HW3_Group9_1031.Rmd

---
title: "Assignment3"
author: "Group 9"
date: '`r format(Sys.Date(), "%Y-%B-%d")`'
editor_options: 
  chunk_output_type: inline
output: pdf_document
---

## Load MASS Package
```{r loadpackages, message=FALSE, warning=FALSE}
knitr::opts_chunk$set(echo = TRUE)
if(!require("data.table")) install.packages("data.table", repos = "http://cran.us.r-project.org")
if(!require("rmarkdown")) install.packages("rmarkdown", repos = "http://cran.us.r-project.org")
if(!require("latexpdf")) install.packages("latexpdf", repos = "http://cran.us.r-project.org")
if(!require("knitr")) install.packages("knitr", repos = "http://cran.us.r-project.org")
if(!require("Rtools")) install.packages("Rtools", repos = "http://cran.us.r-project.org")
if(!require("caret")) install.packages("caret", repos = "http://cran.us.r-project.org")
if(!require("MASS")) install.packages("MASS", repos = "http://cran.us.r-project.org")
if(!require("gains")) install.packages("gains", repos = "http://cran.us.r-project.org")
if(!require("ggplot2")) install.packages("ggplot2", repos = "http://cran.us.r-project.org")
if(!require("e1071")) install.packages("e1071", repos = "http://cran.us.r-project.org")
if(!require("mlr")) install.packages("e1071", repos = "http://cran.us.r-project.org")
if(!require("gains")) install.packages("e1071", repos = "http://cran.us.r-project.org")

library("data.table")
library("rmarkdown")
library("latexpdf")
library("knitr")
library("caret")
library("MASS")
library("gains")
library("ggplot2")
library("e1071")
library("mlr")
library("gains")

```

#Load input file
```{r readdata from Website}
#Read in from UCI Site
spam_df <- read.csv(url("https://archive.ics.uci.edu/ml/machine-learning-databases/spambase/spambase.data"), header = FALSE)

#Rename Columns
colnames(spam_df)<- c("word_freq_make","word_freq_address","word_freq_all","word_freq_3d","word_freq_our","word_freq_over","word_freq_remove","word_freq_internet","word_freq_order","word_freq_mail","word_freq_receive","word_freq_will","word_freq_people","word_freq_report","word_freq_addresses","word_freq_free","word_freq_business","word_freq_email","word_freq_you","word_freq_credit","word_freq_your","word_freq_font","word_freq_000","word_freq_money","word_freq_hp","word_freq_hpl","word_freq_george","word_freq_650","word_freq_lab","word_freq_labs","word_freq_telnet","word_freq_857","word_freq_data","word_freq_415","word_freq_85","word_freq_technology","word_freq_1999","word_freq_parts","word_freq_pm","word_freq_direct","word_freq_cs","word_freq_meeting","word_freq_original","word_freq_project","word_freq_re","word_freq_edu","word_freq_table","word_freq_conference","char_freq_;","char_freq_(","char_freq_[","char_freq_!","char_freq_$","char_freq_#","capital_run_length_average","capital_run_length_longest","capital_run_length_total","s_ns_class")

#Print Table of Spam Values
table(spam_df$s_ns_class)
##spam_df$s_ns_class<-as.character(spam_df$s_ns_class)
#View Entire Dataset as a DT
spam_dt<- setDT(spam_df)
spam_dt

```
##
```{r Question 1}

#Filter by Spam Classification

yes_spam <- spam_dt[which(spam_dt$s_ns_class==1),1:57]
not_spam <- spam_dt[which(spam_dt$s_ns_class == 0),1:57]

#Column Averages

avg_yes_spam <- colMeans(yes_spam)
avg_not_spam <- colMeans(not_spam)

#Difference Between Averages
avg_diff_spam <- abs(avg_yes_spam - avg_not_spam)
print("Differences between Spam and Not Spam Averages")
avg_diff_spam
top_diff_spam <- sort.list(avg_diff_spam, decreasing = TRUE)
print("The Differences Listed from High to Low")
top_diff_spam
print("The most different averages(excluding Spam Class) are: 57, 56, 55, 27, 19, 21, 25, 16, 26, 52")
print("1: Capital Run Length Total")
print("2: Capital Run Length Longest")
print("3: Capital Run Length Average")
print("4: Word Frequency George")
print("5: Word Frequency You")
print("6: Word Frequency Your")
print("7: Word Frequency HP")
print("8: Word Frequency Free")
print("9: Word Frequency HPL")
print("10: Char Frequency !")

#Create Set with Just Predictors
spam_final <- spam_dt[ , c(58, 57, 56, 55, 27, 19, 21, 25, 16, 26, 52)]



