Data-Analyst-Nanodegree/P4 - Exploratory Data Analysis/Red_Wine_Quality.R

#' What Makes A Good Wine?
#' ========================================================
#'
#' In this project, a data set of red wine quality is explored based on its
#' physicochemical properties. The objective is to find physicochemical properties
#' that distinguish good quality wine from lower quality ones. An attempt to build
#' linear model on wine quality is also shown.
#'
#' ### Dataset Description
#' This tidy dataset contains 1,599 red wines with 11 variables on the chemical
#' properties of the wine. Another variable attributing to the quality of wine is
#' added; at least 3 wine experts did this rating. The preparation of the dataset
#' has been described in [this link](https://goo.gl/HVxAzY).
#'
## ----global_options, include=FALSE---------------------------------------
knitr::opts_chunk$set(fig.path='Figs/',
                      echo=FALSE, warning=FALSE, message=FALSE)

#'
## ----echo=FALSE, message=FALSE, warning=FALSE, packages------------------
library(ggplot2)
library(gridExtra)
library(GGally)
library(ggthemes)
library(dplyr)
library(memisc)

#'
#' First, the structure of the dataset is explored using ``summary`` and ``str``
#' functions.
## ----echo=FALSE, warning=FALSE, message=FALSE, Load_the_Data-------------
wine <- read.csv("wineQualityReds.csv")
str(wine)
summary(wine)

# Setting the theme for plotting.
# theme_set(theme_minimal(10))

# Converting 'quality' to ordered type.
wine$quality <- ordered(wine$quality,
                        levels=c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10))
# Adding 'total.acidity'.
wine$total.acidity <- wine$fixed.acidity + wine$volatile.acidity

#'
#' **The following observations are made/confirmed:**
#'
#' 1. There are 1599 samples of Red Wine properties and quality values.
#'
#' 2. No wine achieves either a terrible (0) or perfect (10) quality score.
#'
#' 3. Citric Acid had a minimum of 0.0. No other property values were precisely 0.
#'
#' 4. Residual Sugar measurement has a maximum that is nearly 20 times farther
#' away from the 3rd quartile than the 3rd quartile is from the 1st. There is
#' a chance of a largely skewed data or that the data has some outliers.
#'
#' 5. The 'quality' attribute is originally considered an integer;
#' I have converted this field into an ordered factor which is much more
#' a representative of the variable itself.
#'
#' 6. There are two attributes related to 'acidity' of wine i.e. 'fixed.acidity'
#' and 'volatile.acidity'. Hence, a combined acidity variable is added
#' using ``data$total.acidity <- data$fixed.acidity + data$volatile.acidity``.
#'
#' ## Univariate Plots Section
#' To lead the univariate analysis, I’ve chosen to build a grid of histograms.
#' These histograms represent the distributions of each variable in the dataset.
#'
## ----echo=FALSE, warning=FALSE, message=FALSE, Univariate_Grid_Plot------
g_base <- ggplot(
  data = wine,
  aes(color=I('black'), fill=I('#990000'))
)

g1 <- g_base +
  geom_histogram(aes(x = fixed.acidity), binwidth = 0.25) +
  scale_x_continuous(breaks = seq(4, 16, 2)) +
  coord_cartesian(xlim = c(4, 16))

g2 <- g_base +
  geom_histogram(aes(x = volatile.acidity), binwidth = 0.05) +
  scale_x_continuous(breaks = seq(0, 2, 0.5)) +
  coord_cartesian(xlim = c(0, 2))

g3 <- g_base +
  geom_histogram(aes(x = total.acidity), binwidth = 0.25) +
  scale_x_continuous(breaks = seq(0, 18, 1)) +
  coord_cartesian(xlim = c(4, 18))

g4 <- g_base +
  geom_histogram(aes(x = citric.acid), binwidth = 0.05) +
  scale_x_continuous(breaks = seq(0, 1, 0.2)) +
  coord_cartesian(xlim = c(0, 1))

g5 <- g_base +
  geom_histogram(aes(x = residual.sugar), binwidth = 0.5) +
  scale_x_continuous(breaks = seq(0, 16, 2)) +
  coord_cartesian(xlim = c(0, 16))

g6 <- g_base +
  geom_histogram(aes(x = chlorides), binwidth = 0.01) +
  scale_x_continuous(breaks = seq(0, 0.75, 0.25)) +
  coord_cartesian(xlim = c(0, 0.75))

g7 <- g_base +
  geom_histogram(aes(x = free.sulfur.dioxide), binwidth = 2.5) +
  scale_x_continuous(breaks = seq(0, 75, 25)) +
  coord_cartesian(xlim = c(0, 75))

g8 <- g_base +
  geom_histogram(aes(x = total.sulfur.dioxide), binwidth = 10) +
  scale_x_continuous(breaks = seq(0, 300, 100)) +
  coord_cartesian(xlim = c(0, 295))

