Title: Red Wine By Johnny Sch. Antoine
Introduction
This project is about exploring a red wine dataset in order to see how chemical properties influence the quality of red wines. The dataset is composed of 1599 observations and 13 variables.I will use one variable exploration techniques and two or more variables exploration techniques. I will try to see if there any correlations between variables. I will also use a few plots to explain the dataset. I will fit a Linear model to predict the quality of the wine based on its chemical composition.
Dataset Summary
## [1] 1599 14## [1] "X" "fixed.acidity"
## [3] "volatile.acidity" "citric.acid"
## [5] "residual.sugar" "chlorides"
## [7] "free.sulfur.dioxide" "total.sulfur.dioxide"
## [9] "density" "pH"
## [11] "sulphates" "alcohol"
## [13] "quality" "ratio.freesulfur.dioxide"## 'data.frame': 1599 obs. of 14 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide : num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : int 5 5 5 6 5 5 5 7 7 5 ...
## $ ratio.freesulfur.dioxide: num 0.324 0.373 0.278 0.283 0.324 ...## X fixed.acidity volatile.acidity citric.acid
## Min. : 1.0 Min. : 4.60 Min. :0.1200 Min. :0.000
## 1st Qu.: 400.5 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090
## Median : 800.0 Median : 7.90 Median :0.5200 Median :0.260
## Mean : 800.0 Mean : 8.32 Mean :0.5278 Mean :0.271
## 3rd Qu.:1199.5 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420
## Max. :1599.0 Max. :15.90 Max. :1.5800 Max. :1.000
## residual.sugar chlorides free.sulfur.dioxide
## Min. : 0.900 Min. :0.01200 Min. : 1.00
## 1st Qu.: 1.900 1st Qu.:0.07000 1st Qu.: 7.00
## Median : 2.200 Median :0.07900 Median :14.00
## Mean : 2.539 Mean :0.08747 Mean :15.87
## 3rd Qu.: 2.600 3rd Qu.:0.09000 3rd Qu.:21.00
## Max. :15.500 Max. :0.61100 Max. :72.00
## total.sulfur.dioxide density pH sulphates
## Min. : 6.00 Min. :0.9901 Min. :2.740 Min. :0.3300
## 1st Qu.: 22.00 1st Qu.:0.9956 1st Qu.:3.210 1st Qu.:0.5500
## Median : 38.00 Median :0.9968 Median :3.310 Median :0.6200
## Mean : 46.47 Mean :0.9967 Mean :3.311 Mean :0.6581
## 3rd Qu.: 62.00 3rd Qu.:0.9978 3rd Qu.:3.400 3rd Qu.:0.7300
## Max. :289.00 Max. :1.0037 Max. :4.010 Max. :2.0000
## alcohol quality ratio.freesulfur.dioxide
## Min. : 8.40 Min. :3.000 Min. :0.02273
## 1st Qu.: 9.50 1st Qu.:5.000 1st Qu.:0.25926
## Median :10.20 Median :6.000 Median :0.37500
## Mean :10.42 Mean :5.636 Mean :0.38231
## 3rd Qu.:11.10 3rd Qu.:6.000 3rd Qu.:0.48485
## Max. :14.90 Max. :8.000 Max. :0.85714Univariate Plots Section
## Scale for 'x' is already present. Adding another scale for 'x', which
## will replace the existing scale.## Warning: Removed 78 rows containing non-finite values (stat_bin).## Warning: Removed 2 rows containing missing values (geom_bar).
Fixed acidy appeared positively skewed and we know a big chunk of the data fall between 7 and 9. we took care of a few outliers by excusing the top 5%.
Volatile acidity appeared to be normally distributed and we know a big chunk of the data falls between 0.3 and 0.7. we use the log10 transformation because volatile acidity just works better with that transformation.
## Warning: Removed 78 rows containing non-finite values (stat_bin).
The histogram of citric acid shows that this variable is neither normally distributed nor skewed. There are spikes between 0 and 0.04, between 0.5 and 0.10, between 0.2 and 0.3, and also between 0.4 and 0.6. We also took care of some outliers by excluding the top 5%.
## Warning: Removed 79 rows containing non-finite values (stat_bin).
We have a normal distribution for residual sugar. If I have not excluded the top 5% there would be a tail on the right side of the plot.
