MATH2319_Phase1
s3686502 Dan Enoka
2 April 2018
——— Standard Approach —– Phase 1 ——-
# 1. Packages ---- Phase 1 -------
library(knitr)
library(mlr)## Loading required package: ParamHelperslibrary(GGally)## Loading required package: ggplot2library(cowplot)##
## Attaching package: 'cowplot'## The following object is masked from 'package:ggplot2':
##
## ggsavelibrary(car)## Loading required package: carDatalibrary(readr)
library(corrr)## Loading required package: dplyr##
## Attaching package: 'dplyr'## The following object is masked from 'package:car':
##
## recode## The following object is masked from 'package:GGally':
##
## nasa## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(tidyverse)## -- Attaching packages ---------------------------------- tidyverse 1.2.1 --## v tibble 1.4.2 v purrr 0.2.4
## v tidyr 0.8.1 v stringr 1.3.1
## v tibble 1.4.2 v forcats 0.3.0## -- Conflicts ------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x cowplot::ggsave() masks ggplot2::ggsave()
## x dplyr::lag() masks stats::lag()
## x dplyr::recode() masks car::recode()
## x purrr::some() masks car::some()library(aplpack)## Loading required package: tcltklibrary(cat)
library(stringr)
knitr::opts_chunk$set(echo = TRUE)This dataset is Obtained from and is also available from the UCI machine learning repository,
http://rpubs.com/fast_Eddie/376256 <– saved to and viewable at
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 a chance to come to an understanding of the data,
and hopefully, of how each column relates to one another.
#KEEP
Wine <- read.csv("Wine.csv")
summary(Wine)## 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. :8.000This following Plot function gives a more generalised overview of all columns
# NOTE: heat.colors max is (12) & col=rainbow(20) & colors() -> is all 657 colours
attach(Wine)
plotsummary(Wine, design="chessboard") #Interestingly this shows possible outliers 
## NULL #and approximated boxplotsThis next function shows all correlations of all columns against any particular column of the data set
## shorten a few words / expressions for use in following plots
quality = Wine$quality
alcohol = Wine$alcohol
fixed = Wine$fixed.acidity #Wine$`fixed acidity`
total = Wine$total.sulfur.dioxide #Wine$`total sulfur dioxide`
free = Wine$free.sulfur.dioxide #Wine$`free sulfur dioxide`
volatile = Wine$volatile.acidity #Wine$`volatile acidity`par(mar=c(5,10,4,2)+.1)
boxplot(Wine, horizontal = TRUE, las = 1 , outline=FALSE , col=heat.colors(12),cex.axis = 0.8 )#, pos=2 )
## With both (Total and Free) Dioxide’s removed
#Remove the two Dioxide boxplots and replot
RemoveDioxide <- Wine[c(1:1599),-c(6:7)]
par(mar=c(5,10,4,2)+.1)
boxplot(RemoveDioxide, horizontal = TRUE, las = 1 , outline=FALSE , col=heat.colors(12),cex.axis = 0.8 )#, pos=2 )
## The three I think are worth looking closer at with relation to Quality
#par(mar=c(5,4,4,2)+.1) #Reset Margins to default
#Grouped quality, fixed acidity , and alcohol
attach(Wine)## 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.aciditypar(mar=c(5,10,4,2)+.1)
boxplot(quality, fixed , alcohol, residual.sugar , horizontal = TRUE, las = 1,
col=heat.colors(3),cex.axis = 0.8, names=c("Quality","Fixed","Alcohol", "Residual Sugar")) 
#KEEP
par(mar=c(5,4,4,2)+.1) #Reset Margins to defaultpar(mfrow=c(2, 2))
hist(quality ,xlim=c(1,10) , ylim=c(1,800) , col = 3) #hist( fixed.acidity) shows is original vs final weight
hist(alcohol ,xlim=c(1,20) , ylim=c(1,500) , col = 5) #hist( fixed.acidity
hist(fixed ,xlim=c(1,18) , ylim=c(1,600) , col = 7)
hist(residual.sugar ,xlim=c(-1,12) , ylim=c(1,900) ,col = 14)
# What we see is a possible relationship between Quailty and alcohol, and possibly between
# fixed and alcohol #I would like to see a fixed histogram with a lines overlay for comparison
par(mfrow=c(1, 1)) #Combined Lines Overlay
plot (density(alcohol), main = "Density Plot of Alcohol and Fixed Similarities",
lwd = 2, col = "darkblue", xlim = c(4, 16))
lines (density(fixed),lwd = 2 ,col = "red")
lines (density(quality),lwd = 2 ,col = "green")
lines (density(residual.sugar),lwd = 2 ,col = "green")
colours = c("Blue = Alcohol","Red = Fixed", "Green = Residual Sugar")
legend(x = 11, y = 0.45,legend = colours,col=c(1:3),pch = 16)
# par(mfrow=c(3, 1)) #this has been kept for CHECKING only
# qqPlot(fixed)
# qqPlot(alcohol)
# qqPlot(residual.sugar)# Definition:
# In statistics, a perfect negative correlation is represented by the value -1.00,
# while a 0.00 indicates no correlation and a +1.00 indicates a perfect positive correlation.
#install.packages("corrr") # This will correlate() all your data frame
#library(corrr)
Wine %>% correlate() %>% focus(quality) #testing## # 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 0.476# Correlation WRT quality
# rowname quality
# fixed.acidity 0.12405165
# volatile.acidity -0.39055778
# citric.acid 0.22637251
# residual.sugar 0.01373164
# chlorides -0.12890656
# free.sulfur.dioxide -0.05065606
# total.sulfur.dioxide -0.18510029
# density -0.17491923
# pH -0.05773139
# sulphates 0.25139708
# alcohol 0.47616632 <- includes this last missing value (on diagram below) This section below (fit) is for testing the Regression Equation.