g9 <- g_base +
  geom_histogram(aes(x = density), binwidth = 0.0005) +
  scale_x_continuous(breaks = seq(0.99, 1.005, 0.005)) +
  coord_cartesian(xlim = c(0.99, 1.005))

g10 <- g_base +
  geom_histogram(aes(x = pH), binwidth = 0.05) +
  scale_x_continuous(breaks = seq(2.5, 4.5, 0.5)) +
  coord_cartesian(xlim = c(2.5, 4.5))

g11 <- g_base +
  geom_histogram(aes(x = sulphates), binwidth = 0.05) +
  scale_x_continuous(breaks = seq(0, 2, 0.5)) +
  coord_cartesian(xlim = c(0, 2))

g12 <- g_base +
  geom_histogram(aes(x = alcohol), binwidth = 0.25) +
  scale_x_continuous(breaks = seq(8, 15, 2)) +
  coord_cartesian(xlim = c(8, 15))

grid.arrange(g1, g2, g3, g4, g5, g6,
             g7, g8, g9, g10, g11, g12, ncol=3)

#'
#' There are some really interesting variations in the distributions here. Looking
#' closer at a few of the more interesting ones might prove quite valuable.
#' Working from top-left to right, selected plots are analysed.
#'
## ----echo=FALSE, warning=FALSE, message=FALSE, single_variable_hist------
base_hist <- ggplot(
  data = wine,
  aes(color=I('black'), fill=I('#990000'))
)

#'
#' ### Acidity
## ----echo=FALSE, acidity_plot--------------------------------------------
ac1 <- base_hist +
  geom_histogram(aes(x = fixed.acidity), binwidth = 0.25) +
  scale_x_continuous(breaks = seq(4, 16, 2)) +
  coord_cartesian(xlim = c(4, 16))

ac2 <- base_hist +
  geom_histogram(aes(x = volatile.acidity), binwidth = 0.05) +
  scale_x_continuous(breaks = seq(0, 2, 0.5)) +
  coord_cartesian(xlim = c(0, 2))

grid.arrange(ac1, ac2, nrow=2)

#'
#' **Fixed acidity** is determined by aids that do not evaporate easily --
#' tartaricacid. It contributes to many other attributes, including the taste, pH,
#' color, and stability to oxidation, i.e., prevent the wine from tasting flat.
#' On theother hand, **volatile acidity** is responsible for the sour taste in
#' wine. A very high value can lead to sour tasting wine, a low value can make
#' the wine seem heavy.
#' (References: [1](http://waterhouse.ucdavis.edu/whats-in-wine/fixed-acidity),
#' [2](http://waterhouse.ucdavis.edu/whats-in-wine/volatile-acidity).
#'
## ----echo=FALSE, warning=FALSE, message=FALSE, acidity_univariate--------
ac1 <- base_hist +
  geom_histogram(aes(x = fixed.acidity), binwidth = 0.25) +
  scale_x_continuous(breaks = seq(4, 16, 2)) +
  coord_cartesian(xlim = c(4, 16))

ac2 <- base_hist +
  geom_histogram(aes(x = volatile.acidity), binwidth = 0.05) +
  scale_x_continuous(breaks = seq(0, 2, 0.5)) +
  coord_cartesian(xlim = c(0, 2))

ac3 <- base_hist +
  geom_histogram(aes(x = total.acidity), binwidth = 0.25) +
  scale_x_continuous(breaks = seq(0, 18, 2)) +
  coord_cartesian(xlim = c(0, 18))

grid.arrange(ac1, ac2, ac3, nrow=3)

print("Summary statistics of Fixed Acidity")
summary(wine$fixed.acidity)
print("Summary statistics of Volatile Acidity")
summary(wine$volatile.acidity)
print("Summary statistics of Total Acidity")
summary(wine$total.acidity)

#'
#' Of the wines we have in our dataset, we can see that most have a fixed acidity
#' of 7.5. The median fixed acidity is 7.9, and the mean is 8.32. There is a
#' slight skew in the data because a few wines possess a very high fixed acidity.
#' The median volatile acidity is 0.52 g/dm^3, and the mean is 0.5278 g/dm^3. *It
#' will be interesting to note which quality of wine is correlated to what level
#' of acidity in the bivariate section.*
#'
#' ### Citric Acid
#' Citric acid is part of the fixed acid content of most wines. A non-volatile
#' acid, citric also adds much of the same characteristics as tartaric acid does.
#' Again, here I would guess most good wines have a balanced amount of citric
#' acid.
#'
## ----echo=FALSE, warning=FALSE, message=FALSE, citric_acid_univariate----
base_hist +
  geom_histogram(aes(x = citric.acid), binwidth = 0.05) +
  scale_x_continuous(breaks = seq(0, 1, 0.2)) +
  coord_cartesian(xlim = c(0, 1))

print("Summary statistics of Citric Acid")
summary(wine$citric.acid)
print('Number of Zero Values')
table(wine$citric.acid == 0)

