Project_Modeling_Bindu.Rmd

---
title: "5110_Final_Project"
author: "Bindu Latha Banisetti"
date: "4/25/2022"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

```{r}
library(tidyverse)
library(modelr)
library(gridExtra)
library(randomForest)
library(glmnet)
library(caret)
library(broom)
```


```{r}
dir1 <- file.path("winequality-red.csv")
dir2 <- file.path("winequality-white.csv")
red_wine_df <- read.csv(dir1, header = TRUE, sep = ";")
white_wine_df <- read.csv(dir2, header = TRUE, sep = ";")

which(is.na(red_wine_df))
which(is.na(white_wine_df))
```


# Stepwise Model Selection for red wine

```{r}
#Partition of data
red_wine_std <- data.frame(scale(red_wine_df[1:11]))
red_wine_std$quality <- red_wine_df$quality
set.seed(10)
partition_rw <- resample_partition(red_wine_std,
                                p=c(train=0.5,
                                    valid=0.25,
                                    test=0.25))
```


```{r}
#Function to calculate the RMSE of the predictors
step <- function(response, predictors, candidates, partition)
{
  rhs <- paste0(paste0(predictors, collapse="+"), "+", candidates)
  formulas <- lapply(paste0(response, "~", rhs), as.formula)
  rmses <- sapply(formulas,
                  function(fm) rmse(lm(fm, data=partition$train),
                                    data=partition$valid))
  names(rmses) <- candidates
  attr(rmses, "best") <- rmses[which.min(rmses)]
  rmses
}
```

```{r}
model_rw <- NULL

preds <- "1"
cands <- c("fixed.acidity","volatile.acidity","citric.acid","residual.sugar",
           "chlorides","free.sulfur.dioxide","total.sulfur.dioxide","density",
           "pH","sulphates","alcohol")
s1 <- step("quality", preds, cands, partition_rw)

model_rw <- c(model_rw, attr(s1, "best"))
s1
```

```{r}
preds <- "alcohol"
cands <- c("fixed.acidity","volatile.acidity","citric.acid","residual.sugar",
           "chlorides","free.sulfur.dioxide","total.sulfur.dioxide","density",
           "pH","sulphates")
s1 <- step("quality", preds, cands, partition_rw)

model_rw <- c(model_rw, attr(s1, "best"))
s1
```

```{r}
preds <- c("alcohol","volatile.acidity")
cands <- c("fixed.acidity","citric.acid","residual.sugar",
           "chlorides","free.sulfur.dioxide","total.sulfur.dioxide","density",
           "pH","sulphates")
s1 <- step("quality", preds, cands, partition_rw)

model_rw <- c(model_rw, attr(s1, "best"))
s1
```

```{r}
preds <- c("alcohol","volatile.acidity","sulphates")
cands <- c("fixed.acidity","citric.acid","residual.sugar",
           "chlorides","free.sulfur.dioxide","total.sulfur.dioxide","density",
           "pH")
s1 <- step("quality", preds, cands, partition_rw)

model_rw <- c(model_rw, attr(s1, "best"))
s1
```

```{r}
preds <- c("alcohol","volatile.acidity","sulphates","total.sulfur.dioxide")
cands <- c("fixed.acidity","citric.acid","residual.sugar",
           "chlorides","free.sulfur.dioxide","density",
           "pH")
s1 <- step("quality", preds, cands, partition_rw)

model_rw <- c(model_rw, attr(s1, "best"))
s1
```

```{r}
preds <- c("alcohol","volatile.acidity","sulphates","total.sulfur.dioxide","chlorides")
cands <- c("fixed.acidity","citric.acid","residual.sugar",
           "free.sulfur.dioxide","density",
           "pH")
s1 <- step("quality", preds, cands, partition_rw)

model_rw <- c(model_rw, attr(s1, "best"))
s1
```

```{r}
preds <- c("alcohol","volatile.acidity","sulphates","total.sulfur.dioxide","chlorides","pH")
cands <- c("fixed.acidity","citric.acid","residual.sugar",
           "free.sulfur.dioxide","density")
s1 <- step("quality", preds, cands, partition_rw)

model_rw <- c(model_rw, attr(s1, "best"))
s1
```

```{r}
preds <- c("alcohol","volatile.acidity","sulphates","total.sulfur.dioxide",
           "chlorides","pH","citric.acid")
cands <- c("fixed.acidity","residual.sugar",
           "free.sulfur.dioxide","density")
s1 <- step("quality", preds, cands, partition_rw)

model_rw <- c(model_rw, attr(s1, "best"))
s1
```

```{r}
preds <- c("alcohol","volatile.acidity","sulphates","total.sulfur.dioxide",
           "chlorides","pH","citric.acid", "fixed.acidity")
cands <- c("residual.sugar", "free.sulfur.dioxide","density")
s1 <- step("quality", preds, cands, partition_rw)

model_rw <- c(model_rw, attr(s1, "best"))
s1
```


**Model stopped improving at:**

- fit = quality ~ alcohol + volatile acidity + sulphates + total sulfur dioxide + chlorides + pH + citric acid + fixed acidity