The chlorides histogram is mostly normally distributed with a long tail on the right. The range for this variable is really small it is between 0.012 and 0.37. We use the log10 transformation and it made the histogram look a little bit more normal.
## Warning: Removed 77 rows containing non-finite values (stat_bin).
The histogram of free sulfur dioxide shows that the data is positively skewed and there is a pick between 5 and 8. Most of the data lies between 0 and 40. We excluded the top 5%, which helps with outliers.
## Warning: Removed 80 rows containing non-finite values (stat_bin).## Warning: Removed 1 rows containing missing values (geom_bar).
The histogram of total sulfur dioxide shows that the data is positively skewed. Most of the data fall between 0 and 110. We excluded the top 5%, which helps with outliers.
The density histogram shows a normal distribution when I use the logarithmic scale.
Just like the density Histogram the pHs show a fairly normally distributed plot when using the logarithmic scale.
The sulfate Histogram shows more of a normal shape when we use the logarithmic function as a transformation.
## Warning: Removed 70 rows containing non-finite values (stat_bin).
The alcohol histogram is positively skewed.
## Warning: Ignoring unknown parameters: binwidth, bins, pad
The quality histogram is normally distributed. It also shows that the worst wine and the great one are outliers and most of the wine of just average.
The ratio.freesulfur.dioxide histogram is negatively skewed when using the logarithmic function.
Univariate Analysis
What is the structure of your dataset?
I chose the red wine dataset, the original data set was composed of 1599 observations, and 13 variables. The quality feature is an ordered categorical variable, while all others are either numerical or integer variables. Most of the variables have a skewed distribution with a long tail either on the left or on the right.
What is/are the main feature(s) of interest in your dataset?
The main feature of interest is the quality which is basically the quality of the wine we are going to analyze the data to see which features has a significant influence on the quality of a red wine. The quality of the wine in this dataset lies between 3 and 8.
What other features in the dataset do you think will help support your
investigation into your feature(s) of interest?
Without analyzing the data I would say almost all the variable will help supporting my investigation. The fixed. acidity, the volatile. acidity the citric. acidic, the pH, the residual sugar, etc… I expect all of them to be a factor in the quality of a wine.
Did you create any new variables from existing variables in the dataset?
Without analyzing the data I would say almost all the variable will help supporting my investigation. The fixed. acidity, the volatile. acidity the citric. acidic, the pH, the residual sugar, etc… I expect all of them to be a factor in the quality of a wine.
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?
Yes, while I was plotting the variation I made sure I excluded the top 5% in for some plots to get rid of outliers I also use the logarithmic function in some plots because some features do not work on the normal scale they are much better represented on the logarithmic scale.
Bivariate Plots Section
cor(redwine,method="pearson")## X fixed.acidity volatile.acidity
## X 1.000000000 -0.26848392 -0.008815099
## fixed.acidity -0.268483920 1.00000000 -0.256130895
## volatile.acidity -0.008815099 -0.25613089 1.000000000
## citric.acid -0.153551355 0.67170343 -0.552495685
## residual.sugar -0.031260835 0.11477672 0.001917882
## chlorides -0.119868519 0.09370519 0.061297772
## free.sulfur.dioxide 0.090479643 -0.15379419 -0.010503827
## total.sulfur.dioxide -0.117849669 -0.11318144 0.076470005
## density -0.368372087 0.66804729 0.022026232
## pH 0.136005328 -0.68297819 0.234937294
## sulphates -0.125306999 0.18300566 -0.260986685
## alcohol 0.245122841 -0.06166827 -0.202288027
## quality 0.066452608 0.12405165 -0.390557780
## ratio.freesulfur.dioxide 0.335438942 -0.13081236 -0.072618561
## citric.acid residual.sugar chlorides
## X -0.15355136 -0.031260835 -0.119868519
## fixed.acidity 