MATH2319_Phase1
s3686502 Dan Enoka
2 April 2018
—————————– Standard Approach ———— Phase 1 ————–
This dataset is Obtained from and is also available from the UCI machine learning repository,
Objective: Use machine learning to determine which physiochemical
properties make a wine ‘good’!
For Phase 1 , Regression Analysis will be used.
For phase 2 , Machine Learning will used.
And then one will used to compare against the other.
Definition of physiochemical: (of or pertaining to both physical and chemical properties, changes, and reactions. of or according to physical chemistry.)
Wine Quality in this data set is classified as being, if
equal to “6” = Good , equal to “7” = Good Plus ,
if equal to “8” = Very Good.
The highest value in this data set is “8”
Please Note: Acknowledgements are at the End of this Presentation.
Content: (Or Name per each Column) For more information, read [Cortez et al., 2009]. Input variables (based on physicochemical tests): 1 - fixed acidity 2 - volatile acidity 3 - citric acid 4 - residual sugar 5 - chlorides 6 - free sulfur dioxide 7 - total sulfur dioxide 8 - density 9 - pH 10 - sulphates 11 - alcohol Output variable (based on sensory data): 12 - quality (score between 0 and 10)
What follows is an attempt to come to an understanding of the data,
and hopefully of how each column relates to one another.
## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. : 4.60 Min. :0.1200 Min. :0.000 Min. : 0.900
## 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090 1st Qu.: 1.900
## Median : 7.90 Median :0.5200 Median :0.260 Median : 2.200
## Mean : 8.32 Mean :0.5278 Mean :0.271 Mean : 2.539
## 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420 3rd Qu.: 2.600
## Max. :15.90 Max. :1.5800 Max. :1.000 Max. :15.500
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## Min. :0.01200 Min. : 1.00 Min. : 6.00
## 1st Qu.:0.07000 1st Qu.: 7.00 1st Qu.: 22.00
## Median :0.07900 Median :14.00 Median : 38.00
## Mean :0.08747 Mean :15.87 Mean : 46.47
## 3rd Qu.:0.09000 3rd Qu.:21.00 3rd Qu.: 62.00
## Max. :0.61100 Max. :72.00 Max. :289.00
## density pH sulphates alcohol
## Min. :0.9901 Min. :2.740 Min. :0.3300 Min. : 8.40
## 1st Qu.:0.9956 1st Qu.:3.210 1st Qu.:0.5500 1st Qu.: 9.50
## Median :0.9968 Median :3.310 Median :0.6200 Median :10.20
## Mean :0.9967 Mean :3.311 Mean :0.6581 Mean :10.42
## 3rd Qu.:0.9978 3rd Qu.:3.400 3rd Qu.:0.7300 3rd Qu.:11.10
## Max. :1.0037 Max. :4.010 Max. :2.0000 Max. :14.90
## quality
## Min. :3.000
## 1st Qu.:5.000
## Median :6.000
## Mean :5.636
## 3rd Qu.:6.000
## Max. :8.000Plots and various attempts at understanding the inter-relationship of the columns
You can also embed plots, for example: 
## NULL## The following objects are masked from Wine (pos = 3):
##
## alcohol, chlorides, citric.acid, density, fixed.acidity,
## free.sulfur.dioxide, pH, quality, residual.sugar, sulphates,
## total.sulfur.dioxide, volatile.acidity## # A tibble: 11 x 2
## rowname quality
## <chr> <dbl>
## 1 fixed.acidity 0.124
## 2 volatile.acidity -0.391
## 3 citric.acid 0.226
## 4 residual.sugar 0.0137
## 5 chlorides -0.129
## 6 free.sulfur.dioxide -0.0507
## 7 total.sulfur.dioxide -0.185
## 8 density -0.175
## 9 pH -0.0577
## 10 sulphates 0.251
## 11 alcohol 0.476Note that the , echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.
## The following objects are masked _by_ .GlobalEnv:
##
## alcohol, quality## The following objects are masked from Wine (pos = 3):
##
## alcohol, chlorides, citric.acid, density, fixed.acidity,
## free.sulfur.dioxide, pH, quality, residual.sugar, sulphates,
## total.sulfur.dioxide, volatile.acidity## The following objects are masked from Wine (pos = 4):
##
## alcohol, chlorides, citric.acid, density, fixed.acidity,
## free.sulfur.dioxide, pH, quality, residual.sugar, sulphates,
## total.sulfur.dioxide, volatile.acidity
## # A tibble: 11 x 2
## rowname quality
## <chr> <dbl>
## 1 fixed.acidity 0.124
## 2 volatile.acidity -0.391
## 3 citric.acid 0.226
## 4 residual.sugar 0.0137
## 5 chlorides -0.129
## 6 free.sulfur.dioxide -0.0507
## 7 total.sulfur.dioxide -0.185
## 8 density -0.175
## 9 pH -0.0577
## 10 sulphates 0.251
## 11 alcohol 0.476This section below (fit) is as yet unfinished, in that I intend to use the Regression Model in
the below Equation in testing against a random selection from the actual data set. And from
this try to derive if this Equation is sufficient for prediction purposes.