**Visualizing how adding each variable affects the RMSE**

```{r fig.width= 10, fig.height= 5}
step_model <- tibble(index=seq_along(model_rw),
                     variable=factor(names(model_rw), levels=names(model_rw)),
                     RMSE=model_rw)

ggplot(step_model, aes(y=RMSE)) +
  geom_point(aes(x=variable, color = variable), size =3) +
  geom_line(aes(x=index)) +
  theme_minimal()+
  labs(title = "Stepwise model selection",
               subtitle = "(Red Wine)",
               x = "Predictors",
               y = "RMSE")+
        theme(plot.title = element_text(hjust = 0.5,
                                        color = "darkgreen", 
                                        face = "bold"),
              plot.subtitle = element_text(hjust = 0.5,
                                        color = "darkgreen", 
                                        face = "bold"),
              axis.title = element_text(color = "blue",
                                        face = "bold",
                                        size = 12),
              axis.text.x = element_text(hjust = 0.5,
                                        vjust = 0.5,
                                        color = "brown2",
                                        face = "bold",
                                        size = 9),
              axis.text.y = element_text(color = "brown2",
                                        face = "bold",
                                        size = 10),
              panel.border = element_rect(colour = "grey45",
                                        fill=NA, size=1),
              legend.position = "none")
```

## visualizing how each variable(including the predictors) affects the RMSE for Red wine

```{r}
temp_model_rw <- model_rw
preds <- c("alcohol","volatile.acidity","sulphates","total.sulfur.dioxide",
           "chlorides","pH","citric.acid", "fixed.acidity", "free.sulfur.dioxide")
cands <- c("residual.sugar","density")
s1 <- step("quality", preds, cands, partition_rw)

temp_model_rw <- c(temp_model_rw, attr(s1, "best"))
s1
```

```{r}
preds <- c("alcohol","volatile.acidity","sulphates","total.sulfur.dioxide",
           "chlorides","pH","citric.acid", "fixed.acidity", "free.sulfur.dioxide",
           "density")
cands <- c("residual.sugar")
s1 <- step("quality", preds, cands, partition_rw)

temp_model_rw <- c(temp_model_rw, attr(s1, "best"))
s1
```

```{r fig.width= 11, fig.height= 6}
#Representation of RMSE for all the variables
step_model_temp <- tibble(index=seq_along(temp_model_rw),
                     variable=factor(names(temp_model_rw), levels=names(temp_model_rw)),
                     RMSE=temp_model_rw)

ggplot(step_model_temp, aes(y=RMSE)) +
  geom_point(aes(x=variable, color = variable), size = 2) +
  geom_line(aes(x=index)) +
  theme_minimal()+
  labs(title = "Stepwise model selection",
               subtitle = "(Red Wine)",
               x = "Predictors",
               y = "RMSE")+
        theme(plot.title = element_text(hjust = 0.5,
                                        color = "darkgreen", 
                                        face = "bold"),
              plot.subtitle = element_text(hjust = 0.5,
                                        color = "darkgreen", 
                                        face = "bold"),
              axis.title = element_text(color = "blue",
                                        face = "bold",
                                        size = 12),
              axis.text.x = element_text(hjust = 0.5,
                                        vjust = 0.5,
                                        color = "brown2",
                                        face = "bold",
                                        size = 9),
              axis.text.y = element_text(color = "brown2",
                                        face = "bold",
                                        size = 10),
              panel.border = element_rect(colour = "grey45",
                                        fill=NA, size=1),
              legend.position = "none")
```

**Consider the following fits and extract the best fit model:**

- fit1 <- quality ~ alcohol + volatile acidity + sulphates + total sulfur dioxide + chlorides + pH 
- fit2 <- quality ~ alcohol + volatile acidity + sulphates + total sulfur dioxide + chlorides + pH + citric acid
- fit3 <- quality ~ alcohol + volatile acidity + sulphates + total sulfur dioxide + chlorides + pH + citric acid + fixed acidity

# Cross Validation

```{r}
set.seed(2020)
#partition_rw_train <- red_wine_std[-partition_rw$test$idx,]
#redwine_cv <- crossv_kfold(partition_rw_train, 5)
#redwine_cv

redwine_cv <- crossv_kfold(red_wine_std, 5)
redwine_cv
```

```{r}

#Calculating RMSE for each fold of data
cv_rw <- redwine_cv %>%
  mutate(fit = purrr::map(train,
                   ~ lm(quality ~ alcohol + volatile.acidity + sulphates + 
                          total.sulfur.dioxide + chlorides + pH, data = .)),
         rmse = purrr::map2_dbl(fit, test, ~ rmse(.x, .y)))

cv_rw
```

```{r}
#Average of RMSEs
mean(cv_rw$rmse)
```

## Comparing models using CV

```{r}
do_redwine_cv <- function(formula) {
  redwine_cv %>%
    mutate(fit = map(train,
                     ~ lm(formula, data = .)),
         rmse = map2_dbl(fit, test, ~ rmse(.x, .y)),
         rsq = map2_dbl(fit,test,~rsquare(.x,.y)),
         mae = map2_dbl(fit,test,~mae(.x,.y))) %>%
    summarize(cv_rmse = mean(rmse), cv_rsq = mean(rsq),
              cv_mae = mean(mae)) %>%
    return(c(cv_rmse, cv_rsq, cv_mae))
}
```

**Calling the function**

```{r}
fit1_rmse <- do_redwine_cv(quality ~ alcohol + volatile.acidity + sulphates +
                total.sulfur.dioxide + chlorides + pH )

fit2_rmse <- do_redwine_cv(quality ~ alcohol + volatile.acidity + sulphates + 
                total.sulfur.dioxide + chlorides + pH + citric.acid)

fit3_rmse <- do_redwine_cv(quality ~ alcohol + volatile.acidity + sulphates + 
                total.sulfur.dioxide + chlorides + pH + citric.acid + fixed.acidity)

fit1_rmse
fit2_rmse
fit3_rmse
```


```{r}
#Goodness of fit

gof_fs_rw <- lm( quality ~ alcohol + volatile.acidity + sulphates +
                total.sulfur.dioxide + chlorides + pH , red_wine_df)
glance(gof_fs_rw)
summary(gof_fs_rw)
```