```

```{r Question 2}
# Split the data into training (80%) and validation/test set (20%)
set.seed(42)

# randomly order the dataset
rows <- sample(nrow(spam_final))
spam_final<- spam_final[rows, ]

# find rows to split on
spam_split <- round(nrow(spam_final) * 0.8)
a<-spam_split+1
b<-nrow(spam_final)
spam_training <- spam_final[1:spam_split, ]
##spam_validation <- spam_final[(split+1):nrow(spam_final), ]
spam_validation <- spam_final[a:b, ]



# Normalize the data
    # Estimate preprocessing parameters
norm_values  <- preProcess(spam_training[, -c(1)], method = c("center", "scale"))
norm_values
    # Transform the data using the estimated parameters
spam_train_norm <- predict(norm_values, spam_training)
spam_valid_norm <- predict(norm_values, spam_validation)


spam_lda <- lda(s_ns_class~., spam_train_norm)
spam_lda

#What are the prior probabilities?
print("Question 3")
print("The prior probabilities are 0.604 for No Spam and 0.396 for Yes Spam")

#What are the coefficients of linear discriminants?
print("Question 4")
print("The Coefficients of the Linear Discriminants are shown above.
These are used to classify items in the data set by multiplying the
associated variable by the coefficient and then summing them up.")

#How are linear discriminants used in classifying spams and non-spams?
print("Question 5")
print("Linear discriminants are used to maximize separation between groups and to minimize the variation within groups")

#How many LDs are there and why?
print("Question 6")
print("There is one LD and this is because there are only two classes or groups we're trying to separate")
```

```{r Question 7 LDA Plots}
lda_train <- lda(s_ns_class~., data = spam_train_norm)
plot (lda_train)

lda_valid <- lda(s_ns_class~., data = spam_valid_norm)
plot (lda_valid)

print("Question 7")
print("Both graphs show pretty good separation between the two groups as indicated by the spread of the data above and below the 0 marking.")
```


```{r Confusion Matrix}

#Prediction Using Training Data

pred_1_train <- predict(spam_lda,spam_train_norm)

pred_2_valid <- predict(spam_lda,spam_valid_norm)


#Confusion Matrix
print("Question8: Generate the Relevant Confusion Matrix. What are the sensitivity and specificity.")

spam_matrix <- table(pred_2_valid$class, spam_valid_norm$s_ns_class)
confusionMatrix(spam_matrix)

print("You can see the accuracy is 82 percentage while sensitivity is .9277 and specificity is .6676")

```

```{r Lift and Decile Chart}

print("question 9: Generate Lift and Decile Chart")

## Lift Charts
gain <- gains(spam_validation$s_ns_class,pred_2_valid$posterior[,2],groups=dim(spam_validation)[1])
plot(c(0, gain$cume.pct.of.total*sum(spam_validation$s_ns_class)) ~ c(0, gain$cume.obs), 
     xlab = "# cases", ylab = "Cumulative", type="l",
     col="blue1")
#lines(c(0,sum(spam_validation$s_ns_class))~c(0,dim(spam_validation$s_ns_class)[1]), col="red1", lty=2)


## Decile Lift Charts
gain <- gains(spam_validation$s_ns_class,pred_2_valid$posterior[,2])
gain
barplot(gain$mean.resp / mean(spam_validation$s_ns_class), names.arg = gain$depth, xlab = "Percentile", space = 1.3,
        ylab = "Mean Response", main = "Decile-wise lift chart", col = "seagreen", border = NA)

print("The Model is showing staircase effect and is able to caputure maximum responses in the initial 30%. We're looking for in a good model.")
```


```{r Question 10 Lowered Threshold}
sum(pred_2_valid$posterior[,1] >= 0.5)

sum(pred_2_valid$posterior[,1] >= 0.2)

spam_matrix <- table(pred_2_valid$class, spam_valid_norm$s_ns_class)
confusionMatrix(spam_matrix, threshold=0.2)

print("Question 10")
print("As you lower the threshold the amount of items that are predicted to be spam increase. Which means the model is more inaccurate. This is not inherently good or bad as that's situational and dependent on whether you'd rather be extremely risk-averse to spam or not.")
print("Accuracy is 82 percentage. Lowering the thereshold doesnt have any impact on the accuracy.")
```