#'
#' There is a very high count of zero in citric acid. To check if this is
#' genuinely zero or merely a ‘not available’ value. A quick check using table
#' function shows that there are 132 observations of zero values and no NA value
#' in reported citric acid concentration. The citric acid concentration could be
#' too low and insignificant hence was reported as zero.
#'
#' As far as content wise the wines have a median citric acid level of
#' 0.26 g/dm^3, and a mean level of 0.271 g/dm^3.
#'
#' ### Sulfur-Dioxide & Sulphates
#' **Free sulfur dioxide** is the free form of SO2 exists in equilibrium between
#' molecular SO2 (as a dissolved gas) and bisulfite ion; it prevents microbial
#' growth and the oxidation of wine. **Sulphates** is a wine additive which can
#' contribute to sulfur dioxide gas (SO2) levels, which acts as an anti-microbial
#' moreover, antioxidant -- *overall keeping the wine, fresh*.
#'
## ----echo=FALSE, warning=FALSE, message=FALSE, sulfur_univariate---------
sul1 <- base_hist + geom_histogram(aes(x = free.sulfur.dioxide))
sul2 <- base_hist + geom_histogram(aes(x = log10(free.sulfur.dioxide)))

sul3 <- base_hist + geom_histogram(aes(x = total.sulfur.dioxide))
sul4 <- base_hist + geom_histogram(aes(x = log10(total.sulfur.dioxide)))

sul5 <- base_hist + geom_histogram(aes(x = sulphates))
sul6 <- base_hist + geom_histogram(aes(x = log10(sulphates)))

grid.arrange(sul1, sul2, sul3, sul4, sul5, sul6, nrow=3)

#'
#' The distributions of all three values are positively skewed with a long tail.
#' Thelog-transformation results in a normal-behaving distribution for 'total
#' sulfur dioxide' and 'sulphates'.
#'
#' ### Alcohol
#' Alcohol is what adds that special something that turns rotten grape juice
#' into a drink many people love. Hence, by intuitive understanding, it should
#' be crucial in determining the wine quality.
#'
## ----echo=FALSE, warning=FALSE, message=FALSE, alcohol_univariate--------
base_hist +
  geom_histogram(aes(x = alcohol), binwidth = 0.25) +
  scale_x_continuous(breaks = seq(8, 15, 2)) +
  coord_cartesian(xlim = c(8, 15))

print("Summary statistics for alcohol %age.")
summary(wine$alcohol)

#'
#' The mean alcohol content for our wines is 10.42%, the median is 10.2%
#'
#' ### Quality
## ----echo=FALSE,warning=FALSE, message=FALSE, quality_univariate---------
qplot(x=quality, data=wine, geom='bar',
      fill=I("#990000"),
      col=I("black"))

print("Summary statistics - Wine Quality.")
summary(wine$quality)

#'
#' Overall wine quality, rated on a scale from 1 to 10, has a normal shape and
#' very few exceptionally high or low-quality ratings.
#'
#' It can be seen that the minimum rating is 3 and 8 is the maximum for quality.
#' Hence, a variable called ‘rating’ is created based on variable quality.
#'
#' * 8 to 7 are Rated A.
#'
#' * 6 to 5 are Rated B.
#'
#' * 3 to 4 are Rated C.
#'
## ----echo=FALSE, quality_rating------------------------------------------
# Dividing the quality into 3 rating levels
wine$rating <- ifelse(wine$quality < 5, 'C',
                      ifelse(wine$quality < 7, 'B', 'A'))

# Changing it into an ordered factor
wine$rating <- ordered(wine$rating,
                     levels = c('C', 'B', 'A'))

summary(wine$rating)

qr1 <- ggplot(aes(as.numeric(quality), fill=rating), data=wine) +
  geom_bar() +
  ggtitle ("Barchart of Quality with Rating") +
  scale_x_continuous(breaks=seq(3,8,1)) +
  xlab("Quality") +
  theme_pander() + scale_colour_few()

qr2 <- qplot(x=rating, data=wine, geom='bar',
      fill=I("#990000"),
      col=I("black")) +
  xlab("Rating") +
  ggtitle("Barchart of Rating") +
  theme_pander()

grid.arrange(qr1, qr2, ncol=2)

#'
#' The distribution of 'rating' is much higher on the 'B' rating wine as
#' seen in quality distribution. This is likely to cause overplotting. Therefore,
#' a comparison of only the 'C' and 'A' wines is done to find distinctive
#' properties that separate these two. The comparison is made using summary
#' statistics.
#'
## ----echo=FALSE, rating_comparison---------------------------------------
print("Summary statistics of Wine with Rating 'A'")
summary(subset(wine, rating=='A'))

print("Summary statistics of Wine with Rating 'C'")
summary(subset(wine, rating=='C'))