**Best fit model:**

- quality ~ alcohol + volatile.acidity + sulphates + total.sulfur.dioxide + chlorides + pH 

# Stepwise Model Selection for white wine

```{r}
#Partition of data
white_wine_std <- data.frame(scale(white_wine_df[1:11]))
white_wine_std$quality <- white_wine_df$quality
set.seed(10)
partition_ww <- resample_partition(white_wine_std,
                                p=c(train=0.5,
                                    valid=0.25,
                                    test=0.25))
```

```{r}
model_ww <- NULL

preds <- "1"
cands <- c("fixed.acidity","volatile.acidity","citric.acid","residual.sugar",
           "chlorides","free.sulfur.dioxide","total.sulfur.dioxide","density",
           "pH","sulphates","alcohol")
s2 <- step("quality", preds, cands, partition_ww)

model_ww <- c(model_ww, attr(s2, "best"))
s2
```

```{r}
preds <- "alcohol"
cands <- c("fixed.acidity","volatile.acidity","citric.acid","residual.sugar",
           "chlorides","free.sulfur.dioxide","total.sulfur.dioxide","density",
           "pH","sulphates")
s2 <- step("quality", preds, cands, partition_ww)

model_ww <- c(model_ww, attr(s2, "best"))
s2

```

```{r}
preds <- c("alcohol","volatile.acidity")
cands <- c("fixed.acidity","citric.acid","residual.sugar",
           "chlorides","free.sulfur.dioxide","total.sulfur.dioxide","density",
           "pH","sulphates")
s2 <- step("quality", preds, cands, partition_ww)

model_ww <- c(model_ww, attr(s2, "best"))
s2

```

```{r}
preds <- c("alcohol","volatile.acidity","residual.sugar")
cands <- c("fixed.acidity","citric.acid",
           "chlorides","free.sulfur.dioxide","total.sulfur.dioxide","density",
           "pH","sulphates")
s2 <- step("quality", preds, cands, partition_ww)

model_ww <- c(model_ww, attr(s2, "best"))
s2

```

```{r}
preds <- c("alcohol","volatile.acidity","residual.sugar","fixed.acidity")
cands <- c("citric.acid","chlorides","free.sulfur.dioxide",
           "total.sulfur.dioxide","density","pH","sulphates")
s2 <- step("quality", preds, cands, partition_ww)

model_ww <- c(model_ww, attr(s2, "best"))
s2

```

```{r}
preds <- c("alcohol","volatile.acidity","residual.sugar","fixed.acidity",
           "free.sulfur.dioxide")
cands <- c("citric.acid","chlorides",
           "total.sulfur.dioxide","density","pH","sulphates")
s2 <- step("quality", preds, cands, partition_ww)

model_ww <- c(model_ww, attr(s2, "best"))
s2

```

```{r}
preds <- c("alcohol","volatile.acidity","residual.sugar","fixed.acidity",
           "free.sulfur.dioxide","sulphates")
cands <- c("citric.acid","chlorides",
           "total.sulfur.dioxide","density","pH")
s2 <- step("quality", preds, cands, partition_ww)

model_ww <- c(model_ww, attr(s2, "best"))
s2

```

```{r}
preds <- c("alcohol","volatile.acidity","residual.sugar","fixed.acidity",
           "free.sulfur.dioxide","sulphates", "total.sulfur.dioxide")
cands <- c("citric.acid","chlorides",
           "density","pH")
s2 <- step("quality", preds, cands, partition_ww)

model_ww <- c(model_ww, attr(s2, "best"))
s2

```

```{r}
preds <- c("alcohol","volatile.acidity","residual.sugar","fixed.acidity",
           "free.sulfur.dioxide","sulphates", "total.sulfur.dioxide","pH")
cands <- c("citric.acid","chlorides","density")
s2 <- step("quality", preds, cands, partition_ww)

model_ww <- c(model_ww, attr(s2, "best"))
s2

```

```{r}
preds <- c("alcohol","volatile.acidity","residual.sugar","fixed.acidity",
           "free.sulfur.dioxide","sulphates", "total.sulfur.dioxide",
           "pH","chlorides")
cands <- c("citric.acid","density")
s2 <- step("quality", preds, cands, partition_ww)

model_ww <- c(model_ww, attr(s2, "best"))
s2

```

**Model stopped improving at:**

- fit = quality ~ alcohol + volatile acidity + residual sugar + fixed acidity + free sulfur dioxide + sulphates + total sulfur dioxide + pH + chlorides 

