HomeWork1.Rmd

---
title: "HW1"
output: pdf_document
date: "`r Sys.Date()`"
---

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

## R Markdown

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##Load Packages
```{r loadPackages, warning=FALSE, message=FALSE, results='hide'}
if (!require("pacman")) install.packages("pacman")
pacman::p_load(tidyverse,reshape,ggplots,ggmap,
               mblench,data.table)
search()
theme_set(theme_classic())
```

## Read unitlies data

```{r readData}
#read in Utilities.csv
utilities.df <- fread("Utilities.csv")
str(utilities.df)

#data.table
utilities.dt <- setDT(utilities.df)
str(utilities.dt)
summary(utilities.dt)
```


### 1) min,max,mean,median,std deviation

```{r question1}

class(utilities.dt[,Fuel_Cost])

#get numeric dat table
numeric.utilities.dt <- utilities.dt[, !c("Company")]

#Mean of all columns
numeric.utilities.dt[, lapply(.SD, mean)]

#standard deviation of all varibales
numeric.utilities.dt[, lapply(.SD, sd)]

#min of all varibales
numeric.utilities.dt[, lapply(.SD, min)]

#max of all varibales
numeric.utilities.dt[, lapply(.SD, max)]

#median of all variables
numeric.utilities.dt[, lapply(.SD, median)]

# Compute Statistics - mean, standard dev, min, max, median of Fixed_charge
numeric.utilities.dt[,.(mean=mean(Fixed_charge),sd=sd(Fixed_charge),minimum=min(Fixed_charge)
                ,maximum=max(Fixed_charge),median=median(Fixed_charge),length=length(Fixed_charge))]


# Compute Statistics - mean, standard dev, min, max, median of RoR
utilities.dt[,.(mean=mean(RoR),sd=sd(RoR),minimum=min(RoR)
                ,maximum=max(RoR),median=median(RoR),length=length(RoR))]

# Compute Statistics - mean, standard dev, min, max, median of Cost
utilities.dt[,.(mean=mean(Cost),sd=sd(Cost),minimum=min(Cost)
                ,maximum=max(Cost),median=median(Cost),length=length(Cost))]

# Compute Statistics - mean, standard dev, min, max, median of load_factor
utilities.dt[,.(mean=mean(Load_factor),sd=sd(Load_factor),minimum=min(Load_factor)
                ,maximum=max(Load_factor),median=median(Load_factor),length=length(Load_factor))]

# Compute Statistics - mean, standard dev, min, max, median of demand_growth
utilities.dt[,.(mean=mean(Demand_growth),sd=sd(Demand_growth),minimum=min(Demand_growth)
                ,maximum=max(Demand_growth),median=median(Demand_growth),length=length(Demand_growth))]

# Compute Statistics - mean, standard dev, min, max, median of Sales
utilities.dt[,.(mean=mean(Sales),sd=sd(Sales),minimum=min(Sales)
                ,maximum=max(Sales),median=median(Sales),length=length(Sales))]


# Compute Statistics - mean, standard dev, min, max, median of Nuclear
utilities.dt[,.(mean=mean(Nuclear),sd=sd(Nuclear),minimum=min(Nuclear)
                ,maximum=max(Nuclear),median=median(Nuclear),length=length(Nuclear))]


# Compute Statistics - mean, standard dev, min, max, median of Fuel_cost
utilities.dt[,.(mean=mean(Fuel_Cost),sd=sd(Fuel_Cost),minimum=min(Fuel_Cost)
                ,maximum=max(Fuel_Cost),median=median(Fuel_Cost),length=length(Fuel_Cost))]


print("Sales has the largest variability. The values in Sales variable are more spread apart which can be depicted from Satandard Deviation(s=3549.984)")
```