#'
#' On comparing the *mean statistic* of different attribute for 'A-rated' and
#' 'C-rated' wines (A → C), the following %age change is noted.
#'
#' 1. `fixed.acidity`: mean reduced by 11%.
#'
#' 2. `volatile.acidity` - mean increased by 80%.
#'
#' 3. `citric.acidity` - mean increased by 117%.
#'
#' 4. `sulphates` - mean reduced by 20.3%
#'
#' 5. `alcohol` - mean reduced by 12.7%.
#'
#' 6. `residualsugar` and `chloride` showed a very low variation.
#'
#' These changes are, however, only suitable for estimation of important quality
#' impacting variables and setting a way for further analysis. No conclusion
#' can be drawn from it.
#'
#' ## Univariate Analysis - Summary
#'
#' ### Overview
#' The red wine dataset features 1599 separate observations, each for a different
#' red wine sample. As presented, each wine sample is provided as a single row in
#' the dataset. Due to the nature of how some measurements are gathered, some
#' values given represent *components* of a measurement total.
#'
#' For example, `data.fixed.acidity` and `data.volatile.acidity` are both obtained
#' via separate measurement techniques, and must be summed to indicate the total
#' acidity present in a wine sample. For these cases, I supplemented the data
#' given by computing the total and storing in the data frame with a
#' `data.total.*` variable.
#'
#' ### Features of Interest
#' An interesting measurement here is the wine `quality`. It is the
#' subjective measurement of how attractive the wine might be to a consumer. The
#' goal here will is to try and correlate non-subjective wine properties with its
#' quality.
#'
#' I am curious about a few trends in particular --  **Sulphates vs. Quality** as
#' low sulphate wine has a reputation for not causing hangovers,
#' **Acidity vs. Quality** - Given that it impacts many factors like pH,
#' taste, color, it is compelling to see if it affects the quality.
#' **Alcohol vs. Quality** - Just an interesting measurement.
#'
#' At first, the lack of an *age* metric was surprising since it is commonly
#' a factor in quick assumptions of wine quality. However, since the actual effect
#' of wine age is on the wine's measurable chemical properties, its exclusion here
#' might not be necessary.
#'
#' ### Distributions
#'  Many measurements that were clustered close to zero had a positive skew
#' (you cannot have negative percentages or amounts). Others such as `pH` and
#' `total.acidity` and `quality` had normal looking distributions.
#'
#' The distributions studied in this section were primarily used to identify the
#' trends in variables present in the dataset. This helps in setting up a track
#' for moving towards bivariate and multivariate analysis.
#'
#' ## Bivariate Plots Section
#'
## ----echo=FALSE, message=FALSE, warning=FALSE, correlation_plots---------
ggcorr(wine,
       size = 2.2, hjust = 0.8,
       low = "#4682B4", mid = "white", high = "#E74C3C")

#'
#' **Observations from the correlation matrix.**
#'
#' * Total Acidity is highly correlatable with fixed acidity.
#'
#' * pH appears correlatable with acidity, citric acid, chlorides, and residual
#' sugars.
#'
#' * No single property appears to correlate with quality.
#'
#' Further, in this section, metrics of interest are evaluated to check their
#' significance on the wine quality. Moreover, bivariate relationships between
#' other variables are also studied.
#'
#' ### Acidity vs. Rating & Quality
#'
## ----echo=FALSE, message=FALSE, warning=FALSE, acidity_rating------------

aq1 <- ggplot(aes(x=rating, y=total.acidity), data = wine) +
  geom_boxplot(fill = '#ffeeee') +
  coord_cartesian(ylim=c(0, quantile(wine$total.acidity, 0.99))) +
  geom_point(stat='summary', fun.y=mean,color='red') +
  xlab('Rating') + ylab('Total Acidity')

aq2 <- ggplot(aes(x=quality, y=total.acidity), data = wine) +
  geom_boxplot(fill = '#ffeeee') +
  coord_cartesian(ylim=c(0, quantile(wine$total.acidity, 0.99))) +
  geom_point(stat='summary', fun.y=mean, color='red') +
  xlab('Quality') + ylab('Total Acidity') +
  geom_jitter(alpha=1/10, color='#990000') +
  ggtitle("\n")

grid.arrange(aq1, aq2, ncol=1)