Visualizing how adding each variable affects the RMSE.

```{r fig.width= 10, fig.height= 5}
step_model_ww <- tibble(index=seq_along(model_ww),
                     variable=factor(names(model_ww), levels=names(model_ww)),
                     RMSE=model_ww)

ggplot(step_model_ww, aes(y=RMSE)) +
  geom_point(aes(x=variable, color = variable), size = 2) +
  geom_line(aes(x=index)) +
  theme_minimal()+
  labs(title = "Stepwise model selection",
               subtitle = "(White Wine)",
               x = "Predictors",
               y = "RMSE")+
        theme(plot.title = element_text(hjust = 0.5,
                                        color = "darkgreen", 
                                        face = "bold"),
              plot.subtitle = element_text(hjust = 0.5,
                                        color = "darkgreen", 
                                        face = "bold"),
              axis.title = element_text(color = "blue",
                                        face = "bold",
                                        size = 12),
              axis.text.x = element_text(hjust = 0.5,
                                        vjust = 0.5,
                                        color = "brown2",
                                        face = "bold",
                                        size = 9),
              axis.text.y = element_text(color = "brown2",
                                        face = "bold",
                                        size = 10),
              panel.border = element_rect(colour = "grey45",
                                        fill=NA, size=1),
              legend.position = "none")
```


## visualizing how each variable(including the predictors) affects the RMSE for Red wine

```{r}
temp_model_ww <- model_ww
preds <- c("alcohol","volatile.acidity","residual.sugar","fixed.acidity",
           "free.sulfur.dioxide","sulphates", "total.sulfur.dioxide",
           "pH","chlorides", "citric.acid")
cands <- c("density")
s2 <- step("quality", preds, cands, partition_ww)

temp_model_ww <- c(temp_model_ww, attr(s2, "best"))
s2
```

```{r fig.width= 10, fig.height= 5}
step_model_ww_temp <- tibble(index=seq_along(temp_model_ww),
                     variable=factor(names(temp_model_ww), levels=names(temp_model_ww)),
                     RMSE=temp_model_ww)

ggplot(step_model_ww_temp, aes(y=RMSE)) +
  geom_point(aes(x=variable, color = variable), size = 2) +
  geom_line(aes(x=index)) +
  theme_minimal()+
  labs(title = "Stepwise model selection",
               subtitle = "(White Wine)",
               x = "Predictors",
               y = "RMSE")+
        theme(plot.title = element_text(hjust = 0.5,
                                        color = "darkgreen", 
                                        face = "bold"),
              plot.subtitle = element_text(hjust = 0.5,
                                        color = "darkgreen", 
                                        face = "bold"),
              axis.title = element_text(color = "blue",
                                        face = "bold",
                                        size = 12),
              axis.text.x = element_text(hjust = 0.5,
                                        vjust = 0.5,
                                        color = "brown2",
                                        face = "bold",
                                        size = 9),
              axis.text.y = element_text(color = "brown2",
                                        face = "bold",
                                        size = 10),
              panel.border = element_rect(colour = "grey45",
                                        fill=NA, size=1),
              legend.position = "none")
```


**Consider the following fits and extract the best fit model:**

- fit1 <- quality ~ alcohol + volatile.acidity + residual.sugar + fixed.acidity + free.sulfur.dioxide + sulphates + total.sulfur.dioxide + pH
- fit2 <- quality ~ alcohol + volatile.acidity + residual.sugar + fixed.acidity + free.sulfur.dioxide + sulphates + total.sulfur.dioxide + pH + chlorides

# Cross Validation

```{r}
set.seed(2020)
#partition_ww_train <- white_wine_std[-partition_ww$test$idx,]
#whitewine_cv <- crossv_kfold(partition_ww_train, 5)
#whitewine_cv

whitewine_cv <- crossv_kfold(white_wine_std, 5)
whitewine_cv
```

```{r}

#Calculating RMSE for each fold of data
cv_rw <- whitewine_cv %>%
  mutate(fit = purrr::map(train,
                   ~ lm(quality ~ alcohol + volatile.acidity + residual.sugar + 
                             fixed.acidity + free.sulfur.dioxide + 
                             sulphates + total.sulfur.dioxide + pH, data = .)),
         rmse = purrr::map2_dbl(fit, test, ~ rmse(.x, .y)))

cv_rw
```

```{r}
#Average of RMSEs
mean(cv_rw$rmse)
```

## Comparing models using CV

```{r}
do_whitewine_cv <- function(formula) {
  whitewine_cv %>%
    mutate(fit = map(train,
                     ~ lm(formula, data = .)),
         rmse = map2_dbl(fit, test, ~ rmse(.x, .y)),
         rsq = map2_dbl(fit,test, ~rsquare(.x,.y)),
         mae = map2_dbl(fit,test,~mae(.x,.y))) %>%
    summarize(cv_rmse = mean(rmse), cv_rsq = mean(rsq),
              cv_mae = mean(mae)) %>%
    return(c(cv_rmse, cv_rsq, cv_mae))
}
```


**Calling the function**

```{r}

fit1_rmse_ww <- do_whitewine_cv(quality ~ alcohol + volatile.acidity + residual.sugar + 
                             fixed.acidity + free.sulfur.dioxide + 
                             sulphates + total.sulfur.dioxide + pH)

fit2_rmse_ww <- do_whitewine_cv(quality ~ alcohol + volatile.acidity + residual.sugar + 
                             fixed.acidity + free.sulfur.dioxide + 
                             sulphates + total.sulfur.dioxide + pH + chlorides)

fit1_rmse_ww
fit2_rmse_ww
```