0.67170343 0.114776724 0.093705186
## volatile.acidity -0.55249568 0.001917882 0.061297772
## citric.acid 1.00000000 0.143577162 0.203822914
## residual.sugar 0.14357716 1.000000000 0.055609535
## chlorides 0.20382291 0.055609535 1.000000000
## free.sulfur.dioxide -0.06097813 0.187048995 0.005562147
## total.sulfur.dioxide 0.03553302 0.203027882 0.047400468
## density 0.36494718 0.355283371 0.200632327
## pH -0.54190414 -0.085652422 -0.265026131
## sulphates 0.31277004 0.005527121 0.371260481
## alcohol 0.10990325 0.042075437 -0.221140545
## quality 0.22637251 0.013731637 -0.128906560
## ratio.freesulfur.dioxide -0.16693889 -0.070626080 -0.105156413
## free.sulfur.dioxide total.sulfur.dioxide
## X 0.090479643 -0.11784967
## fixed.acidity -0.153794193 -0.11318144
## volatile.acidity -0.010503827 0.07647000
## citric.acid -0.060978129 0.03553302
## residual.sugar 0.187048995 0.20302788
## chlorides 0.005562147 0.04740047
## free.sulfur.dioxide 1.000000000 0.66766645
## total.sulfur.dioxide 0.667666450 1.00000000
## density -0.021945831 0.07126948
## pH 0.070377499 -0.06649456
## sulphates 0.051657572 0.04294684
## alcohol -0.069408354 -0.20565394
## quality -0.050656057 -0.18510029
## ratio.freesulfur.dioxide 0.327240869 -0.37143493
## density pH sulphates alcohol
## X -0.36837209 0.13600533 -0.125306999 0.24512284
## fixed.acidity 0.66804729 -0.68297819 0.183005664 -0.06166827
## volatile.acidity 0.02202623 0.23493729 -0.260986685 -0.20228803
## citric.acid 0.36494718 -0.54190414 0.312770044 0.10990325
## residual.sugar 0.35528337 -0.08565242 0.005527121 0.04207544
## chlorides 0.20063233 -0.26502613 0.371260481 -0.22114054
## free.sulfur.dioxide -0.02194583 0.07037750 0.051657572 -0.06940835
## total.sulfur.dioxide 0.07126948 -0.06649456 0.042946836 -0.20565394
## density 1.00000000 -0.34169933 0.148506412 -0.49617977
## pH -0.34169933 1.00000000 -0.196647602 0.20563251
## sulphates 0.14850641 -0.19664760 1.000000000 0.09359475
## alcohol -0.49617977 0.20563251 0.093594750 1.00000000
## quality -0.17491923 -0.05773139 0.251397079 0.47616632
## ratio.freesulfur.dioxide -0.26497991 0.18489507 -0.010459139 0.24627450
## quality ratio.freesulfur.dioxide
## X 0.06645261 0.33543894
## fixed.acidity 0.12405165 -0.13081236
## volatile.acidity -0.39055778 -0.07261856
## citric.acid 0.22637251 -0.16693889
## residual.sugar 0.01373164 -0.07062608
## chlorides -0.12890656 -0.10515641
## free.sulfur.dioxide -0.05065606 0.32724087
## total.sulfur.dioxide -0.18510029 -0.37143493
## density -0.17491923 -0.26497991
## pH -0.05773139 0.18489507
## sulphates 0.25139708 -0.01045914
## alcohol 0.47616632 0.24627450
## quality 1.00000000 0.19411335
## ratio.freesulfur.dioxide 0.19411335 1.00000000
This graph shows correlationships between variables in the dataset.
This graph shows correlationships between variables in the dataset.
By looking at this graph we can see there is a trend that the quality of the wine increase when we add more alcohol to the wine.
The correlation is not that big, but it is a positive one the more sulphates we have in the wine the better the quality.
Quality and volatile acidity are negatively correlated, it means that as long as we have volatile acidity the less we have the better the quality will be.
The quality of the wine is strongly and positively correlate to citric acid.
The following plots are some features other than quality that are strongly correlated
pH and fixed acidity are strongly and negatively correlated
Free sulfur dioxide and total Sulfur dioxide are strongly and positively correlated.
Fixed acidity and density are strongly and positively correlated
citric acid and fixed acidity are positively and strongly correlated
Bivariate Analysis
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?
Did you observe any interesting relationships between the other features
(not the main feature(s) of interest)?
There were some very strong correlations between PH and fixed acidity, free sulfure dioxide and total sulfur dioxide, density and fixed acidity, citric acid and volatile acid, citric acid and fixed acidity. Fixed acidity has strong correlation with several of other features.
What was the strongest relationship you found?
