redwine.rmd

 ```{r global_options, echo=FALSE}
 library("knitr")
 knitr::opts_chunk$set(fig.width=7,fig.height=6,fig.path='Figs/',
                      fig.align='center',tidy=TRUE,
                      echo=FALSE,warning=FALSE,message=FALSE)
 ```
---
title: "Red Wine Quality by Anav Gupta"
output: html_notebook
author: "Anav Gupta"
---

Red Wine Quality by Anav Gupta
========================================================

# Packages
Before we start exploring the data, we will first load the packages that we will need for this exploration. 

```{r packages, echo=FALSE, message=FALSE, warning=FALSE}
# Load all of the packages that you end up using in your analysis in this code
# chunk.

# Notice that the parameter "echo" was set to FALSE for this code chunk. This
# prevents the code from displaying in the knitted HTML output. You shoecho=FALSE echo=FALSEuld set
# echo=FALSE for all code chunks in your file, unless it makes sense for your
# report to show the code that generated a particular plot.

# The other parameters for "message" and "warning" should also be set to FALSE
# for other code chunks once you have verified that each plot comes out as you
# want it to. This will clean up the flow of your report.

library(ggplot2)
library(ggthemes)
library(dplyr)
library(tidyr)
library(gridExtra)
library(RColorBrewer)
library(GGally)
```

***

# Load the Data
Lets load the data necessary for this exploration.

```{r Load_the_Data, echo=FALSE}
# Load the Data
redwine <- read.csv('wineQualityReds.csv')
str(redwine)

# Converting the quality into a factor variable
redwine$quality <- factor(redwine$quality, levels = seq(1, 10, 1))
str(redwine)

# Converting the quality into a numerical variable
redwine$quality.num <- as.numeric(redwine$quality)

# Creating a group variable of the qualities of wine
redwine$quality.group <- as.factor(cut(redwine$quality.num, c(2, 4, 6, 8)))
```


This tidy data set contains 1,599 red wines with 11 variables on the chemical
properties of the wine. At least 3 wine experts rated the quality of each wine,
providing a rating between 0 (very bad) and 10 (very excellent).

***

# Univariate Plots Section
In this section we will try to analyze the variable individually.

```{r Data Summary, echo=FALSE}
summary(redwine)
```

### Quality

Now lets have a look at the quality variable

```{r Qualitym, echo=FALSE}
qplot(data = redwine, quality, fill = I('#f79420'))
```

It seems the most of the wines in this sample have quality score of 5 and 6 .

***

### Fixed.Acidity

```{r echo=FALSE}
summary(redwine$fixed.acidity)
```

```{r echo=FALSE}
table(cut(redwine$fixed.acidity, c(4, 5, 6, 7, 8, 9, 10, 12, 16)))
quantile(redwine$fixed.acidity, seq(0, 1, .1))
quantile(redwine$fixed.acidity, seq(0.9, 1, .01))
```


```{r echo=FALSE}
qplot(data = redwine, x = fixed.acidity, fill = I('#f79420'), bins = 60) +
  xlim(4, 14)
```

The Fixed Acidity of the wine seems to max out around the 6 to 8 units.
We can clearly see the presence of the outliers in the data set.
This seems appropriate as higher values of fixed acidity will turn the wine more acidic in nature.

***

### Volatile Acidity

```{r echo=FALSE}
summary(redwine$volatile.acidity)
table(cut(redwine$volatile.acidity, c(.1, .3, .4, .5,.6, .7, .8, 1, 1.6)))
quantile(redwine$volatile.acidity, seq(0, 1, .1))
quantile(redwine$volatile.acidity, seq(0.9, 1, .01))
```

```{r echo=FALSE}
qplot(data = subset(redwine, volatile.acidity <= quantile(redwine$volatile.acidity,
      .99)), x = volatile.acidity, fill = I('#f79420'), bins = 60)
```

High levels of Volatile Acidity can lead to a unpleasant and vinegar like taste.
This seems to the reason why only few percentage of wines have higher volatile 
Acidity. Most of the wines seems to contain .4 to .6 levels of volatile acidity.

***

### Citric Acid

```{r echo=FALSE}
summary(redwine$citric.acid)
```


```{r echo=FALSE}
qplot(data = redwine, x = citric.acid, fill = I('#f79420'), bins = 60)
```

It seems that citric Acid is not present in many of wine samples. The citric acid 
distribution is quite flat. It will be nice to explore the quality of the wines 
that don't have any citric Acid.