##Boxplots for each numeric varibales
```{r BoxPlots}
#Boxplot for Fixed Charge
ggplot(utilities.dt)+
  geom_boxplot(aes(x="",y=Fixed_charge), fill="gold1", outlier.colour = "firebrick2")+
  ylab("Fixed Charge income/debt") + ggtitle("Fixed Charge Boxplot")

#utilities.dt[, sum(!is.na(Fixed_charge))]

#Boxplot for Rate of return
ggplot(utilities.dt)+
  geom_boxplot(aes(x="",y=RoR), fill="gold2", outlier.colour = "firebrick2")+
  ylab("Rate of Return") + ggtitle("Rate of Return Boxplot")

#Boxplot for Cost per kilowatt
ggplot(utilities.dt)+
  geom_boxplot(aes(x="",y=Cost), fill="gold3", outlier.colour = "firebrick2")+
  ylab("Cost/kilowatt") + ggtitle("Cost Boxplot")

#boxplot for Anual Load Factor
ggplot(utilities.dt)+
  geom_boxplot(aes(x="",y=Load_factor), fill="gold4", outlier.colour = "firebrick2")+
  ylab("Load Factor") + ggtitle("Load Factor Boxplot")

#bocplot for peak kilowatthour demand growth from 1974 to 1975
ggplot(utilities.dt)+
  geom_boxplot(aes(x="",y=Demand_growth), fill="gold1", outlier.colour = "firebrick2")+
  ylab("Demand Growth") + ggtitle("Peak Kilowatt Hour Demand Growth Boxplot")

#boxplot for sales (kilowatthour use per year)
ggplot(utilities.dt)+
  geom_boxplot(aes(x="",y=Sales), fill="gold2", outlier.colour = "firebrick2")+
  ylab("Sales Kilowatthour/year") + ggtitle("Sales Boxplot")

#utilities.dt[, sum(is.na(Sales))]

#boxplot for percent nuclear
ggplot(utilities.dt)+
  geom_boxplot(aes(x="",y=Nuclear), fill="gold3", outlier.colour = "firebrick2")+
  ylab("Percent Nuclear") + ggtitle("Nuclear Boxplot")

#boxplot for total fuel costs (cents per kilowatthour)
ggplot(utilities.dt)+
  geom_boxplot(aes(x="",y=Fuel_Cost), fill="gold4", outlier.colour = "firebrick2")+
  ylab("Fuel Cost cents/kilowatthour") + ggtitle("Fuel Cost Boxplot")

print("Yes there are extreme values. The Varibale Fixed_charge and Sales has outliers which is highlighted in firebrick color.")

```


#Heatmap for numeric variables
```{r heatmap}
#heatmap(utilities.dt$Cost , Rowv = NULL, Colv = NULL)
heatmap(cor(utilities.dt[,!c("Company")]), Rowv = NA, Colv = NA)

num.utilities.df <- utilities.df[, !c("Company")]
round(cor(num.utilities.df),2)

heatmap.2(cor(num.utilities.df), dendrogram = "none", 
          cellnote = round(cor(num.utilities.df),2), notecol = "navy", 
          key = FALSE, trace = "none")

print("Fixed_charge & RoR have positive correlation i.e higher the Fixed-charge higher the Rate of return. Sales & Fuel_Cost have high negative correlation.")

# heatmap using ggplot
# using reshape package to to generate input for the plot 
#library(reshape)
#cor.mat <- round(cor(utilities.dt[,!c("Company")]),2) # rounded correlation matrix 
#melted.cor.mat <- melt(cor.mat) 
#ggplot(data=melted.cor.mat) + 
  #scale_fill_gradient(low="wheat", high="orangered") +
  #geom_tile( aes(x = Cost, y = RoR, fill = value)) + 
  #geom_text(aes(x = X1,y = X2, label = value)) +
  #ggtitle("Which Variables Are Highly Correlated?")


```

### Principal Component Analysis using Unscaled Data
```{r PCA, warning=FALSE}

  ### compute PCs on two dimensions
pcs <- prcomp(data.frame(utilities.df$Fixed_charge, utilities.df$RoR)) 
pcs
summary(pcs) 
pcs$rot # rotation matrix
scores <- pcs$x
head(scores, 5)

  ### PCA on 13 variables
pcs13 <- prcomp(na.omit(utilities.df[,-c("Company")])) 
pcs13
summary(pcs13)
pcs13$rot

print("PC1 covers maximum proportion of variance i.e. 99%. The firs two componets accounts for 99% of the total variance. Hence using 2 components in the model may be suffiecient.")
```

## Principal Component Analysis after scaling numeric data
```{r PCA}
  ### PCA using Normalized variables
pcs.cor <- prcomp(na.omit(utilities.df[,-c("Company")]), scale. = T)
summary(pcs.cor)
pcs.cor$rot
print("The weights of the normalised components changed. For example Sales had the higest vakue before normalising and after normalising the value increaded to prositive in 1st component.")

install.packages("tinytex")
tinytex::install_tinytex()
```


Note that the `echo = FALSE` parameter was added to the code chunk to prevent printing of the R code that generated the plot.