Quality

The distribution of wine shows that most of wines have a quality between 5-6 points. The mean value is 5.64 and the median 6.

Figure 3.1: Quality distribution

Fixed and volatile acidity, citric acidity

The plot 3.2 shows the distribution of fixed acidity, volatile acidity and citric acidity.

• Fixed acidity is negatively skewed with mean 8.32 and median 7.9.

• The volatile acidity is positively skewed with mean 0.53 and median 0.52.

• The citric acidity appears to be a bimodal or even a trimodal distribution with overall mean 0.27 and median 0.26.

Figure 3.2: Fixed acidity, volatile acidity and citric acid distribution

Residual sugar

• The plot of residual suggar (3.3 ) is positively skewed with mean 2.54 and median 2.2.
• There was a noticeable presence of outliers in the upper part of the graphic. These outliers were removed by applying a filter and keeping the values of the residual sugar in the range $x > \mu \pm3\sigma$.

Figure 3.3: Residual sugar distribution

Chlorides, free sulfur dioxide and total sulfur dioxide

The plot 3.4 shows chlorides, free sulfur dioxide and total sulfur dioxide levels distribution.

• The distribution of chlorides is positively skewed with mean 0.087 and median 0.079. Outliers 3 standard deviation away from the mean were removed as in the case of residual sugar.

• The free sulfur dioxide is positively skewed with mean 16 and median 14.

• The total sulfur dioxide is positively skewed with mean 46 and median 38.

Figure 3.4: Chlorides and sulfur dioxide distributions

Density, pH, sulphates and alcohol

The plot 3.5 shows density, pH, sulphates and alcohol distributions.

• The distribution of density seems to be a symmetrical normal distribution with mean 0.9967 and median 0.9968.

• The pH distribution seems to be negatively skewed with mean 3.31 and median 3.31.

• The sulphates distribution is positively skewed with mean 0.66 and median 0.62.

• The alcohol distribution is positively skewed with mean 10.4 and median 10.2.
  

  Figure 3.5: Density, pH, sulphates and alcohol distributions

What is the structure of your dataset?

There are 1599 red wines with 12 features (fixed.acidity, volatile.acidity, citric.acid, residual.sugar, chlorides, free.sulfur.dioxide, total.sulfur.dioxide, density, pH, sulphates, alcohol and quality).

Other observations:

Table 3.1 shows that the mean quality of the red wines is 5.636 and the median is 6. Q1 division corresponds to 5 and Q3 to 6, hence, 50% of the data lays within 5-6 range of quality, this is the level MEDIUM.

What is/are the main feature(s) of interest in your dataset?

The main feature of interest in this dataset is 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?

In [1] it is shown that the most imporant features for assessing Red Wine quality are: sulphates, pH and total sulfur dioxide. An analysis will be performed in order to certify whether these are the most importart features for the analysis or others are.

Did you create any new variables from existing variables in the dataset?

I did not create any new variables to support the analysis since the amount of information available is enough to assess the quality of the wine.

However, the variable quality was converted in a factor variable (adding a new variable named quality.cat) with the following levels:

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?

Most of the features had a normal distribution. Some of the them had quite skewed distributions and many oultiers.

In the histograms, some of the varaibles, like residual sugar or chlorides show long tails, what indicates the presence of outliers. For a better view, I tried to remove those outliers located 3 standard deviations away from the mean ($x > \mu \pm3\sigma$).

Figure 3.6: Residual sugar and Chlorides distributions with original and log10() transformed axis

It could also be also useful to perform a log10 tranformation in order to have a better view. The efect of this transformation can be observed in figure 3.7, where charateristics of plots in the left side are seen better after the x axis is transformed.

Figure 3.7: Residual sugar and Chlorides distributions with original and log10() transformed axis

Correlation betweeen variables

In the next figure (fig.4.1) it is shown the correlation factor between the different variables in the Red Wines dataset. Significant correlation values ($|\rho|>0.3$) are highlighted with stronger color density the higher the correlation value is.

Figure 4.1: Correlation bewteen Red Wine’s dataset features

For the purpose of this analysis, the focus will be placed in the relationship between quality and other variables.

Correlation between variables by quality range

Let us now analyze the correlation between the variables for each quality range in figure 4.2. It can be seen that some features are more correlated between them for lower quality wine. Some strong relationships between variables are kept for all quality ranges, as pH-density, pH-citric acidity and ph-fixed acidity, or fixed acidity-volatile acidity and fixed acid-fixed acidity.

Figure 4.2: Correlation vs Quality

From the general correlation matrix (fig.4.1), three main variables can be selected due to their high correlation with quality: alcohol ($\rho=$ 0.48 ), volatile.acidity ($\rho=$ -0.39 ) and sulphates ($\rho=$ 0.25 ). In order to see if they are suitable to perform an analysis let us explore the correlation between them and also the distribution of samples in bivariate plots in figure 4.3.