***

### Residual sugar

```{r echo=FALSE}
summary(redwine$residual.sugar)
```

```{r echo=FALSE}
grid.arrange(
  ggplot(redwine, aes( x = 1, y = residual.sugar)) +
    geom_jitter(alpha = 0.1) +
    geom_boxplot(alpha = 0.2, color = 'red') ,
  ggplot(redwine, aes(x = residual.sugar)) +
    geom_histogram(bins=60),
  ncol=2)
```

It seems that majority of the wines have residual sugar level between 1 and 3. 
As you can see from the above graph that there are wine samples that far more 
residual sugar. It will be interesting to compare the quality of wines based on
the residual sugar.

***

### Chlorides

```{r echo=FALSE}
summary(redwine$chlorides)
```

```{r echo=FALSE}
grid.arrange(
  ggplot(data = redwine, aes(x = 1, y = chlorides)) +
    geom_jitter(alpha = 0.1) +
    geom_boxplot(alpha = 0.2, color = 'red') +
    scale_y_continuous(breaks = c(seq(0, .2, .05), .6)),
  ggplot(data = redwine, aes(x = chlorides)) +
  geom_histogram(fill = I('#f79420'), bins = 60),
  ncol = 2
)

```


```{r echo=FALSE}
ggplot(data = subset(redwine, chlorides <= quantile(redwine$chlorides, .95)),
       aes(x = chlorides)) +
  geom_histogram(fill = I('#f79420'), bins = 60)
```

We can clearly see that the chlorides are found in very minute quantities in the
wine samples. The chlorides seems to have a Normal distribution with many 
outliers. About 95 % of the wines contain chlorides in the range of 0.040 to
0.125.
 
***

### Free Sulphar Dioxide

```{r echo=FALSE}
summary(redwine$free.sulfur.dioxide)
```

```{r echo=FALSE}
quantile(redwine$free.sulfur.dioxide, seq(0, 1, .1))
quantile(redwine$free.sulfur.dioxide, seq(0.9, 1, .01))
```


```{r echo=FALSE}
qplot(data = redwine, x = (free.sulfur.dioxide), fill = I('orange'), 
      bins = 60)
```



```{r echo=FALSE}
ggplot(aes(free.sulfur.dioxide), data = subset(redwine, free.sulfur.dioxide <=
      quantile(redwine$free.sulfur.dioxide, .99))) +
  geom_histogram(fill = I('orange'), bins = 60)
```

From the graph as well as from the Quintilian function we can clearly see that in 
majority of the wines(90%) the amount of free sulfur dioxide is with in 31 units.
The presence of sulfur dioxide in the low concentration is undetectable, but at
free concentration over 50 ppm, the sulfur dioxide become evident in the nose as
well as the taste of the wine. 
I suppose this is why only 1 percent of wines have it's concentration greater 
than 50.


***

### Total Sulfur Dioxide

```{r echo=FALSE}
summary(redwine$total.sulfur.dioxide)
```

```{r echo=FALSE}
quantile(redwine$total.sulfur.dioxide, seq(0, 1, .1))
```

```{r echo=FALSE}
qplot(x = total.sulfur.dioxide, data = redwine, 
      fill = I('Orange'), bins = 60) +
  scale_x_continuous(limits = c(0, 165), breaks = seq(0, 160, 20))
```

Total Sulfur Dioxide is the the total amount of sulfur dioxide in the wine and
hence there will be some kind of relation between the free and total sulfur 
dioxide.

***

### Density

```{r echo=FALSE}
summary(redwine$density)
```

```{r echo=FALSE}
ggplot(data = redwine, aes(x = density)) +
  geom_histogram(fill = I('Orange'), bins = 60) +
  geom_vline(aes(xintercept = mean(density), color = I('black')))
```

we can clearly see that the density of the wine varies over a narrow range.
Median and mean of the density is equal. This suggest that it has a normal
distribution.

***

### pH

```{r echo=FALSE}
summary(redwine$pH)
```

```{r echo=FALSE}
ggplot(data = redwine, aes(x = pH)) +
  geom_histogram(fill = I('Orange'), bins = 60) +
  scale_x_continuous(breaks = seq(2.5, 4, .1)) +
  geom_vline(aes(xintercept = mean(pH), color = I('black')))
```

Ph is an index which indicates the acidity or the alkalinity of the water soluble 
substance. we can clearly see that the density of the wine varies over a narrow
range.Median and mean of the density is equal. This suggest that it has a normal
distribution. We can see that the ph value for a wine range over a narrow values
of 3 to 4.