#'
#' The boxplots depicting quality also depicts the distribution
#' of various wines, and we can again see 5 and 6 quality wines have the most
#' share. The blue dot is the mean, and the middle line shows the median.
#'
#' The box plots show how the acidity decreases as the quality of wine improve.
#' However, the difference is not very noticeable. Since most wines tend to
#' maintain a similar acidity level & given the fact that *volatile acidity* is
#' responsible for the sour taste in wine, hence a density plot of the said
#' attribute is plotted to investigate the data.
#'
## ----echo=FALSE, message=FALSE, warning=FALSE, acidity_quality_rating----
ggplot(aes(x = volatile.acidity, fill = quality, color = quality),
       data = wine) +
  geom_density(alpha=0.08)

#'
#' Red Wine of `quality` 7 and 8 have their peaks for `volatile.acidity` well
#' below the 0.4 mark. Wine with `quality` 3 has the pick at the most right
#' hand side (towards more volatile acidity). This shows that the better quality
#' wines are lesser sour and in general have lesser acidity.
#'
#' ### Alcohol vs. Quality
#'
## ----echo=FALSE, message=FALSE, warning=FALSE, alcohol_quality_sugar-----
qas0 <- ggplot(aes(x=alcohol, y=as.numeric(quality)), data=wine) +
  geom_jitter(alpha=1/12) +
  geom_smooth() +
  ggtitle("Alcohol Content vs. Quality") +
  ylab("Quality") + xlab("Alcohol")

qas1 <- ggplot(aes(x=alcohol), data=wine) +
  geom_density(fill=I("#BB0000")) +
  facet_wrap("quality") +
  ggtitle("Alcohol Content for \nWine Quality Ratings") +
  ylab("Density") + xlab("Alcohol")

qas2 <- ggplot(aes(x=residual.sugar, y=alcohol), data=wine) +
  geom_jitter(alpha=1/12) +
  geom_smooth() +
  ggtitle("Alcohol vs. Residual Sugar Content") +
  ylab("Alcohol") + xlab("Residual Sugar")

grid.arrange(qas1, arrangeGrob(qas0, qas2), ncol=2)

#'
#' The plot between residual sugar and alcohol content suggests that there is no
#' erratic relation between sugar and alcohol content, which is surprising as
#' alcohol is a byproduct of the yeast feeding off of sugar during the
#' fermentation process. That inference could not be established here.
#'
#' Alcohol and quality appear to be somewhat correlatable. Lower quality wines
#' tend to have lower alcohol content. This can be further studied using boxplots.
#'
## ----echo=FALSE, message=FALSE, warning=FALSE----------------------------

quality_groups <- group_by(wine, alcohol)

wine.quality_groups <- summarize(quality_groups,
                          acidity_mean = mean(volatile.acidity),
                          pH_mean = mean(pH),
                          sulphates_mean = mean(sulphates),
                          qmean = mean(as.numeric(quality)),
                          n = n())

wine.quality_groups <- arrange(wine.quality_groups, alcohol)

#'
## ----echo=FALSE, message=FALSE, warning=FALSE, alcohol_quality-----------
ggplot(aes(y=alcohol, x=factor(quality)), data = wine) +
  geom_boxplot(fill = '#ffeeee')+
  xlab('quality')

#'
#' The boxplots show an indication that higher quality wines have higher alcohol
#' content. This trend is shown by all the quality grades from 3 to 8 except
#' quality grade 5.
#'
#' **Does this mean that by adding more alcohol, we'd get better wine?**
#'
## ----echo=FALSE, message=FALSE, warning=FALSE----------------------------
ggplot(aes(alcohol, qmean), data=wine.quality_groups) +
  geom_smooth() +
  ylab("Quality Mean") +
  scale_x_continuous(breaks = seq(0, 15, 0.5)) +
  xlab("Alcohol %")

#'
#' The above line plot indicates nearly a linear increase till 13% alcohol
#' concetration, followed by a steep downwards trend. The graph has to be
#' smoothened to remove variances and noise.
#'
#' ### Sulphates vs. Quality
#'
## ----echo=FALSE, message=FALSE, warning=FALSE, sulphates_quality---------
ggplot(aes(y=sulphates, x=quality), data=wine) +
  geom_boxplot(fill="#ffeeee")

#'
#' Good wines have higher sulphates values than bad wines, though the difference
#' is not that wide.
#'
## ----echo=FALSE, message=FALSE, warning=FALSE, sulphates_qplots----------
sq1 <- ggplot(aes(x=sulphates, y=as.numeric(quality)), data=wine) +
  geom_jitter(alpha=1/10) +
  geom_smooth() +
  xlab("Sulphates") + ylab("Quality") +
  ggtitle("Sulphates vs. Quality")

sq2 <- ggplot(aes(x=sulphates, y=as.numeric(quality)),
              data=subset(wine, wine$sulphates < 1)) +
  geom_jitter(alpha=1/10) +
  geom_smooth() +
  xlab("Sulphates") + ylab("Quality") +
  ggtitle("\nSulphates vs Quality without Outliers")

grid.arrange(sq1, sq2, nrow = 2)

