0.05684
+## 8   0.56234 0.2088    0.05653
+## 9   1.00000 0.2000    0.06095
+## 10  1.77828 0.1938    0.04497
+## 11  3.16228 0.1862    0.04185
+## 12  5.62341 0.1837    0.03336
+## 13 10.00000 0.1837    0.04042
+```
+```
+svm.poly = svm(Purchase ~ ., data = OJ.train, kernel = "poly", degree = 2, cost = tune.out$best.parameters$cost)
+train.pred = predict(svm.poly, OJ.train)
+table(OJ.train$Purchase, train.pred)
+```
+```
+##     train.pred
+##       CH  MM
+##   CH 455  37
+##   MM  84 224
+```
+```
+(37 + 84)/(455 + 37 + 84 + 224)
+```
+```
+## [1] 0.1512
+```
+```
+test.pred = predict(svm.poly, OJ.test)
+table(OJ.test$Purchase, test.pred)
+```
+```
+##     test.pred
+##       CH  MM
+##   CH 148  13
+##   MM  34  75
+```
+```
+(13 + 34)/(148 + 13 + 34 + 75)
+```
+```
+## [1] 0.1741
+```
+