***

### Sulphates

```{r echo=FALSE}
summary(redwine$sulphates)
```

```{r echo=FALSE}
quantile(redwine$sulphates, seq(0, 1, .1))
quantile(redwine$sulphates, seq(0.9, 1, .01))

table(cut(redwine$sulphates, c(0, .5 , .6, .7, .8, .9, 1, 2)))
```


```{r echo=FALSE}
qplot(data = redwine, x = sulphates, fill = I('orange'), bins = 60) +
  scale_x_continuous(breaks = seq(0, 1.5, .1)) +
  geom_vline(aes(xintercept = mean(sulphates), color = I('black'))) +
  geom_vline(aes(xintercept = median(sulphates), color = I('blue'))) 
```


From the histogram as well as from the table information we can clearly see that
majority of the wines have 0.5 to 0.7 units of sulphates concentration in the 
wine.

***

### Alcohol

```{r echo=FALSE}
summary(redwine$alcohol)
```

```{r echo=FALSE}
table(cut(redwine$alcohol, c(8, 9, 10, 11, 12, 13, 15)))

```


```{r echo=FALSE}
ggplot(data = redwine, aes(x = alcohol)) +
  geom_histogram(fill = I('orange'), bins = 60) +
  scale_x_continuous(breaks = c(seq(6, 16, 1), 10.5), minor_breaks = seq(10, 11, .1)) +
  geom_vline(aes(xintercept = mean(alcohol), color = I('black'))) +
  geom_vline(aes(xintercept = median(alcohol), color = I('blue')))
```

From the histogram as well as the table summary, we can see that that 50 percent
of the wines have 9-10 percent of alcohol content.

***


# Univariate Analysis
In this section we will list the analysis of the univariate exploration.

### What is the structure of your dataset?
Our data set consists of 1599 observation having 11 physicochemical inputs and a output that gives the quality of the wine. The quality variable is an ordered 
factor variable with following levels :

(Worst) ----------------> (Best)
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10

Other Observations: 

* Most Wines have a ph of 3 to 4.
* Most Wine have an alcohol content of 9 to 10 percent.


### What is/are the main feature(s) of interest in your dataset?
We can see that the variables Free sulfur Dioxide and Total Sulfur Dioxide will
be connected in some way. In the same manner, Fixed and Total acidity are 
connected to each other.
It will be interesting to find that whether the quantity of alcohol in the wine
have any influence on the quality of the wine or not.
How does the quantity of Citric Acid, which add freshness and flavor to wines effect the quality of the wine.

### What other features in the dataset do you think will help support your \
investigation into your feature(s) of interest?
Chlorides, Sugar and Ph are some of the variables that will support my investigation into my features of interest.

### Did you create any new variables from existing variables in the dataset?
Yes, I created two new variables out of the existing quality variable. Firstly, 
I created a factor of quality variable. Secondly, I created a variable 
'quality.group' which is created by cutting the quality variable into 3 equal 
sizes.

### Of the features you investigated, were there any unusual distributions? \
Did you perform any operations on the data to tidy, adjust, or change the form \
of the data? If so, why did you do this?
I have converted the quality into a factored variable. This will aid me to 
visualize the input variable that lead to different quality of wines.


# Bivariate Plots Section
This section will try to explore two variables at a time.

```{r echo=FALSE}
ggcorr(subset(redwine, select = c(-X, -quality, -quality.group)),
       label = TRUE, label_size = 2, label_alpha = TRUE,
       angle = -45) +
  theme(legend.title = element_text(size = 14))

my_fn <- function(data, mapping, method="loess", ...){
      p <- ggplot(data = data, mapping = mapping) + 
      geom_point(shape = I('.')) + 
      geom_smooth(method=method, ...)
      p
    }
```

From the above graph we can see some significant correlation among the following
variables :
* pH and Fixed Acidity : - 0.683
* Fixed Acidity and Citric Acid : 0.672
* Density and Fixed Acidity : 0.668
* Free Sulfuric Dioxide and Total Sulfuric Dioxide : 0.668
* Volatile Acidity and Citric Acid : - 0.552
* Citric and pH : - 0.542
* Density and Alcohol : - 0.5


```{r message=FALSE,warning=FALSE,echo=FALSE, fig.width=20, fig.height=30}
ggpairs(subset(redwine, select = c(-X, -quality, -quality.group)),
       lower = list(continuous = wrap(my_fn, method = 'lm')),
        upper = list(combo = wrap('box', outlier.shape = I('.'))),
        axisLabels = 'internal',
       corSize = 10)
```

Now let test all the physicochemical input of the wine with the Quality (output) 
of the wine.