The strongest relationship (correlation) is between fixed acidity and pH(-0.68). It’s followed by fixed acidity and citric acid (0.67), then fixed acidity and density(0.668), and total sulfur dioxide and free sulfur dioxide (0.667).
Multivariate Plots Section
We can see that quality is better as volatile acidity is low and alcohol is high.
We can see that quality is better as alcohol and sulphate increase.
We can see that quality is better with increasing sulphates and a lower volatile acidity
We can see that the quality is better with increase of citric acid and a decreasing volatile acidity.
##
## Calls:
## m1: lm(formula = quality ~ log10(volatile.acidity), data = redwine)
## m2: lm(formula = quality ~ log10(volatile.acidity) + alcohol, data = redwine)
## m3: lm(formula = quality ~ log10(volatile.acidity) + alcohol + log10(sulphates),
## data = redwine)
## m4: lm(formula = quality ~ log10(volatile.acidity) + alcohol + log10(sulphates) +
## citric.acid, data = redwine)
## m5: lm(formula = quality ~ log10(volatile.acidity) + alcohol + log10(sulphates) +
## citric.acid + fixed.acidity, data = redwine)
## m6: lm(formula = quality ~ log10(volatile.acidity) + alcohol + log10(sulphates) +
## citric.acid + fixed.acidity + residual.sugar, data = redwine)
## m7: lm(formula = quality ~ log10(volatile.acidity) + alcohol + log10(sulphates) +
## citric.acid + fixed.acidity + residual.sugar + log10(pH),
## data = redwine)
## m8: lm(formula = quality ~ log10(volatile.acidity) + alcohol + log10(sulphates) +
## citric.acid + fixed.acidity + residual.sugar + log10(pH) +
## log10(chlorides), data = redwine)
## m9: lm(formula = quality ~ log10(volatile.acidity) + alcohol + log10(sulphates) +
## citric.acid + fixed.acidity + residual.sugar + log10(pH) +
## log10(chlorides) + log10(density), data = redwine)
## m10: lm(formula = quality ~ log10(volatile.acidity) + alcohol + log10(sulphates) +
## citric.acid + fixed.acidity + residual.sugar + log10(pH) +
## log10(chlorides) + log10(density) + free.sulfur.dioxide,
## data = redwine)
## m11: lm(formula = quality ~ log10(volatile.acidity) + alcohol + log10(sulphates) +
## citric.acid + fixed.acidity + residual.sugar + log10(pH) +
## log10(chlorides) + log10(density) + free.sulfur.dioxide +
## total.sulfur.dioxide, data = redwine)
## m12: lm(formula = quality ~ log10(volatile.acidity) + alcohol + log10(sulphates) +
## citric.acid + fixed.acidity + residual.sugar + log10(pH) +
## log10(chlorides) + log10(density) + free.sulfur.dioxide +
## total.sulfur.dioxide + ratio.freesulfur.dioxide, data = redwine)
##
## ====================================================================================================================================================================================================
## m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12
## ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
## (Intercept) 5.012*** 1.938*** 2.415*** 2.438*** 1.969*** 1.970*** 3.397*** 3.505*** 3.073*** 3.140*** 4.024*** 3.942***
## (0.041) (0.165) (0.171) (0.172) (0.207) (0.208) (0.659) (0.657) (0.796) (0.797) (0.819) (0.820)
## log10(volatile.acidity) -2.057*** -1.567*** -1.300*** -1.372*** -1.455*** -1.455*** -1.452*** -1.301*** -1.273*** -1.277*** -1.151*** -1.166***
## (0.121) (0.112) (0.114) (0.133) (0.134) (0.135) (0.135) (0.140) (0.143) (0.143) (0.145) (0.145)
## alcohol 0.309*** 0.299*** 0.299*** 0.308*** 0.308*** 0.318*** 0.299*** 0.279*** 0.275*** 0.267*** 0.267***
## (0.016) (0.016) (0.016) (0.016) (0.016) (0.017) (0.017) (0.026) (0.027) (0.027) (0.027)
## log10(sulphates) 1.517*** 1.557*** 1.549*** 1.549*** 1.544*** 1.760*** 1.810*** 1.837*** 1.832*** 1.819***
## (0.177) (0.181) (0.181) (0.181) (0.181) (0.188) (0.195) (0.196) (0.195) (0.195)
## citric.acid -0.109 -0.466*** -0.465*** -0.519*** -0.414** -0.406** -0.403** -0.242 -0.235
## (0.105) (0.137) (0.138) (0.140) (0.142) (0.142) (0.142) (0.146) (0.146)