I then intend to see if the the Machine Learning derived Equation
would be a better fit.
##
## Call:
## lm(formula = quality ~ alcohol + sulphates + citric.acid + volatile.acidity,
## data = Wine)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.71408 -0.38590 -0.06402 0.46657 2.20393
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.64592 0.20106 13.160 < 2e-16 ***
## alcohol 0.30908 0.01581 19.553 < 2e-16 ***
## sulphates 0.69552 0.10311 6.746 2.12e-11 ***
## citric.acid -0.07913 0.10381 -0.762 0.446
## volatile.acidity -1.26506 0.11266 -11.229 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6588 on 1594 degrees of freedom
## Multiple R-squared: 0.3361, Adjusted R-squared: 0.3345
## F-statistic: 201.8 on 4 and 1594 DF, p-value: < 2.2e-16## Quality = - 2.646 x alcohol + 0.309 x alcohol + 0.696 x sulphates -0.079 x citric.acid -1.265 x volatile.acidity
## 2.5 % 97.5 %
## (Intercept) 2.2515575 3.0402782
## alcohol 0.2780728 0.3400835
## sulphates 0.4932780 0.8977542
## citric.acid -0.2827462 0.1244961
## volatile.acidity -1.4860436 -1.0440733## Analysis of Variance Table
##
## Response: quality
## Df Sum Sq Mean Sq F value Pr(>F)
## alcohol 1 236.29 236.295 544.413 < 2.2e-16 ***
## sulphates 1 44.98 44.977 103.624 < 2.2e-16 ***
## citric.acid 1 14.32 14.318 32.987 1.109e-08 ***
## volatile.acidity 1 54.72 54.724 126.081 < 2.2e-16 ***
## Residuals 1594 691.85 0.434
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## (Intercept) alcohol sulphates citric.acid
## (Intercept) 0.040423190 -2.717029e-03 -6.257782e-03 -0.004778726
## alcohol -0.002717029 2.498724e-04 -7.273176e-05 0.000019016
## sulphates -0.006257782 -7.273176e-05 1.063090e-02 -0.002245641
## citric.acid -0.004778726 1.901600e-05 -2.245641e-03 0.010776802
## volatile.acidity -0.012160812 2.942844e-04 1.189162e-03 0.005945653
## volatile.acidity
## (Intercept) -0.0121608117
## alcohol 0.0002942844
## sulphates 0.0011891619
## citric.acid 0.0059456529
## volatile.acidity 0.0126931742—————————– Attempt at Machine Learning ———— Phase 2 ————–
## name type na mean disp median mad min max
## 1 fixed.acidity character 0 NA 0.9581119 NA NA 1 134
## 2 volatile.acidity character 0 NA 0.9706158 NA NA 1 94
## 3 citric.acid character 0 NA 0.9174742 NA NA 1 264
## 4 residual.sugar character 0 NA 0.9024695 NA NA 1 312
## 5 chlorides character 0 NA 0.9587371 NA NA 1 132
## 6 free.sulfur.dioxide character 0 NA 0.9137230 NA NA 1 276
## 7 total.sulfur.dioxide character 0 NA 0.9731166 NA NA 1 86
## 8 density character 0 NA 0.9774930 NA NA 1 72
## 9 pH character 0 NA 0.9643639 NA NA 1 114
## 10 sulphates character 0 NA 0.9568615 NA NA 1 138
## 11 alcohol character 0 NA 0.9130978 NA NA 1 278
## 12 quality character 0 NA 0.5742420 NA NA 1 1362
## nlevs
## 1 97
## 2 144
## 3 81
## 4 92
## 5 154
## 6 61
## 7 145
## 8 437
## 9 90
## 10 97
## 11 66
## 12 7## 'data.frame': 3199 obs. of 12 variables:
## $ fixed.acidity : chr "fixed acidity" "7.4" "7.8" "7.8" ...
## $ volatile.acidity : chr "volatile acidity" "0.7" "0.88" "0.76" ...
## $ citric.acid : chr "citric acid" "0" "0" "0.04" ...
## $ residual.sugar : chr "residual sugar" "1.9" "2.6" "2.3" ...
## $ chlorides : chr "chlorides" "0.076" "0.098" "0.092" ...
## $ free.sulfur.dioxide : chr "free sulfur dioxide" "11" "25" "15" ...
## $ total.sulfur.dioxide: chr "total sulfur dioxide" "34" "67" "54" ...
## $ density : chr "density" "0.9978" "0.9968" "0.997" ...
## $ pH : chr "pH" "3.51" "3.2" "3.26" ...
## $ sulphates : chr "sulphates" "0.56" "0.68" "0.65" ...
## $ alcohol : chr "alcohol" "9.4" "9.8" "9.8" ...
## $ quality : chr "quality" "5" "5" "5" ...