### Volatile Acidity and Quality

```{r echo=FALSE}
  # scale_y_continuous(breaks = seq(0.3, 1.6, .2))
ggplot(data = subset(redwine, volatile.acidity <=  
       quantile(redwine$volatile.acidity, .95)), 
       aes(quality, volatile.acidity)) + 
    geom_point(alpha = 1/5, position = 'jitter') +
  geom_boxplot(aes(fill = quality), alpha = .5) +
  scale_y_continuous() +
  stat_summary(geom = 'point', fun.y = 'mean', shape = 8, color = "red")
```

From the above Box plot of the Volatile Acidity, we can make some connection 
between the volatile acidity and the Quality of the wine.
In lower quality wines, volatile acidity is very dispersed and the dispersion 
lowers down as we move to better quality wines. 
We can see that the median as well as the mean of the volatile acidity in the 
wine starts to reduce with the increase in the quality of wine. 
From the Boxplot it seems that .3 to .5 is the ideal range for volatile acidity.

***

### Fixed Acidity and Quality


Fixed Acidity for the wines having quality 3 or 4 is very dispersed.
For the wines with quality score 5, 6 and 7 we can see from the a


```{r echo=FALSE}
ggplot(data = redwine, aes(quality, fixed.acidity)) + 
  geom_boxplot(aes(fill = redwine$quality)) +
  scale_y_continuous(breaks = seq(4, 16, 2)) +
  stat_summary(geom = 'point', fun.y = 'mean', shape = 22, fill = I('black'))
```

It's difficult to sight some trend from the above boxplots. Although it can be 
said that for each quality of wine 50 percent time, the fixed acidity lies 
between 7 to 10 units.


***

### Citric Acid and Quality

```{r echo=FALSE}
subset(redwine, citric.acid != 0) %>%
  group_by(quality) %>%
  summarise(n = n())
```

```{r echo=FALSE}
ggplot(data = redwine, aes(quality, citric.acid)) + 
  geom_boxplot(aes(fill = redwine$quality)) +
  stat_summary(geom = 'point', fun.y = 'mean', shape = 22, fill = I('black'))

```

The trend we can make about the citric acid content and quality of the wine is
that the content of citric acid (mean as well as median) increases with the increase in the quality of the wine.

***

### Ph and Quality


```{r echo=FALSE}
ggplot(data = redwine, aes(x = quality, y = pH)) + 
  geom_boxplot(aes(fill = redwine$quality)) +
  scale_y_continuous(breaks = seq(3, 4, .1)) +
  stat_summary(geom = 'point', fun.y = 'mean', shape = 22, fill = I('black'))
```

From the boxplot you can't find out much about the quality of the wine from it's  
pH value. One thing is sure from the boxplot that the pH of the wine generally 
remains within the range of 3 to 4, with about 50 percent of times within 3.2 to
3.4.

***

### Residual Sugar vs Quality


```{r echo=FALSE}
ggplot(data = redwine, aes(x = quality, y = residual.sugar)) + 
  geom_boxplot(aes(fill = redwine$quality)) +
  scale_y_continuous(limits = c(0.8, quantile(redwine$residual.sugar, 0.90)), minor_breaks = seq(1, 3, .5)) +
  stat_summary(geom = 'point', fun.y = 'mean', shape = 4)
```

From the boxplot above, we don't seem to have any kind of relation ship or trend 
between residual sugar content and the quality of the wine. For 87 percent of 
times, the residual sugar falls with the range of 1 to 3.
Median of the residual sugar content remain constant for all the qualities of 
wine.
some wines with quality 5 and 6 have high amount of residual sugar.
More than 50 percent of times for all qualities of wine, residual sugar remains 
within the range of 2 - 3.

***

### Chlorides vs Quality

```{r warning=FALSE, echo=FALSE}
ggplot(data = redwine, aes(x = chlorides)) +
  geom_histogram(aes(fill = quality.group), bins = 60) +
  scale_x_continuous(limits = c(0.025, quantile(redwine$chlorides, 0.95)))
```


```{r echo=FALSE}
ggplot(data = redwine, aes(x = quality, y = chlorides)) + 
  geom_boxplot(aes(fill = redwine$quality))  +
  scale_y_continuous(limits = c(0, quantile(redwine$chlorides, 0.95)),
                     minor_breaks = seq(0.05, .2, .05)) +
  stat_summary(geom = 'point', fun.y = 'mean', shape = 22, fill = I('black'))
```

It looks like that there doesn't seem to be any trend between the quantity of 
chlorides and the quality of the wine.
For most of the wines, the quantity of chloride falls within 0.05 and 0.1 units.

***

### Free Sulfur Dioxide vs Quality

```{r echo=FALSE}
ggplot(data = subset(redwine, total.sulfur.dioxide <=  
       quantile(redwine$total.sulfur.dioxide, .95)),
       aes(x = quality, y = free.sulfur.dioxide)) + 
  geom_boxplot(aes(fill = quality)) +
  scale_y_continuous(breaks = seq(0, 70, 10), minor_breaks = seq(0, 20, 2)) +
  stat_summary(geom = 'point', fun.y = 'mean', shape = 22, fill = I('black'))
```

From the Boxplot above it doesn't seem like that the free sulfur dioxide has any
effect on the quality of the wine.

