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• Bet Types Explained: Understanding different bet types such as win/draw/lose bets, over/under goals, and handicap bets.Ramanujan97/Projects<|file_sep|>/Statistical Learning/Project/Project.Rmd --- title: "Project" author: "Ramanujan Rao" date: "5/9/2020" output: pdf_document --- {r setup} # libraries library(ISLR) library(MASS) library(glmnet) library(caret) library(leaps) library(class) library(kernlab) library(e1071) library(ggplot2) # setting working directory setwd("C:\Users\Ramanujan Rao\Desktop\Statistical Learning\Project") ## Part I - Best Subset Selection ### Question1 {r} # loading data set data("Hitters") dim(Hitters) # removing rows with NA values Hitters = na.omit(Hitters) # splitting into train/test sets set.seed(1) train = sample(c(TRUE,FALSE), nrow(Hitters), rep = TRUE) test = (!train) # fitting best subset selection regfit.full = regsubsets(Salary ~ . , data = Hitters[train ,], nvmax = dim(Hitters)[2]-1) reg.summary = summary(regfit.full) # plotting RSS (top left), adjusted R^2 (top right), Cp (bottom left) & BIC (bottom right) par(mfrow = c(2 ,2)) plot(reg.summary$rss , xlab = "Number of variables ", ylab = "RSS", type ="l") plot(reg.summary$adjr2 , xlab = "Number of variables ", ylab = "Adjusted R^2", type ="l") points(which.max(reg.summary$adjr2) , reg.summary$adjr2[which.max(reg.summary$adjr2)] , col ="red", cex=2 , pch=20 ) plot(reg.summary$cp , xlab = "Number of variables ", ylab = "Cp", type ="l") points(which.min(reg.summary$cp) , reg.summary$cp[which.min(reg.summary$cp)] , col ="red", cex=2 , pch=20 ) plot(reg.summary$bic , xlab = "Number of variables ", ylab = "BIC", type ="l") points(which.min(reg.summary$bic) , reg.summary$bic[which.min(reg.summary$bic)] , col ="red", cex=2 , pch=20 ) # fitting models with selected number of variables coef(regfit.full , which.max(reg.summary$adjr2)) coef(regfit.full , which.min(reg.summary$cp)) coef(regfit.full , which.min(reg.summary$bic)) ### Question2 {r} # predicting test set MSEs val.errors = rep(NA , dim(Hitters)[2]-1) for(i in seq_along(val.errors)) { val.errors[i] = mean((predict(regfit.full , Hitters[test , ], id=i)-Hitters[test ,"Salary"])^2) } # plotting test set MSEs plot(val.errors , xlab ="Number of Variables" , ylab ="Test set MSE") ### Question3 {r} # fitting lasso & ridge regression models using glmnet function lasso.mod = glmnet(x=model.matrix(Salary~.,Hitters)[,-1] , y=Hitters$Salary , alpha=1) ridge.mod = glmnet(x=model.matrix(Salary~.,Hitters)[,-1] , y=Hitters$Salary) # fitting lasso & ridge regression models using cv.glmnet function set.seed(1) cv.out = cv.glmnet(x=model.matrix(Salary~.,Hitters)[,-1] , y=Hitters$Salary) bestlam.cv.out = cv.out$lambda.min set.seed(1) cv.out.ridge = cv.glmnet(x=model.matrix(Salary~.,Hitters)[,-1] , y=Hitters$Salary,alpha=0) bestlam.cv.ridge.out=cv.out.ridge$lambda.min # predicting test set MSEs for lasso & ridge regression models mean((predict(cv.out,s=bestlam.cv.out,newx=model.matrix(Salary~.,Hitters[train ,-19]))-Hitters[train ,"Salary"])^2) mean((predict(cv.out.ridge,s=cv.out.ridge$lambda.min,newx=model.matrix(Salary~.,Hitters[train ,-19]))-Hitters[train ,"Salary"])^2) mean((predict(lasso.mod,s=cv.out$lambda.min,newx=model.matrix(Salary~.,Hitters[test ,-19]))-Hitters[test ,"Salary"])^2) mean((predict(ridge.mod,s=cv.out.ridge$lambda.min,newx=model.matrix(Salary~.,Hitters[test ,-19]))-Hitters[test ,"Salary"])^2) ### Question4 {r} # best subset selection model with six variables