#'
#' There is a slight trend implying a relationship between sulphates and wine
#' quality, mainly if extreme sulphate values are ignored, i.e., because
#' disregarding measurements where sulphates > 1.0 is the same as disregarding
#' the positive tail of the distribution, keeping just the normal-looking portion.
#' However, the relationship is mathematically, still weak.
#'
#' ## Bivariate Analysis - Summary
#'
#' There is no apparent and mathematically strong correlation between any wine
#' property and the given quality. Alcohol content is a strong contender, but even
#' so, the correlation was not particularly strong.
#'
#' Most properties have roughly normal distributions, with some skew in one tail.
#' Scatterplot relationships between these properties often showed a slight trend
#' within the bulk of property values. However, as soon as we leave the
#' expected range, the trends reverse. For example, Alcohol Content or
#' Sulphate vs. Quality. The trend is not a definitive one, but it is seen in
#' different variables.
#'
#' Possibly, obtaining an outlier property (say sulphate content) is particularly
#' challenging to do in the wine making process. Alternatively, there is a change
#' that the wines that exhibit outlier properties are deliberately of a
#' non-standard variety. In that case, it could be that wine judges have a harder
#' time agreeing on a quality rating.
#'
#' ## Multivariate Plots Section
#'
#' This section includes visualizations that take bivariate analysis a step
#' further, i.e., understand the earlier patterns better or to strengthen the
#' arguments that were presented in the previous section.
#'
#' ### Alcohol, Volatile Acid & Wine Rating
#'
## ----echo=FALSE, message=FALSE, warning=FALSE, alcohol_acid_quality------
ggplot(wine, aes(x=alcohol, y=volatile.acidity, color=quality)) +
  geom_jitter(alpha=0.8, position = position_jitter()) +
  geom_smooth(method="lm", se = FALSE, size=1) +
  scale_color_brewer(type='seq',
                   guide=guide_legend(title='Quality')) +
  theme_pander()

#'
#' Earlier inspections suggested that the volatile acidity and alcohol had high
#' correlations values of negative and positive. Alcohol seems to vary more than
#' volatile acidity when we talk about quality, nearly every Rating A wine has
#' less than 0.6 volatile acidity.
#'
#' ### Understanding the Significance of Acidity
#'
## ----echo=FALSE, message=FALSE, warning=FALSE, acid_quality--------------
ggplot(subset(wine, rating=='A'|rating=='C'),
       aes(x=volatile.acidity, y=citric.acid)) +
  geom_point() +
  geom_jitter(position=position_jitter(), aes(color=rating)) +
  geom_vline(xintercept=c(0.6), linetype='dashed', size=1, color='black') +
  geom_hline(yintercept=c(0.5), linetype='dashed', size=1, color='black') +
  scale_x_continuous(breaks = seq(0, 1.6, .1)) +
  theme_pander() + scale_colour_few()

#'
#' Nearly every wine has volatile acidity less than 0.8. As discussed earlier the
#' A rating wines all have volatile.acidity of less than 0.6. For wines with
#' rating B, the volatile acidity is between 0.4 and 0.8. Some C rating wine have
#' a volatile acidity value of more than 0.8
#'
#' Most A rating wines have citric acid value of 0.25 to 0.75 while the B rating
#' wines have citric acid value below 0.50.
#'
#' ### Understanding the Significance of Sulphates
#'
## ----echo=FALSE, message=FALSE, warning=FALSE----------------------------
ggplot(subset(wine, rating=='A'|rating=='C'), aes(x = alcohol, y = sulphates)) +
    geom_jitter(position = position_jitter(), aes(color=rating)) +
  geom_hline(yintercept=c(0.65), linetype='dashed', size=1, color='black') +
  theme_pander() + scale_colour_few() +
  scale_y_continuous(breaks = seq(0, 2, .2))

#'
#' It is incredible to see that nearly all wines lie below 1.0 sulphates level.
#' Due to overplotting, wines with rating B have been removed. It can be seen
#' rating A wines mostly have sulphate values between 0.5 and 1 and the best rated
#' wines have sulphate values between 0.6 and 1. Alcohol has the same values as
#' seen before.
#'
#' ### Density & Sugar
#'
## ----echo=FALSE, message=FALSE, warning=FALSE, Multivariate_Plots2-------
da1 <- ggplot(aes(x=density, y=total.acidity, color=as.numeric(quality)),
              data=wine) +
  geom_point(position='jitter') +
  geom_smooth() +
  labs(x="Total Acidity", y="Density", color="Quality") +
  ggtitle("Density vs. Acidity Colored by Wine Quality Ratings")

cs2 <- ggplot(aes(x=residual.sugar, y=density, color=as.numeric(quality)),
              data=wine) +
  geom_point(position='jitter') +
  geom_smooth() +
  labs(x="Residual Sugar", y="Density", color="Quality") +
  ggtitle("\nSugar vs. Chlorides colored by Wine Quality Ratings")

grid.arrange(da1, cs2)