***

### Total Sulfur Dioxide vs Quality


```{r echo=FALSE}
ggplot(data = subset(redwine, total.sulfur.dioxide <=  
        quantile(redwine$total.sulfur.dioxide, .99)), 
        aes(x = quality, y = total.sulfur.dioxide)) + 
  geom_boxplot(aes(fill = quality)) +
  scale_y_continuous() +
  stat_summary(geom = 'point', fun.y = 'mean', shape = 22, fill = I('black'))
```

Total Sulfur Dioxide doesn't seem to have any kind of relationship with the 
quality of an alcohol. It just so happens that for more that 50 percent of time
total sulfur dioxide present in the wine is less than or equal to 50.

***

### Sulphates vs Quality

```{r echo=FALSE}
ggplot(data = subset(redwine, sulphates <=  
        quantile(redwine$sulphates, .99)), 
        aes(x = quality, y = sulphates)) + 
  geom_boxplot(aes(fill = quality)) +
  scale_y_continuous() +
  stat_summary(geom = 'point', fun.y = 'mean', shape = 22, fill = I('black'))
```

The median as well as the mean of quantity of the sulphate increases with the 
increase in the quality of the wine.

***

### Density vs Quality

```{r echo=FALSE}
ggplot (data = redwine, aes( density)) +
  geom_histogram(aes(x = density, fill = quality.group), bins = 60)
```

```{r echo=FALSE}
ggplot (data = redwine, aes(quality, density)) +
  geom_boxplot(aes(fill = quality)) + 
  stat_summary(geom = 'point', fun.y = 'mean', shape = 22, fill = I('black'))
```

As we had already seen that the density of the wine varies over a narrow period.
It's difficult to find the trend between the density and the quality of a wine.

***

### Alcohol vs Quality 

```{r echo=FALSE}
ggplot (data = redwine, aes(alcohol)) +
  geom_histogram(aes(x = alcohol, fill = quality), bins = 60)
```

```{r echo=FALSE}
ggplot(data = subset(redwine, volatile.acidity <= quantile(
      redwine$volatile.acidity, .98)), aes(quality, alcohol)) +
  geom_boxplot(aes(fill = quality)) + 
  stat_summary(geom = 'point', fun.y = 'mean', shape = 22, fill = I('black'))
```

```{r}
ggplot(data = redwine, aes(x = quality.group, y = alcohol)) +
  geom_jitter(alpha = 0.3) +
  geom_boxplot(aes(fill = quality.group), alpha  = 0.5) + 
  stat_summary(geom = 'point', stat = 'summary', fun.y = mean, 
               color = 'red', shape = 8, size = 4)
```

The above boxplots seems to suggest that as the alcohol content increases in the 
wine, it's quality increases. However this cannot be said with surety since, we 
can see that some of the wines of quality 5 have such high alcohol content.

***

Now that we have tried to compare the physicochemical properties of wine with the 
quality of the wine. Now lets try to relate the physicochemical properties 
itself.

### Fixed Acidiy and Citric Acid

We know that the citric acid is a non-volatile acid and the fixed acidity tend
to calculate the non-volatile acid content of the wine.

```{r message=FALSE, echo=FALSE}
ggplot(data = redwine, aes(fixed.acidity, citric.acid)) + 
  geom_point(color = I('orange'), alpha = 1 / 5) +
  geom_smooth()
```


```{r echo=FALSE}
with (data = redwine, cor.test(fixed.acidity, citric.acid))
```

We do see some kind of correlation between the citric acid and the fixed 
acidity which was somewhat expected.

***

### Fixed Acidity and pH

```{r message=FALSE, echo=FALSE}
ggplot(data = redwine, aes(round(fixed.acidity / .2) * .2, pH)) + 
  geom_point(color = I('orange'), alpha = 1 / 5) +
  geom_smooth()
```

In the graph, it seems that the smooth line is going through the middle of the 
major portion of points.

```{r echo=FALSE}
with (data = redwine, cor.test(fixed.acidity, pH))
```

From above we can say that Fixed acidity and pH are negatively correlated. 
This seems plausible as well. As the acidic content of the wine increase, the 
pH value which gives the extent of the alkalinity/acidity should decrease.
A substance with pH with value 0 is most acidic.

***

### Density and Fixed Acidity

```{r message=FALSE, echo=FALSE}
ggplot(data = redwine, aes(fixed.acidity, density)) + 
  geom_point(color = I('orange'), alpha = 1/5) +
  stat_smooth()
```

The data is dispersed in the upper half of the smooth line. I guess we do see 
some correlation. The smooth line somewhats affirm our belief.

```{r echo=FALSE}
with(data = redwine, cor.test(density, fixed.acidity))
```

From the graph as well as from the R's coefficient, we can say that density and 
fixed acidity are positively correlated.

