5Linear_Regressions_comparative.ipynb

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    "#Comparative of Least Squares, Lasso, Ridge Regressions and PCR, PLS \n",
    "library(ISLR)\n",
    "library(glmnet)\n",
    "library(MXM)\n",
    "library(pls) \n",
    "\n",
    "data = College\n",
    "head(data)\n",
    "\n",
    "#Creating the predictive and response variables \n",
    "y = scale(data[,2])\n",
    "X = cbind(data[,1],scale(data[,3:18]))\n",
    "\n",
    "#Split of the data set into train and test\n",
    "set.seed(10)\n",
    "n = 777\n",
    "ind = sample(c(TRUE, FALSE), n, replace=TRUE, prob=c(0.7, 0.3))\n",
    "X_train = X[ind, ]\n",
    "X_test = X[!ind, ]\n",
    "y_train = y[ind]\n",
    "y_test = y[!ind]\n",
    "\n",
    "print(c(dim(X_train),dim(X_test),length(y_train),length(y_test)))\n",
    "\n",
    "df_train=as.data.frame(cbind(X_train,y_train))\n",
    "df_test=as.data.frame(cbind(X_test,y_test))\n",
    "\n",
    "colnames(df_train) = c('Private','Accept','Enroll','Top10perc','Top25perc','F.Undergrad','P.Undergrad','Outstate','Room.Board','Books','Personal','PhD','Terminal','S.F.Ratio','perc.alumni','Expend','Grad.Rate','y_train')\n",
    "colnames(df_test ) = c('Private','Accept','Enroll','Top10perc','Top25perc','F.Undergrad','P.Undergrad','Outstate','Room.Board','Books','Personal','PhD','Terminal','S.F.Ratio','perc.alumni','Expend','Grad.Rate','y_train')\n",
    "\n",
    "#Regresión mínimos cuadrados\n",
    "model = lm(y_train ~ Private+Accept+Enroll+Top10perc+Top25perc+F.Undergrad+P.Undergrad+Outstate+Room.Board+Books+Personal+PhD+Terminal+S.F.Ratio+perc.alumni+Expend+Grad.Rate,\n",
    "   data = df_train)\n",
    "print(\"RMSE mínimos cuadrados\")\n",
    "mean((df_test[,18] - predict(model,df_test[,1:17]))^2)\n",
    "\n",
    "#Regresión Ridge \n",
    "grid = 10^seq(10,-3,length =100)\n",
    "lambda_opt = cv.glmnet(data.matrix(X_train),y_train,alpha =0,lambda=grid)$lambda.min\n",
    "ridge.mod = glmnet(data.matrix(df_train[1:17]),as.numeric(unlist(df_train[18])),alpha =0,lambda = lambda_opt)\n",
    "ridge.pred = predict(ridge.mod,s=lambda_opt,newx=data.matrix(df_test[1:17])) \n",
    "print(\"RMSE Ridge\")\n",
    "mean((df_test[,18] - ridge.pred)^2)\n",
    "\n",
    "#Regresión Lasso \n",
    "grid = 10^seq(10,-3,length =100)\n",
    "lambda_opt = cv.glmnet(data.matrix(X_train),y_train,alpha = 1,lambda=grid)$lambda.min\n",
    "lasso.mod = glmnet(data.matrix(df_train[1:17]),as.numeric(unlist(df_train[18])),alpha = 1,lambda = lambda_opt)\n",
    "lasso.pred = predict(lasso.mod,s=lambda_opt,newx=data.matrix(df_test[1:17])) \n",
    "print(\"RMSE Lasso\")\n",
    "mean((df_test[,18] - lasso.pred)^2)\n",
    "\n",
    "#Regresión PCR\n",
    "pcr.mod = pcr(y_train~.,data=df_train,validation=\"CV\")\n",
    "validationplot(pcr.mod,val.type=\"MSEP\")\n",
    "#Entonces escogemos M=15\n",
    "print(\"RMSE PCR\")\n",
    "mean((df_test[,18] - predict(pcr.mod,df_test[,1:17],ncomp =15))^2)\n",
    "\n",
    "#Regresión PLS\n",
    "plsr.mod = plsr(y_train~.,data=df_train,validation=\"CV\")\n",
    "validationplot(plsr.mod,val.type=\"MSEP\")\n",
    "#Entonces escogemos M=6\n",
    "print(\"RMSE PLS\")\n",
    "mean((df_test[,18] - predict(plsr.mod,df_test[,1:17],ncomp =6))^2)"
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