**Best fit Model**

- quality ~ alcohol + volatile.acidity + residual.sugar + fixed.acidity + free.sulfur.dioxide + sulphates + total.sulfur.dioxide + pH

```{r}
fit_rw <- lm(quality ~ alcohol + volatile.acidity + sulphates + total.sulfur.dioxide + chlorides + pH, red_wine_std )

summary(fit_rw)

fit_ww <- lm(quality ~ alcohol + volatile.acidity + residual.sugar + fixed.acidity + free.sulfur.dioxide + sulphates + total.sulfur.dioxide + pH, white_wine_std)

summary(fit_ww)
```

```{r}
#Data partition

#Redwine
set.seed(1)
train <- createDataPartition(red_wine_std$quality, p=0.6, list=FALSE)

table(red_wine_std$quality[train])

reddf_train <- red_wine_std[as.integer(train),]
reddf_test <- red_wine_std[-as.integer(train),]

#Whitewine
set.seed(1)
train_w <- createDataPartition(white_wine_std$quality, p=0.6, list=FALSE)

table(white_wine_std$quality[train_w])

whitedf_train <- white_wine_std[as.integer(train_w),]
whitedf_test <- white_wine_std[-as.integer(train_w),]
```


## Random Forest Regression

```{r}

#Red wine
fit_rw_rf <- randomForest(quality ~ alcohol + volatile.acidity +
                            sulphates + total.sulfur.dioxide + 
                            chlorides + pH, reddf_train, 
                          mtry = 3,
                          importance = TRUE, 
                          na.action = na.omit)
summary(fit_rw_rf)

fit_rw_rf_prediction<-predict(fit_rw_rf,newdata=reddf_test)
rf_rw_results<-as.data.frame(cbind(fit_rw_rf_prediction,reddf_test$quality))
colnames(rf_rw_results)<-c("prediction","real")

```

```{r}
#White Wine - Random forest regression
fit_ww_rf <- randomForest(quality ~ alcohol + volatile.acidity + 
                            residual.sugar + fixed.acidity + 
                            free.sulfur.dioxide + sulphates +
                            total.sulfur.dioxide + pH, whitedf_train, 
                          mtry = 3,
                          importance = TRUE, 
                          na.action = na.omit)
fit_ww_rf

fit_ww_rf_prediction<-predict(fit_ww_rf,newdata=whitedf_test)
rf_ww_results<-as.data.frame(cbind(fit_ww_rf_prediction,whitedf_test$quality))
colnames(rf_ww_results)<-c("prediction","real")
```

## Ridge Regression


```{r}
#Ridge regression for red wine


ctrl <- trainControl(method="repeatedcv", number=10, repeats=10)

grd <- expand.grid(lambda=exp(seq(from=-7, to=-2, length.out=20)),
                   alpha=0)

set.seed(1)
fit_rw_ridge <- train(quality ~ alcohol + volatile.acidity +
                            sulphates + total.sulfur.dioxide + 
                            chlorides + pH, data=reddf_train,
              method="glmnet",
              preProcess=c("center", "scale"),
              trControl=ctrl, tuneGrid=grd)
fit_rw_ridge
```

```{r}
#Ridge regression for white wine


ctrl <- trainControl(method="repeatedcv", number=10, repeats=10)

grd <- expand.grid(lambda=exp(seq(from=-7, to=-2, length.out=20)),
                   alpha=0)

set.seed(1)
fit_ww_ridge <- train(quality ~ alcohol + volatile.acidity + 
                            residual.sugar + fixed.acidity + 
                            free.sulfur.dioxide + sulphates +
                            total.sulfur.dioxide + pH, data=whitedf_train,
              method="glmnet",
              preProcess=c("center", "scale"),
              trControl=ctrl, tuneGrid=grd)
fit_ww_ridge
```

## Lasso Regression

## Lasso Regression

```{r}
#Lasso regression for red wine
actual_quality_rw<-red_wine_df$quality
response_rw<-red_wine_df$quality
predictors_rw<-data.matrix(red_wine_df[,c("fixed.acidity","volatile.acidity","citric.acid",
                          "residual.sugar","chlorides","free.sulfur.dioxide",
                          "total.sulfur.dioxide","density","pH","sulphates",
                          "alcohol")])


red_ls_model<-glmnet(predictors_rw,response_rw,alpha=1)

coef_rw<-plot(red_ls_model,xvar="lambda",label=TRUE)
# Using k-fold cv to get best optimal lambda value
red_cv_ls_model<-cv.glmnet(predictors_rw,response_rw,alpha=1)

#produce plot of MSE values for each lambda 
plot(red_cv_ls_model)

#find optimal lambda value that minimizes the MSE
best_lambda_rw<-red_cv_ls_model$lambda.min
best_lambda_rw

best_model_ls_rw<-glmnet(predictors_rw,response_rw,alpha=1,lambda=best_lambda_rw)
coef(best_model_ls_rw)

# To find the rsquare of our best model

#To obtain predicted values
predicted_quality_rw<-predict(best_model_ls_rw,s=best_lambda_rw,newx=predictors_rw)

#Finding the SST and SSE and Rsquare
sst_rw<-sum((actual_quality_rw-mean(actual_quality_rw))^2)
sse_rw<-sum((actual_quality_rw-predicted_quality_rw)^2)
rsq_ls_rw<-1-(sse_rw/sst_rw)
rsq_ls_rw

#Finding the RMSE and MAE
n_rw<-nrow(red_wine_df)
rmse_ls_rw<-sqrt(sum((actual_quality_rw-predicted_quality_rw)^2)/n_rw)
rmse_ls_rw
mae_ls_rw<-sum(abs(actual_quality_rw-predicted_quality_rw))/n_rw
mae_ls_rw

view(data.frame(RMSE=rmse_ls_rw,MAE=mae_ls_rw,R_Square=rsq_ls_rw))