***

### Free vs Total sulfur Dioxide

These are two variables that tell us about of concentration of the sulfur 
dioxide in the wine either free or fixed.
So even from the definition of these two variables itself, we can postulate that
these two variables must be correlated. Lets try out our postulation.

```{r message=FALSE, warning=FALSE, echo=FALSE}
ggplot(data = redwine, aes(free.sulfur.dioxide, total.sulfur.dioxide)) +
  scale_x_continuous(limits =
                       c(0, quantile(redwine$total.sulfur.dioxide, .95))) +
  scale_y_continuous(limits =
                       c(0, quantile(redwine$total.sulfur.dioxide, .95))) +
  geom_point(color = I('orange'), alpha = 1/5) +
  stat_smooth()
```

```{r echo=FALSE}
with (data = redwine, cor.test(free.sulfur.dioxide, total.sulfur.dioxide))
```

From the above analysis, it seems that they both are positively correlated.


```{r echo=FALSE}
with(data = redwine, cor.test(quality.num, alcohol))
with(data = redwine, cor.test(quality.num, fixed.acidity))
```

### Density vs Alcohol

```{r echo=FALSE}
with (data = redwine, cor.test(density, alcohol))
```


```{r message=FALSE, echo=FALSE}
ggplot(data = redwine, aes(alcohol, density)) +
  geom_point(color = I('orange'), alpha = .5) +
  geom_smooth()
```

We can see that there is about negative correlation among the density and 
alcohol. The smooth line does passes through most of important places.

***

# Bivariate Analysis
This section lists the analysis of the bi-variate explorations.

### Talk about some of the relationships you observed in this part of the \
investigation. How did the feature(s) of interest vary with other features in \
the dataset?

The alcohol content in the wine correlates with the quality of the wine.
With the increase in the quality of the wine, the average (mean and median)
of the wine's alcohol content increases.

The Volatile Acidity correlates mildly correlates (Negatively) with the quality
of the wine. 

With the increase in the quality of the wine, the median as well as the mean 
quantity of the volatile acidity decreases.

The content of citric acid (mean as well as median) increases with the increase
in the quality of the wine.

The median as well as the mean of quantity of the sulphate increases with the 
increase in the quality of the wine.

The pH value of all wines remain in the range of 3-4. Specially, it can be seen
that as the quality of the wine increases, about more than 50 percent of times,
the pH value of the wine will remain within 3.2 to 3.4.

There doesn't seem to be any kind of relation between residual sugar and the 
quality of the wine, but it must be noted that for more than 50 percent of time,
the residual sugar was within 2-3 units.


### Did you observe any interesting relationships between the other features \
(not the main feature(s) of interest)?

Fixed acidity and Citric acid tends to correlate with each other. Since Citric 
acid is also a non-volatile acid, the fixed acidity gives the total 
non-volatile acid content, this relationship makes sense.

Fixed Acidity and pH are negatively correlated to each other. If the fixed 
acidity of the wine will increase, it's pH value will decrease. This makes 
sense as with more non-volatile acid in the wine, it's acidity will increase
and hence it's pH will decrease. Solution with 0 pH value is a most acidic 
substance.

Density and Fixed Acidity tend to correlate with each other (mildly). If we 
increase the fixed acidity of the wine, the density of the wine tend to 
increase.

### What was the strongest relationship you found?
Our feature of interest, Quality have the strongest relationship with it's 
alcohol content. The Quality of the wine is positively correlated with it's 
alcohol content. This is the strongest relation we found.

# Multivariate Plots Section

In this section we will try to examine multiple variable at a time.

### Density vs Fixed Acidity by Quality

```{r message=FALSE, echo=FALSE}
ggplot(data = redwine, aes(fixed.acidity, density)) + 
  geom_point(aes(color = quality.group)) +
  geom_smooth(aes(color = quality.group)) +
  scale_color_brewer(type  = 'seq', guide = guide_legend("Quality"),
                     labels = c('worst', 'normal', 'better')) 
  
```

It can be clearly seen that the density of the wine increases with the increase 
in the fixed acidity of the wine. From above, we can see that the trend is 
followed irrespective of the wine quality.

***

### Citric Acid vs Fixed Acidity by Quality


```{r message=FALSE, echo=FALSE}
ggplot(data = redwine, aes(fixed.acidity, citric.acid)) + 
  geom_point(aes(color = quality.group)) +
  geom_smooth(aes(color = quality.group)) +
  scale_color_brewer(type  = 'seq', guide = guide_legend("Quality"),
                     labels = c('worst', 'normal', 'better')) 
```

We can in all quality groups, with the increase of the fixed acidity the citric 
acid content all tend to increase.

