train=read.csv(file="train.csv",head=FALSE,sep=",")
test=read.csv(file="test.csv",head=FALSE,sep=",")

bls<-function(x0,x,y){
  x0 <- as.matrix(x0)
  x0%*%solve(t(x)%*%x,t(x)%*%y)
}
 knn<-function(x0,x,y,k){
       x=as.matrix(x)
       p=dim(x)[2]	
       n=dim(x)[1]        
       dis=rep(0,n)
       for(i in 1:p){
         dis= (x0[i]-x[,i])^2+dis
       }
       ind=order(dis)[1:k]
       mean(y[ind])
 }

x_train=as.matrix(train[(train[,1]>1 & train[,1]<4),])
y_train=as.matrix(x_train[,1])
x_train=x_train[,-1]
x_test=as.matrix(test[(test[,1]>1 & test[,1]<4),])
y_test=as.matrix(x_test[,1])
x_test=x_test[,-1]
 
##testing error for least square##
n_test=nrow(x_test)
y_test_hat=rep(0, n_test) 
y_test_hat=bls(x_test, x_train, y_train)
test_error_bls=0
for( i in 1:n_test){
	test_error_bls=test_error_bls+(y_test[i]-y_test_hat[i])^2}
test_error_bls=test_error_bls/n_test
test_error_bls


##traing error for least square##
n_train=nrow(x_train)
y_train_hat=rep(0, n_train) 
y_train_hat=bls(x_train, x_train, y_train)
train_error_bls=0
for( i in 1:n_train){
	train_error_bls=train_error_bls+(y_train[i]-y_train_hat[i])^2}
train_error_bls=train_error_bls/n_train
train_error_bls

##testing error for KNN##
n_test=nrow(x_test)
k=c(1,3,5,7,15)
y_test_hat=matrix(0, nrow=n_test, ncol=length(k)) 
test_error_knn=rep(0,length(k))
for(j in 1: length(k)){
  for(r in 1:n_test){
  y_test_hat[r,j]=knn(x_test[r,], x_train, y_train,k[j])}
  
for( i in 1:n_test){
	test_error_knn[j]=test_error_knn[j]+(y_test[i]-y_test_hat[i,j])^2}
test_error_knn[j]=test_error_knn[j]/n_test}
test_error_knn

##training error for KNN##
n_train=nrow(x_train)
k=c(1,3,5,7,15)
y_train_hat=matrix(0, nrow=n_train, ncol=length(k)) 
train_error_knn=rep(0,length(k))
for(j in 1: length(k)){
  for(r in 1:n_train){
  y_train_hat[r,j]=knn(x_train[r,], x_train, y_train,k[j])}
  
for( i in 1:n_train){
	train_error_knn[j]=train_error_knn[j]+(y_train[i]-y_train_hat[i,j])^2}
train_error_knn[j]=train_error_knn[j]/n_train}
train_error_knn