Figure 4.3: Correlation between alcohol, volatile acidity and sulphates

From plot 4.3 it is observed that there is a strong relationship between the sulphates and volatile acidity, and less strong between alcohol and volatile acidity.

Let us now explore the three variables suggested in [1] as the most imporant features for assessing Red Wine quality are: sulphates, pH and total sulfur dioxide.

Figure 4.4: Correlation between total sulfur dioxide, pH and sulphates

Figure 4.3 shows that the strongest relationship is between sulphates and pH ($\rho=-0.2$) followed by pH-total sulfur dioxide.

From figure 4.4 and 4.3 it can be concluded the varibles in the second figure, sulphates, pH and total sulfur dioxide (the ones suggested by [1]), are less correlated between them and lead to a more accurate analysis.

Fixed and volatile acidity, citric acid

In the next plot (fig.4.5) it is deduced that:

• the quality of the wine is directly proportional to the fixed acidity and citric acidity levels.

• the quality of the wine is inversely proportional to the volatile acidity.

• Better wines tend to have an acid hint but with low vinegar reminiscence. They tend to have a frehser taste, related to citric notes.

• Worse wines have dominant pressence of vinegar taste.

Figure 4.5: Fixed and volatile acidity distributions per quality segment

Residual sugar

The plot of residual suggar (4.6) shows that:

• the better the wine the higher the residual sugar levels.

Outliers further than $\pm 3 \sigma$ from the mean have been removed.

Figure 4.6: Residual sugar distribution per quality segment

Chlorides, free sulfur dioxide and total sulfur dioxide

• In the plot of the chlorides, it can be observed that the better the wine, the lower the chloride levels.
• For the sulfur dioxide, either the free or the total sulfur dioxide, high levels are indicator of medium quality, whereas bad and good wine have the same low amount of sulfure dioxide. There is not a linear relationship between sulfur dioxide (SO2) and the wine quality.

Outliers further than $\pm 3 \sigma$ from the mean have been removed for chlorides.

• Better wines are not salty

• Worse wines have a salty taste

Figure 4.7: Chlorides and sulfur dioxide distributions per quality segment

Density, pH, sulphates and alcohol

The next plot shows that:

• generally, the lower the density, the better the quality of the wine.

• low pH levels are sign of better quality.

• the higher the sulphates level, the better quality of the wine.

• the higher amount of alcohol the better the wine.

• Better wines tend to be less dense (density is related to sugar and alcohol), more acid (lower pH, we already commented this), with more sulphates (related to SO2) and more alcohol pressence.

• Worse wines are denser, and have less alcohol percentage per volume. They also tend to be more basic (higher pH, less acid) and have lower levels of sulphates

Figure 4.8: Density, pH, suplhates and alcohol distributions per quality segment

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 correlation between three main variables (fig.4.9) and the quality of wine is:

• sulphates vs quality: $\rho=$ 0.25.
• pH vs quality: $\rho=$ -0.06.
• total sulfur dioxide vs quality: $\rho=$ -0.19.

Figure 4.9: Sulphates, pH and total sulfur dioxide vs quality

From the plot it can be concluded that:

• Better wines tend to be more acid (lower pH, we already commented this), with more sulphates (related to SO2) and more total sulfur dioxide levels (also related to SO2).

• Worse wines tend to be more basic (higher pH, less acid) and have lower levels of sulphates and total sulfur dioxide

Did you observe any interesting relationships between the other features (not the main feature(s) of interest)? What was the strongest relationship you found?

Figure 4.1 shows the correlation between the variables in the dataset. The strongest are these pairs: citric acid -fixed acidity, total sulfur dioxide - free sulfur dioxide, density- fixed acidity and pH - fixed acidity.

It is logical that citric acidity influences fixed acidity, as does free sulfur dioxide with total sulfur dioxide. pH is known to be related to the acid levels, so no surprise here. I did not know there was such a strong relationship between density and fixed acidity.

Figure 4.10 shows the relationship between fixed acidity and density, and between fixed acidity and pH. Fixed acidity and density have a strong positive correlation ($\rho=$ 0.67) and fixed acidity and pH show a strong negative correlation ($\rho=$ -0.68).

Figure 4.10: Density and pH vs fixed acidity

Description Three

Figure 7.3 shows the distribution of citric acid vs quality. It can be observed how higher quality wines have more levels of citic acid than lower quality wine. I really liked this conclusion, and that is why it is included here, because I always thought it would be the opposite, that lower quality wine would be the more acid.