***

### Fixed Acidity vs pH by Quality

```{r echo=FALSE}
ggplot(data = redwine, aes(fixed.acidity, pH)) +
  geom_point(aes(color = quality.group)) +
  geom_smooth(aes(color = quality.group)) +
  scale_color_brewer(type  = 'seq', guide = guide_legend("Quality"),
                     labels = c('worst', 'normal', 'better'))  
```

We can see that for the wine of the better quality, regression line's slope 
remain almost constant, but for the wine with worst quality regression line's
slope changes very frequently as the fixed acidity is increased.

***

### Density vs Alcohol by Quality

```{r echo=FALSE}
ggplot(data = redwine, aes(alcohol, density )) +
  geom_point(aes(color = quality.group), alpha = 0.5) +
  geom_smooth(aes(color = quality.group)) +
  scale_color_brewer(type  = 'seq', guide = guide_legend("Quality"),
                     labels = c('worst', 'normal', 'better'))  
```

It can be clearly seen that for the wine of worst quality, the regression line's
slope tend to remain constant thoughout the graph. In a totaly opposite sense,
the regression line of the wine with better qualities tend to wobble as the
alcohol concentration increases. Generally, as the alcohol concentration 
increases the density decreases.

***

### Free sulfur dioxide vs Total Sulfur Dioxide by Quality

```{r message=FALSE, warning=FALSE, echo=FALSE}
ggplot(data = redwine, aes(total.sulfur.dioxide, free.sulfur.dioxide)) +
  scale_y_continuous(limits = 
                       c(0, quantile(redwine$free.sulfur.dioxide, 0.95))) +
  scale_x_continuous(limits = 
                       c(0, quantile(redwine$total.sulfur.dioxide, 0.95))) +
  geom_point(aes(color = quality.group), alpha = 0.5) +
  geom_smooth(aes(color = quality.group)) +
  scale_color_brewer(type  = 'seq', guide = guide_legend("Quality"),
                     labels = c('worst', 'normal', 'better')) 
```

We can see that for lower values of total sulfur dioxide there is very less 
amount of variance in the value of free sulfur dioxide. As the total sulfur dioxide starts to increase the variation in the amount of free sulfur dioxide.
With the help of quality group we can see there is very frequent change for the wines in the normal category. The change is not that frequent in other group of
wines.

***

### Density vs Alcohol over Fixed Acidity by Quality 

```{r}
ggplot(data = redwine, aes(alcohol / fixed.acidity, density)) +
  geom_point(aes(color = quality.group), alpha = 1 / 3, size = 1) +
  scale_color_brewer(type = "qual", palette = 2,
                     labels = c('worst', 'normal', 'best')) +
  labs(color = 'Qaulity group') +
  geom_smooth(aes(color = quality.group))
```

The Density of the Wine is strongly correlated with the Alcohol content of the 
wine and it's fixed acidity. We can see that for all qualities of wine, the 
smooth tend to pass through the middle of the graph, suggesting correlation.

So as the concentration of the alcohol over fixed acidity increases, the density 
tend to decrease. 

***
### Linear model for density
Here we will create linear model with density, alcohol and fixed acidity.

```{r echo=FALSE}
densityLm <- lm(data = redwine, I(density) ~ I(alcohol) + I(fixed.acidity))
summary(densityLm)
```

So it turns out that 65 percent of variance in density is explained by alcohol 
content and the fixed acidity of the wine.

***

### Quality Linear Model
Now lets try to make a linear model for the quality of the wine.

One to check before making the linear model is that the variables in the model 
should not be correlated with each other. This can create ambiguity in deciding 
which component is responsible for the change in model.

From the correlation matrix we know that these variables are not correlated with
each other.

* Alcohol
* pH
* Sulphates
* residual.sugar
* Fixed Acidity
* Chlorides
* Total Sulfur Dioxide

```{r echo=FALSE}
m1 <- lm(data = redwine, I(quality.num) ~ alcohol + sulphates + pH +  
           residual.sugar + chlorides + total.sulfur.dioxide)

summary(m1)
```

A model that tries to explain the variation in the quality of the wine.
We get a r-squared value of 0.3142.

***

# Multivariate Analysis

### Talk about some of the relationships you observed in this part of the \
investigation. Were there features that strengthened each other in terms of \
looking at your feature(s) of interest?
  
There seems to be a strong relationship between Density and the Alcohol and the 
fixed acidity.