```

```{r}
# Lasso Regression on White wine 
response_ww<-white_wine_df$quality
actual_quality_ww<-white_wine_df$quality
predictors_ww<-data.matrix(white_wine_df[,c("fixed.acidity","volatile.acidity","citric.acid",
                            "residual.sugar","chlorides","free.sulfur.dioxide",
                            "total.sulfur.dioxide","density","pH","sulphates",
                            "alcohol")])


white_ls_model<-glmnet(predictors_ww,response_ww,alpha=1)

coef_ww<-plot(white_ls_model,xvar="lambda",label=TRUE)
# Using k-fold cv to get best optimal lambda value
library("glmnet")
white_cv_ls_model<-cv.glmnet(predictors_ww,response_ww,alpha=1)

plot(white_cv_ls_model)

#find optimal lambda value that minimizes the MSE
best_lambda_ww<-white_cv_ls_model$lambda.min
best_lambda_ww

best_model_ls_ww<-glmnet(predictors_ww,response_ww,alpha=1,lambda=best_lambda_ww)
coef(best_model_ls_ww)

# To find the rsquare of our best model

#To obtain predicted values
predicted_quality_ww<-predict(best_model_ls_ww,s=best_lambda_ww,newx=predictors_ww)

#find the SST and SSE
sst_ww<-sum((actual_quality_ww-mean(actual_quality_ww))^2)
sse_ww<-sum((actual_quality_ww-predicted_quality_ww)^2)

rsq_ls_ww<-1-(sse_ww/sst_ww)
rsq_ls_ww

n_ww<-nrow(white_wine_df)
rmse_ls_ww<-sqrt(sum((actual_quality_ww-predicted_quality_ww)^2)/n_ww)
rmse_ls_ww

mae_ls_ww<-sum(abs(actual_quality_ww-predicted_quality_ww))/n_ww
mae_ls_ww

ls_results_df <- tibble(wine_type = c("Red Wine","White wine"),
                            rmse = c(rmse_ls_rw,rmse_ls_ww),
                            mae = c(mae_ls_rw,rmse_ls_rw),
                            rsquare = c(rsq_ls_rw,rsq_ls_ww))
view(ls_results_df)

plot(red_ls_model,xvar="lambda",label=TRUE)
plot(white_ls_model,xvar="lambda",label=TRUE)
#grid.arrange(coef_rw,coef_ww,nrow=1)