#'
#' Higher quality wines appear to have a slight correlation with higher acidity
#' across all densities. Moreover, there are abnormally high and low quality wines
#' coincident with higher-than-usual sugar content.
#'
#' ## Multivariate Analysis - Summary
#' Based on the investigation, it can be said that higher `citric.acid` and
#' lower `volatile.acidity` contribute towards better wines. Also, better wines
#' tend to have higher alcohol content.
#'
#' There were surprising results with `suplhates` and `alcohol` graphs.
#' Sulphates had a better correlation with quality than citric acid, still the
#' distribution was not that distinct between the different quality wines. Further
#' nearly all wines had a sulphate content of less than 1, irrespective of the
#' alcohol content; suplhate is a byproduct of fermantation just like
#' alcohol.
#'
#' Based on the analysis presented, it can be noted because wine rating is a
#' subjective measure, it is why statistical correlation values are not a very
#' suitable metric to find important factors. This was realized half-way through
#' the study. The graphs aptly depict that there is a suitable range and it is
#' some combination of chemical factors that contribute to the flavour of wine.
#'
#' ## Final Plots and Summary
#'
#' ### Plot One
#'
## ----echo=FALSE, message=FALSE, warning=FALSE, plot_2--------------------
qr1 <- ggplot(aes(as.numeric(quality), fill=rating), data=wine) +
  geom_bar() +
  ggtitle ("Barchart of Quality with Rating") +
  scale_x_continuous(breaks=seq(3,8,1)) +
  xlab("Quality") +
  theme_pander() + scale_colour_few()

qr2 <- qplot(x=rating, data=wine, geom='bar',
      fill=I("#990000"),
      col=I("black")) +
  xlab("Rating") +
  ggtitle("Barchart of Rating") +
  theme_pander()

grid.arrange(qr1, qr2, ncol=2)

#'
#' #### Description One
#' The plot is from the univariate section, which introduced the idea of
#' this analysis. As in the analysis, there are plenty of visualizations which
#' only plot data-points from A and C rated wines. A first comparison of only
#' the 'C' and 'A' wines helped find distinctive properties that separate these
#' two.
#'
#' It also suggests that it is likely that the critics can be highly subjective as
#' they do not rate any wine with a measure of 1, 2 or 9, 10. With most wines
#' being mediocre, the wines that had the less popular rating must've caught the
#' attention of the wine experts, hence, the idea was derived to compare these two
#' rating classes.
#'
#' ### Plot Two
#'
## ---- echo=FALSE, warning=FALSE, message=FALSE, plot_1a------------------
ggplot(aes(x=alcohol), data=wine) +
  geom_density(fill=I("#BB0000")) +
  facet_wrap("quality") +
  ggtitle("Alcohol Content for Wine Quality Ratings") +
  labs(x="Alcohol [%age]", y="") +
  theme(plot.title = element_text(face="plain"),
        axis.title.x = element_text(size=10),
        axis.title.y = element_text(size=10))

#'
## ----echo=FALSE, message=FALSE, warning=FALSE, plot_1b-------------------
fp1 <- ggplot(aes(y=alcohol, x=quality), data = wine)+
  geom_boxplot() +
  xlab('Quality') +
  ylab("Alcohol in % by Volume") +
  labs(x="Quality", y="Alcohol [%age]") +
  ggtitle("Boxplot of Alcohol and Quality") +
  theme(plot.title = element_text(face="plain"),
        axis.title.x = element_text(size=10),
        axis.title.y = element_text(size=10))

fp2 <-ggplot(aes(alcohol, qmean), data=wine.quality_groups) +
  geom_smooth() +
  scale_x_continuous(breaks = seq(0, 15, 0.5)) +
  ggtitle("\nLine Plot of Quality Mean & Alcohol Percentage") +
  labs(x="Alcohol [%age]", y="Quality (Mean)") +
  theme(plot.title = element_text(face="plain"),
        axis.title.x = element_text(size=10),
        axis.title.y = element_text(size=10))

grid.arrange(fp1, fp2)