### Were there any interesting or surprising interactions between features?
There is a surprising interaction between Density and the combination of alcohol and fixed acidity. It may have to do something with the chemistry of the fluids,
but nonetheless it is an interesting relation that one find without the innate 
knowledge of the chemistry behind this interactions.

### OPTIONAL: Did you create any models with your dataset? Discuss the \
strengths and limitations of your model.
I created a model for the examination of the quality of the wine variable with 
the help of some of the physicochemical inputs that were provided with the 
dataset.
This model contain seven of the original 11 inputs in the wine data set.
All these are pretty much not correlated to each other. This is good as it will
not create any kind of ambiguity as which variable is moving the model.

Albeit, their combination seems to explain only 31 percent of variance in the 
quality of the wines.

------

# Final Plots and Summary

### Plot One
```{r Plot_One, message=FALSE, warning=FALSE, echo=FALSE}
ggplot(data = redwine, aes(alcohol / fixed.acidity, density)) +
  geom_point(aes(color = quality.group), alpha = 1 / 3, size = 1) +
  scale_color_brewer(type = "qual", palette = 2,
                     labels = c('worst', 'normal', 'best')) +
  labs(color = 'Qaulity group') +
  geom_smooth(aes(color = quality.group)) +
  xlab("Concentration of Alcohol per Fixed Acidity") +
  ylab("Density of the Wine") +
  ggtitle(label = "Density vs Alcohol and Fixed Acidity by Quality group")
```


```{r echo=FALSE}
with (data = redwine, cor.test(density, alcohol / fixed.acidity))
```


### Description One
Here we see that the Density of the Wine is strongly correlated with the Alcohol 
content of the wine and it's fixed acidity. We can as the concentration of the 
alcohol over fixed acidity increases, the density tend to decrease. We can very 
high concentration of the points 

### Plot Two

```{r Plot_Two, echo=FALSE}
ggplot(data = redwine, aes(x = quality.group, y = alcohol)) +
  geom_jitter(alpha = 0.3) +
  geom_boxplot(aes(fill = quality.group), alpha  = 0.5) + 
  stat_summary(geom = 'point', fun.y = mean, 
               color = 'red', shape = 8, size = 4) +
  scale_fill_discrete(labels = c('worst', 'normal', 'better')) +
  labs(x = "Quality Groups", y = "Concentration of Alcohol", 
            fill = 'Quality Groups') +
  ggtitle("Alcohol vs Quality Groups")
```

### Description Two
The above plot contains a lot of information. It is a boxplot of alcohol by the 
quality groups. It clearly suggests that wines of better quality tend to have
higher concentration of alcohol. This is also significant because alcohol from 
all other variables, has the strongest relationship with the wine quality.

***

### Plot Three

```{r Plot_Three, message=FALSE, warning=FALSE, echo=FALSE}
ggplot(data = redwine, aes(round(fixed.acidity / .2) * .2, pH)) + 
  geom_point(color = I('orange'), alpha = 1 / 3, size = 1) +
  geom_smooth() +
  xlab ("Fixed Acidity of the wine") +
  ylab ("pH of the wine") +
  ggtitle("pH of the wine vs it's Fixed Acidity")
  
```

### Description Three
We all know that ph and acid content have a relation among each other. we are
taught this in middle school. A liquid is consumable only at particular level of 
acidity. This graph help us showcase that innate relation between pH value of 
the wine and it's Fixed Acidity. With enough correlation, we can say that the
wine data do states the same relation among ph and acidity as it would have
been normally accepted.

------

# Reflection
Red Wine data set contained 11 physicochemical variables. I have explored all 
the variable against the output i.e the quality of the wine. While some 
variables like, alcohol, sulphates tend to have a effect on the quality of the
wine, some didn't. 

From the exploration it seems that wines with more alcohol content tend to have 
higher quality. Same goes with the sulphates as well.

The relationship between the density of the wine and the Alcohol concentration 
plus the fixed acidity comes to me as a surprise. It wasn't expected. This is 
what you get when you explore the data. For a chemist this may seems like a 
predefined relation, but for a guy with very limited knowledge with the 
chemistry of fluids this relation is a revelation. 

The main problem that I face is that, we have limited amount of data. The fact 
we have only 10, 52 and only 18 wines with qualities 3, 4 and 8, is a sense of
concern. Limited data does not help. 

While I have explored the data set to my fullest abilities, I still feel that we 
could explore the data even further by taking complex combinations of alcohol 
and sulphates at a time. These two variable have shown to have stronger 
correlation with quality of the wine that any other variables. 

This exploration will be of very menial value if we can't increase the data 
available for the lower qualities as well as higher qualities of wine. To 
understand what parameters really make the wine bad or good, we will need to 
access more data.