```

```{r}
fit_fs_rmse_rw<-as.numeric(fit1_rmse["cv_rmse"])
fit_fs_rsq_rw<-as.numeric(fit1_rmse["cv_rsq"])
fit_fs_rmse_ww<-as.numeric(fit1_rmse_ww["cv_rmse"])
fit_fs_rsq_ww<-as.numeric(fit1_rmse_ww["cv_rsq"])
fit_fs_mae_rw<-as.numeric(fit1_rmse["cv_mae"])
fit_fs_mae_ww<-as.numeric(fit1_rmse_ww["cv_mae"])

fit_rd_rmse_rw<-rmse(fit_rw_ridge,reddf_test)
fit_rd_rsq_rw<-rsquare(fit_rw_ridge,reddf_test)
fit_rd_rmse_ww<-rmse(fit_ww_ridge,whitedf_test)
fit_rd_rsq_ww<-rsquare(fit_ww_ridge,whitedf_test)
fit_rd_mae_rw<-mae(fit_rw_ridge,reddf_test)
fit_rd_mae_ww<-mae(fit_ww_ridge,whitedf_test)

fit_ls_rmse_rw<-rmse_ls_rw
fit_ls_rsq_rw<-rsq_ls_rw
fit_ls_rmse_ww<-rmse_ls_ww
fit_ls_rsq_ww<-rsq_ls_ww
fit_ls_mae_rw<-mae_ls_rw
fit_ls_mae_ww<-mae_ls_ww

fit_rf_rmse_rw<-rmse(fit_rw_rf,reddf_test)
fit_rf_rsq_rw<- rsquare(fit_rw_rf,reddf_test)
fit_rf_rmse_ww<-rmse(fit_ww_rf,whitedf_test)
fit_rf_rsq_ww<- rsquare(fit_ww_rf,whitedf_test)
fit_rf_mae_rw<-mae(fit_rw_rf,reddf_test)
fit_rf_mae_ww<-mae(fit_ww_rf,whitedf_test)
```

```{r}
fs_results_df <- tibble(wine_type = c("Red Wine","White wine"),
                            rmse = c(fit_fs_rmse_rw,fit_fs_rmse_ww), 
                            mae = c(fit_fs_mae_rw,fit_fs_mae_ww),
                            rsquare = c(fit_fs_rsq_rw,fit_fs_rsq_ww))
view(fs_results_df)


rd_results_df <- tibble(wine_type = c("Red Wine","White wine"),
                            rmse = c(fit_rd_rmse_rw,fit_rd_rmse_ww), 
                            mae = c(fit_rd_mae_rw,fit_rd_mae_ww),
                            rsquare = c(fit_rd_rsq_rw,fit_rd_rsq_ww))
view(rd_results_df)

ls_results_df <- tibble(wine_type = c("Red Wine","White wine"),
                            rmse = c(fit_ls_rmse_rw,fit_ls_rmse_ww), 
                            mae = c(fit_ls_mae_rw,fit_ls_mae_ww),
                            rsquare = c(fit_ls_rsq_rw,fit_ls_rsq_ww))
view(ls_results_df)


rf_results_df <- tibble(wine_type = c("Red Wine","White wine"),
                            rmse = c(fit_rf_rmse_rw,fit_rf_rmse_ww), 
                            mae = c(fit_rf_mae_rw,fit_rf_mae_ww),
                            rsquare = c(fit_rf_rsq_rw,fit_rf_rsq_ww))
view(rf_results_df)
```



```{r}

rmse_of_plots_rw<-data.frame(rmse_value=c(fit_fs_rmse_rw,fit_rd_rmse_rw,fit_ls_rmse_rw,fit_rf_rmse_rw),model=c("Forward","Ridge","Lasso","RandomF"))
rmse_of_plots_ww<-data.frame(rmse_value=c(fit_fs_rmse_ww,fit_rd_rmse_ww,fit_ls_rmse_ww,fit_rf_rmse_ww),model=c("Forward","Ridge","Lasso","RandomF"))


rsq_of_plots_rw<-data.frame(rsq_value=c(fit_fs_rsq_rw,fit_rd_rsq_rw,fit_ls_rsq_rw,fit_rf_rsq_rw),model=c("Forward","Ridge","Lasso","RandomF"))
rsq_of_plots_ww<-data.frame(rsq_value=c(fit_fs_rsq_ww,fit_rd_rsq_ww,fit_ls_rsq_ww,fit_rf_rsq_ww),model=c("Forward","Ridge","Lasso","RandomF"))

mae_of_plots_rw<-data.frame(mae_value=c(fit_fs_mae_rw,fit_rd_mae_rw,fit_ls_mae_rw,fit_rf_mae_rw),model=c("Forward","Ridge","Lasso","RandomF"))
mae_of_plots_ww<-data.frame(mae_value=c(fit_fs_mae_ww,fit_rd_mae_ww,fit_ls_mae_ww,fit_rf_mae_ww),model=c("Forward","Ridge","Lasso","RandomF"))

rmse_plot_rw<-ggplot(data=rmse_of_plots_rw)+
  geom_point(aes(x=model,y=rmse_value,color=model),size=3)+
  theme_minimal()+
  labs(x="Model",
       y="RMSE",
       title="RMSE of each model",
       subtitle="(Red wine)")+
   theme(plot.title = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                plot.subtitle = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                axis.title = element_text(color = "blue",
                                          face = "bold",
                                          size = 12),
                axis.text.x = element_text(hjust = 0.5,
                                          vjust = 0.5,
                                          color = "brown2",
                                          face = "bold",
                                          size = 10),
                axis.text.y = element_text(color = "brown2",
                                          face = "bold",
                                          size = 10),
                panel.border = element_rect(colour = "grey45",
                                          fill=NA, size=1),
         legend.position = "none")

rmse_plot_ww<-ggplot(data=rmse_of_plots_ww)+
  geom_point(aes(x=model,y=rmse_value,color=model),size=3)+
  theme_minimal()+
  labs(x="Model",
       y="RMSE",
       title="RMSE of each model",
       subtitle="(White wine)")+
   theme(plot.title = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                plot.subtitle = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                axis.title = element_text(color = "blue",
                                          face = "bold",
                                          size = 12),
                axis.text.x = element_text(hjust = 0.5,
                                          vjust = 0.5,
                                          color = "brown2",
                                          face = "bold",
                                          size = 10),
                axis.text.y = element_text(color = "brown2",
                                          face = "bold",
                                          size = 10),
                panel.border = element_rect(colour = "grey45",
                                          fill=NA, size=1),
         legend.position = "none")

rsq_plot_rw<-ggplot(data=rsq_of_plots_rw)+
  geom_point(aes(x=model,y=rsq_value,color=model),size=3)+
  theme_minimal()+
  labs(x="Model",
       y="RSquared Value",
       title="RSquared of each model",
       subtitle="(Red wine)")+
   theme(plot.title = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                plot.subtitle = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                axis.title = element_text(color = "blue",
                                          face = "bold",
                                          size = 12),
                axis.text.x = element_text(hjust = 0.5,
                                          vjust = 0.5,
                                          color = "brown2",
                                          face = "bold",
                                          size = 10),
                axis.text.y = element_text(color = "brown2",
                                          face = "bold",
                                          size = 10),
                panel.border = element_rect(colour = "grey45",
                                          fill=NA, size=1),
         legend.position = "none")

rsq_plot_ww<-ggplot(data=rsq_of_plots_ww)+
  geom_point(aes(x=model,y=rsq_value,color=model),size=3)+
  theme_minimal()+
  labs(x="Model",
       y="RSquared Value",
       title="RSquare of each model",
       subtitle="(White wine)")+
   theme(plot.title = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                plot.subtitle = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                axis.title = element_text(color = "blue",
                                          face = "bold",
                                          size = 12),
                axis.text.x = element_text(hjust = 0.5,
                                          vjust = 0.5,
                                          color = "brown2",
                                          face = "bold",
                                          size = 10),
                axis.text.y = element_text(color = "brown2",
                                          face = "bold",
                                          size = 10),
                panel.border = element_rect(colour = "grey45",
                                          fill=NA, size=1),
         legend.position = "none")

mae_plot_rw<-ggplot(data=mae_of_plots_rw)+
  geom_point(aes(x=model,y=mae_value,color=model),size=3)+
  theme_minimal()+
  labs(x="Model",
       y="MAE",
       title="MAE of each model",
       subtitle="(Red wine)")+
   theme(plot.title = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                plot.subtitle = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                axis.title = element_text(color = "blue",
                                          face = "bold",
                                          size = 12),
                axis.text.x = element_text(hjust = 0.5,
                                          vjust = 0.5,
                                          color = "brown2",
                                          face = "bold",
                                          size = 10),
                axis.text.y = element_text(color = "brown2",
                                          face = "bold",
                                          size = 10),
                panel.border = element_rect(colour = "grey45",
                                          fill=NA, size=1),
         legend.position = "none")

mae_plot_ww<-ggplot(data=mae_of_plots_ww)+
  geom_point(aes(x=model,y=mae_value,color=model),size=3)+
  theme_minimal()+
  labs(x="Model",
       y="MAE",
       title="MAE of each model",
       subtitle="(White wine)")+
   theme(plot.title = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                plot.subtitle = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                axis.title = element_text(color = "blue",
                                          face = "bold",
                                          size = 12),
                axis.text.x = element_text(hjust = 0.5,
                                          vjust = 0.5,
                                          color = "brown2",
                                          face = "bold",
                                          size = 10),
                axis.text.y = element_text(color = "brown2",
                                          face = "bold",
                                          size = 10),
                panel.border = element_rect(colour = "grey45",
                                          fill=NA, size=1),
         legend.position = "none")


grid.arrange(rmse_plot_rw,rmse_plot_ww,nrow = 1)
grid.arrange(mae_plot_rw,mae_plot_ww,nrow = 1)
grid.arrange(rsq_plot_rw,rsq_plot_ww,nrow = 1)
```

```{r}

red_rf_results<-ggplot(data=rf_rw_results)+
  geom_point(aes(x=real,y=prediction,color=factor(real)))+
  theme_minimal()+
  labs(x="Real Quality",
       y="Predicted Quality Values",
       title="Real Vs Predicted Response Variable",
       subtitle="(Red wine)")+
   theme(plot.title = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                plot.subtitle = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                axis.title = element_text(color = "blue",
                                          face = "bold",
                                          size = 12),
                axis.text.x = element_text(hjust = 0.5,
                                          vjust = 0.5,
                                          color = "brown2",
                                          face = "bold",
                                          size = 10),
                axis.text.y = element_text(color = "brown2",
                                          face = "bold",
                                          size = 10),
                panel.border = element_rect(colour = "grey45",
                                          fill=NA, size=1),
         legend.position = "none")


white_rf_results<-ggplot(data=rf_ww_results)+
  geom_point(aes(x=real,y=prediction,color=factor(real)))+
  theme_minimal()+
  labs(x="Real Quality",
       y="Predicted Quality Values",
       title="Real Vs Predicted Response Variable",
       subtitle="(White wine)")+
   theme(plot.title = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                plot.subtitle = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
                axis.title = element_text(color = "blue",
                                          face = "bold",
                                          size = 12),
                axis.text.x = element_text(hjust = 0.5,
                                          vjust = 0.5,
                                          color = "brown2",
                                          face = "bold",
                                          size = 10),
                axis.text.y = element_text(color = "brown2",
                                          face = "bold",
                                          size = 10),
                panel.border = element_rect(colour = "grey45",
                                          fill=NA, size=1),
         legend.position = "none")

grid.arrange(red_rf_results,white_rf_results,nrow=1)