## fixed.acidity 0.052*** 0.052*** 0.036* 0.030* 0.049 0.047 0.023 0.020
## (0.013) (0.013) (0.015) (0.015) (0.025) (0.025) (0.026) (0.026)
## residual.sugar -0.000 -0.000 0.003 0.012 0.016 0.018 0.017
## (0.012) (0.012) (0.012) (0.015) (0.015) (0.015) (0.015)
## log10(pH) -2.649* -3.392** -2.579 -2.566 -3.730* -3.737*
## (1.161) (1.171) (1.443) (1.442) (1.460) (1.460)
## log10(chlorides) -0.534*** -0.510*** -0.517*** -0.583*** -0.576***
## (0.134) (0.137) (0.137) (0.137) (0.137)
## log10(density) -49.448 -52.290 -34.609 -20.123
## (51.307) (51.337) (51.230) (51.959)
## free.sulfur.dioxide -0.002 0.004 -0.001
## (0.002) (0.002) (0.004)
## total.sulfur.dioxide -0.003*** -0.001
## (0.001) (0.001)
## ratio.freesulfur.dioxide 0.354
## (0.216)
## ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
## R-squared 0.153 0.311 0.341 0.342 0.348 0.348 0.350 0.357 0.357 0.358 0.365 0.366
## adj. R-squared 0.153 0.310 0.340 0.340 0.346 0.346 0.347 0.353 0.353 0.354 0.361 0.361
## sigma 0.743 0.671 0.656 0.656 0.653 0.653 0.652 0.649 0.649 0.649 0.646 0.645
## F 288.647 359.989 275.225 206.705 170.163 141.714 122.534 110.189 98.045 88.466 82.943 76.337
## p 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -1793.802 -1628.955 -1593.104 -1592.555 -1584.495 -1584.495 -1581.883 -1573.978 -1573.511 -1572.601 -1563.504 -1562.150
## Deviance 882.635 718.183 686.690 686.218 679.335 679.335 677.119 670.457 670.066 669.303 661.731 660.611
## AIC 3593.604 3265.910 3196.209 3197.110 3182.990 3184.990 3181.765 3167.956 3169.022 3169.202 3153.009 3152.299
## BIC 3609.735 3287.419 3223.095 3229.372 3220.630 3228.007 3230.159 3221.728 3228.170 3233.728 3222.912 3227.579
## N 1599 1599 1599 1599 1599 1599 1599 1599 1599 1599 1599 1599
## ====================================================================================================================================================================================================The linear regression we fit can only predict 36.6% of the quality of a wine.
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?
Alcohol is the feature with the strongest correlationship with quality. I was rather surprised to see that residual sugar did not have a stronger correlation with quality. Fixed acidity has a strong correlation with 3 other features. It has a strong relationship with citric acid, with density and with pH.
Were there any interesting or surprising interactions between features?
Like we have mentioned before, fixed acidity has a strong correlation with pH, density and free sulfur dioxide. I think it’s interesting to see one feature has a strong correlation with three other features.
OPTIONAL: Did you create any models with your dataset? Discuss the strengths and limitations of your model.
Yes, I did create one linear regression and it can only account for 36.6% of wine quality prediction.
Final Plots and Summary
Plot One
## Warning: Ignoring unknown parameters: binwidth, bins, pad
Description One
The graph above show that most of the wines have a quality of 5 or 6 just a few have a quality of 3 or 4 or 8. It just showed the distribution of the wines by quality.
Plot Two
## Warning: Removed 3 rows containing non-finite values (stat_smooth).## Warning: Removed 3 rows containing missing values (geom_point).
Description Two
Those two features have on of the strongest correlationship in the dataset. I find it interesting because people tend to think because a correlation is negative it’s not strong correlationship. I wanted to show a graph with a strong negative correlation, and that’s the kind of relationship we have between fixed acidity and pH in that dataset.
Plot Three
Description Three
This graph above shows the correlation between quality and alcohol, it’s positive and it is the strongest correlation that quality have with any feature in the datasett.