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E6_2021.R

+library(class)
+
+#Exercise 3
+
+credit=read.csv("credit.csv")
+attach(credit)
+#Make test and training samples
+train=duration%%2==0
+test=!train
+credit.train=credit[train,]
+credit.test=credit[test,]
+Default.train=credit.train$Default
+Default.test=credit.test$Default
+
+#b)
+train.X=cbind(duration,amount,installment,age,history,purpose,foreign,rent)[train,]
+test.X=cbind(duration,amount,installment,age,history,purpose,foreign,rent)[!train,]
+set.seed(1)
+knn.pred=knn(train.X,test.X,Default.train,k=1)
+table(knn.pred,Default.test)
+mean(knn.pred!=Default.test)
+#MSE 33.33%
+knn.pred=knn(train.X,test.X,Default.train,k=3)
+table(knn.pred,Default.test)
+mean(knn.pred!=Default.test)
+#MSE 28.6%
+knn.pred=knn(train.X,test.X,Default.train,k=5)
+table(knn.pred,Default.test)
+mean(knn.pred!=Default.test)
+#MSE 29%
+knn.pred=knn(train.X,test.X,Default.train,k=10)
+table(knn.pred,Default.test)
+mean(knn.pred!=Default.test)
+#MSE 26.5%
+knn.pred=knn(train.X,test.X,Default.train,k=25)
+table(knn.pred,Default.test)
+mean(knn.pred!=Default.test)
+#MSE 24.3%
+
+#All methods perform worse than LDA QDA and Logit
+
+#c)
+
+#(i)
+library(leaps)
+library(ISLR)
+College=ISLR::College
+attach(College)
+regfit.full = regsubsets(Outstate~.,data=College,nvmax=1)
+summary(regfit.full)
+#We choose Expend
+
+#(ii) Smoothing spline
+
+#Picking the degree of smoothing by cross-validation
+
+par(mfrow=c(1,1))
+
+fit=smooth.spline(Expend,Outstate,cv=TRUE)
+fit
+fit2=smooth.spline(Expend,Outstate,df=2)
+plot(Expend,Outstate,cex=.5)
+lines(fit,col="red",lwd=2)
+lines(fit2,col="blue",lwd=2)
+legend(35000,10000,legend=c("df=5","df=2"),col=c("red","purple"),lty=1)
+
+#(iii) Local regression
+
+fit=loess(Outstate~Expend,span=0.1,data=College)
+fit
+fit2=loess(Outstate~Expend,span=0.5,data=College)
+fit2
+
+expendlims=range(Expend)
+expend.grid=seq(from=expendlims[1],to=expendlims[2])
+
+plot(Expend,Outstate,cex=.5)
+lines(expend.grid,predict(fit,data.frame(Expend=expend.grid)),col="red",lwd=2)
+lines(expend.grid,predict(fit2,data.frame(Expend=expend.grid)),col="blue",lwd=2)
+
+