```


```{r fig.width= 8, fig.height=8}

red_rf_plot<-ggplot(data=rf_rw_results)+
  geom_histogram(aes(x= prediction,fill=factor(real)))+
  facet_wrap(~ factor(real),  scales="free")+
  theme_minimal()+
  labs(x="Predicted Quality",
       title="Real Vs Predicted Response Variable",
       subtitle="(Red wine)")+
   theme(plot.title = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
          plot.subtitle = element_text(hjust = 0.5,
                                    color = "darkgreen", 
                                    face = "bold"),
          axis.title = element_text(color = "blue",
                                    face = "bold",
                                    size = 12),
          axis.text.x = element_text(hjust = 0.5,
                                    vjust = 0.5,
                                    color = "brown2",
                                    face = "bold",
                                    size = 10),
          axis.text.y = element_text(color = "brown2",
                                    face = "bold",
                                    size = 10),
          panel.border = element_rect(colour = "grey45",
                                    fill=NA, size=1),
         strip.background = element_rect(fill = "lightgrey"),
         strip.text = element_text(color = "black", face = "bold"),
         legend.position = "none")

white_rf_plot<-ggplot(data=rf_ww_results)+
  geom_histogram(aes(x= prediction,fill=factor(real)))+
  facet_wrap(~ factor(real),  scales="free")+
  theme_minimal()+
  labs(x="Predicted Quality",
       title="Real Vs Predicted Response Variable",
       subtitle="(white wine)")+
   theme(plot.title = element_text(hjust = 0.5,
                                          color = "darkgreen", 
                                          face = "bold"),
          plot.subtitle = element_text(hjust = 0.5,
                                    color = "darkgreen", 
                                    face = "bold"),
          axis.title = element_text(color = "blue",
                                    face = "bold",
                                    size = 12),
          axis.text.x = element_text(hjust = 0.5,
                                    vjust = 0.5,
                                    color = "brown2",
                                    face = "bold",
                                    size = 10),
          axis.text.y = element_text(color = "brown2",
                                    face = "bold",
                                    size = 10),
          panel.border = element_rect(colour = "grey45",
                                    fill=NA, size=1),
         strip.background = element_rect(fill = "lightgrey"),
         strip.text = element_text(color = "black", face = "bold"),
         legend.position = "none")

grid.arrange(red_rf_plot, white_rf_plot, nrow = 2)

```