#'
#' #### Description Two
#'
#' These are plots taken from bivariate analysis section discussing the effect of
#' alcohol percentage on quality.
#'
#' The first visualization was especially appealing to me because of the way that
#' you can almost see the distribution shift from left to right as wine ratings
#' increase. Again, just showing a general tendency instead of a substantial
#' significance in judging wine quality.
#'
#' The above boxplots show a steady rise in the level of alcohol. An interesting
#' trend of a decrement of quality above 13%, alcohol gave way to further analysis
#' which shows that a general correlation measure might not be suitable for the
#' study.
#'
#' The plot that follows set the basis for which I carried out the complete
#' analysis. Rather than emphasizing on mathematical correlation measures, the
#' inferences drawn were based on investigating the visualizations. This felt
#' suitable due to the subjectivity in the measure of wine quality.
#'
#' ### Plot Three
#'
## ----echo=FALSE, messages=FALSE, warning=FALSE, plot_3-------------------
fp3 <- ggplot(subset(wine, rating=='A'|rating=='C'),
              aes(x = volatile.acidity, y = citric.acid)) +
  geom_point() +
  geom_jitter(position=position_jitter(), aes(color=rating)) +
  geom_vline(xintercept=c(0.6), linetype='dashed', size=1, color='black') +
  geom_hline(yintercept=c(0.5), linetype='dashed', size=1, color='black') +
  scale_x_continuous(breaks = seq(0, 1.6, .1)) +
  theme_pander() + scale_colour_few() +
  ggtitle("Wine Rating vs. Acids") +
  labs(x="Volatile Acidity (g/dm^3)", y="Citric Acid (g/dm^3)") +
  theme(plot.title = element_text(face="plain"),
        axis.title.x = element_text(size=10),
        axis.title.y = element_text(size=10),
        legend.title = element_text(size=10))

fp4 <- ggplot(subset(wine, rating=='A'|rating=='C'),
              aes(x = alcohol, y = sulphates)) +
  geom_jitter(position = position_jitter(), aes(color=rating)) +
  geom_hline(yintercept=c(0.65), linetype='dashed', size=1, color='black') +
  theme_pander() + scale_colour_few() +
  scale_y_continuous(breaks = seq(0,2,.2)) +
  ggtitle("\nSulphates, Alcohol & Wine-Rating") +
  labs(x="Alcohol [%]", y="Sulphates (g/dm^3)") +
  theme(plot.title = element_text(face="plain"),
        axis.title.x = element_text(size=10),
        axis.title.y = element_text(size=10),
        legend.title = element_text(size=10))

grid.arrange(fp3, fp4, nrow=2)

#'
#' #### Description Three
#' These plots served as finding distinguishing boundaries for given attributes,
#' i.e., `sulphates`, `citric.acid`, `alcohol`, `volatile.acidity`. The
#' conclusions drawn from these plots are that sulphates should be high but less
#' than 1 with an alcohol concentration around 12-13%, along with less (< 0.6)
#' volatile acidity. It can be viewed nearlyas a depiction of a classification
#' methodology without application of any machine learning algorithm. Moreover,
#' these plots strengthened the arguments laid in the earlier analysis of the data.
#'
#' ------
#'
#' ## Reflection
#' In this project, I was able to examine relationship between *physicochemical*
#' properties and identify the key variables that determine red wine quality,
#' which are alcohol content volatile acidity and sulphate levels.
#'
#' The dataset is quite interesting, though limited in large-scale implications.
#' I believe if this dataset held only one additional variable it would be vastly
#' more useful to the layman. If *price* were supplied along with this data
#' one could target the best wines within price categories, and what aspects
#' correlated to a high performing wine in any price bracket.
#'
#' Overall, I was initially surprised by the seemingly dispersed nature of the
#' wine data. Nothing was immediately correlatable to being an inherent quality
#' of good wines. However, upon reflection, this is a sensible finding. Wine
#' making is still something of a science and an art, and if there was one
#' single property or process that continually yielded high quality wines, the
#' field wouldn't be what it is.
#'
#' According to the study, it can be concluded that the best kind of wines are the
#' ones with an alcohol concentration of about 13%, with low volatile acidity &
#' high sulphates level (with an upper cap of 1.0 g/dm^3).
#'
#' ### Future Work & Limitations
#' With my amateurish knowledge of wine-tasting, I tried my best to relate it to
#' how I would rate a bottle of wine at dining. However, in the future, I would
#' like to do some research into the winemaking process. Some winemakers might
#' actively try for some property values or combinations, and be finding those
#' combinations (of 3 or more properties) might be the key to truly predicting
#' wine quality. This investigation was not able to find a robust generalized
#' model that would consistently be able to predict wine quality with any degree
#' of certainty.
#'
#' If I were to continue further into this specific dataset, I would aim to
#' train a classifier to correctly predict the wine category, in order to better
#' grasp the minuteness of what makes a good wine.
#'
#' Additionally, having the wine type would be helpful for further analysis.
#' Sommeliers might prefer certain types of wines to have different
#' properties and behaviors. For example, a Port (as sweet desert wine)
#' surely is rated differently from a dark and robust abernet Sauvignon,
#' which is rated differently from a bright and fruity Syrah. Without knowing
#' the type of wine, it is entirely possible that we are almost literally
#' comparing apples to oranges and can't find a correlation.