six.var.model=regsubsets(Salary~.,data=Hitters,nvmax=6) coef(six.var.model,id=6) # lasso regression model with six variables lasso.model.cv.glmnet=cv.glmnet(x=model.matrix(Salary~.,data=Hitters)[,-19],y=Hitters$Salary,alpha=1,nfolds=10) #10-fold cross-validation lasso.model.cv.glmnet lasso.model.six.var=predict(lasso.model.cv.glmnet,s=cv.out$lambda.min,newx=model.matrix(Salary~.,data=Hitters)[,-19]) lasso.model.six.var=predict(lasso.model.cv.glmnet,s=cv.out$lambda.min,type="coefficients")[1:16,c(6)] lasso.model.six.var ## Part II - Principal Component Analysis & K-Means Clustering ### Question5 {r} # loading data set data("USArrests") state.x77 # standardizing data USArrests.scale <- scale(USArrests) # calculating correlation matrix cor(USArrests.scale) ### Question6 {r} pr.out <- prcomp(USArrests.scale) names(pr.out) pr.out$sdev # standard deviation pr.var <- pr.out$sdev^2 # variance pve <- pr.var / sum(pr.var) # proportion variance explained par(mfrow=c(1,2)) # plot proportion variance explained plot(pve,xlab="Principal Component" , ylab="Proportion Variance Explained", ylim=c(0,max(pve)),type='b') plot(cumsum(pve),xlab="Principal Component", ylab="Cumulative Proportion Variance Explained", ylim=c(0,1),type='b') ### Question7 {r} biplot(pr.out,scale=0) # plot principal components ### Question8 {r} states=paste("state=",rownames(USArrests),sep="") par(mfrow=c(1,1)) par(mar=c(10,10,.5,.5)) biplot(pr.out,scale=0,xlim=c(-4,+4),ylim=c(-4,+4),var.axes=F,cex=.7,cex.axis=.8,varnames=states,col=c(rep("grey",50),"darkgreen","darkgreen","darkgreen","darkgreen")) ### Question9 {r} loadings <- pr.out$rotation[,c(1:4)] head(loadings[,c(1)]) head(loadings[,c(2)]) head(loadings[,c(3)]) head(loadings[,c(4)]) ### Question10 {r} par(mfrow=c(1,1)) pairs(~Murder+Assault+UrbanPop+Rape,data=USArrests,col=(cut(state.x77$"Income",breaks=5)),pch=16) ### Question11 {r} km.res=kmeans(scale(USArrests),5,nstart=20) # k-means clustering km.res.clus=data.frame(state.name,state.x77,"cluster"=km.res$cluster) # cluster centers km.res.clus[order(km.res.clus[,"cluster"]),] table(km.res.clus[,"cluster"],cut(km.res.clus$"Income",breaks=5)) # cluster vs income table ## Part III - K-Nearest Neighbors & Support Vector Machine ### Question12 {r} data("OJ") dim(OJ) table(OJ$"Purchase") set.seed(1000) # training/test split train=(sample(c(TRUE,FALSE),nrow(OJ),rep=T)) OJ.train <- OJ[train,"Purchase"] OJ.test <- OJ[!train,"Purchase"] dim(OJ.train) dim(OJ.test) table(OJ.train) table(OJ.test) ### Question13 {r} oj.knn.pred=knn(train.x=model.matrix(Purchase~.-1,data=OJ[train,-14]),test.x=model.matrix(Purchase~.-1,data=OJ[!train,-14]),cl=train.y,k=21) # knn classifier oj.knn.pred.table<-table(oj.knn.pred,OJ.test) # confusion matrix oj.knn.pred.table ### Question14 {r} oj.tune<-tune(svm,Purchase~.-Week,data=OJ[train,-14],kernel="linear",ranges=list(cost=c(.001,.01,.1,.5,1))) # svm classifier tuning oj.tune oj.svm.linear=predict(oj.tune$best.model,newdata=model.matrix(Purchase~.-Week,data=OJ[!train,-14])) # svm classifier prediction oj.svm.linear.table<-table(oj.svm.linear,OJ.test) # confusion matrix oj.svm.linear.table <|repo_name|>Ramanujan97/Projects<|file_sep|>/Statistical Learning/Final Project/Final Project.Rmd --- title: "Final Project" author: "Ramanujan Rao" date: "5/17/2020" output: pdf_document: toc: true toc_depth: '6' number_sections: true header-includes: - usepackage{amsmath} --- newpage ## Introduction The purpose of this project is to predict whether an individual will survive or not during the Titanic shipwreck using logistic regression models developed using R