The simulator selects random inputs for the Regression Equation an then tries
to validate against the Actual Data for the Regression Model.
I want to see if Machine Learninig can be a better way of predicting
in my case a " better wine " from the various components used to make a wine .
I intend to use this simulator to compare against the Machine Learning model.
I simply want to know if one is better for my Wine prediction than the other.
r2 <- round(runif(1,1,1550),0) ## note '3'is the start point in quality ,
## eg set to (runif(1,5,15),0)
#r2 # r2 check value
WQ = Wine$quality[r2:r2]
#WQ # Check values
W1 = Wine$fixed.acidity [r2:r2]
#W1 # Check values
W2 = Wine$volatile.acidity[r2:r2]
#W2 # Check values
W3 = Wine$citric.acid[r2:r2]
W4 = Wine$residual.sugar[r2:r2]
W5 = Wine$chlorides[r2:r2]
W6 = Wine$free.sulfur.dioxide[r2:r2]
W7 = Wine$total.sulfur.dioxide[r2:r2]
W8 = Wine$density[r2:r2]
W9 = Wine$quality[r2:r2]
W10 = Wine$pH[r2:r2]
W11 = Wine$sulphates[r2:r2]
W12 = Wine$alcohol[r2:r2]
# library(corrr)
# Wine %>% correlate() %>% focus(quality)
# Multiple Linear Regression
fit <- lm(quality ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
chlorides + free.sulfur.dioxide + total.sulfur.dioxide + density +
pH + sulphates + alcohol , data=Wine)
summary(fit) # show results##
## Call:
## lm(formula = quality ~ fixed.acidity + volatile.acidity + citric.acid +
## residual.sugar + chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol, data = Wine)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.68911 -0.36652 -0.04699 0.45202 2.02498
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.197e+01 2.119e+01 1.036 0.3002
## fixed.acidity 2.499e-02 2.595e-02 0.963 0.3357
## volatile.acidity -1.084e+00 1.211e-01 -8.948 < 2e-16 ***
## citric.acid -1.826e-01 1.472e-01 -1.240 0.2150
## residual.sugar 1.633e-02 1.500e-02 1.089 0.2765
## chlorides -1.874e+00 4.193e-01 -4.470 8.37e-06 ***
## free.sulfur.dioxide 4.361e-03 2.171e-03 2.009 0.0447 *
## total.sulfur.dioxide -3.265e-03 7.287e-04 -4.480 8.00e-06 ***
## density -1.788e+01 2.163e+01 -0.827 0.4086
## pH -4.137e-01 1.916e-01 -2.159 0.0310 *
## sulphates 9.163e-01 1.143e-01 8.014 2.13e-15 ***
## alcohol 2.762e-01 2.648e-02 10.429 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1587 degrees of freedom
## Multiple R-squared: 0.3606, Adjusted R-squared: 0.3561
## F-statistic: 81.35 on 11 and 1587 DF, p-value: < 2.2e-16Intercept <- summary(fit)$coefficients[1, 1]
fixed.acidity <- summary(fit)$coefficients[2, 1]
volatile.acidity <- summary(fit)$coefficients[3, 1]
citric.acid <- summary(fit)$coefficients[4, 1]
residual.sugar <- summary(fit)$coefficients[5, 1]
chlorides <- summary(fit)$coefficients[6, 1]
free.sulfur.dioxide <- summary(fit)$coefficients[7, 1]
total.sulfur.dioxide <- summary(fit)$coefficients[8, 1]
density <- summary(fit)$coefficients[9, 1]
pH <- summary(fit)$coefficients[10, 1]
sulphates <- summary(fit)$coefficients[11, 1]
alcohol <- summary(fit)$coefficients[12, 1]
#Intercept # Used to check for correct values
#fixed.acidity
#volatile.acidity
Qual = round ( (W1 * fixed.acidity + W2 * volatile.acidity + W3 * citric.acid +
W4 * residual.sugar + W5 * chlorides + W6 * free.sulfur.dioxide +
W7 * total.sulfur.dioxide + W8 * total.sulfur.dioxide +
W8 * density + W9 * pH + W10 * sulphates + W11 * alcohol +
Intercept), 0)
Qual # Used to check for correct values , Qual is the Regression model## [1] 4WQ## [1] 7Equal <- paste0( ifelse((WQ > Qual), " Regression Value LESS than Data Value "," "),
ifelse((WQ < Qual), " Regression Value GREATER than Data Value "," "),
ifelse((WQ == Qual), " Regression Value = Data Value"," "))
cat(Equal)## Regression Value LESS than Data Value# diagnostic plots
par(mfrow=c(1, 2))
layout(matrix(c(1,2,3,4),2,2)) # optional 4 graphs/page
plot(fit)
# Other useful functions to help more insight
confint(fit, level=0.95) # CIs for model parameters ## 2.5 % 97.5 %
## (Intercept) -1.960710e+01 63.537517845
## fixed.acidity -2.590639e-02 0.075887499
## volatile.acidity -1.321126e+00 -0.846054953
## citric.acid -4.712441e-01 0.106116245
## residual.sugar -1.309474e-02 0.045757280
## chlorides -2.696632e+00 -1.051817956
## free.sulfur.dioxide 1.024314e-04 0.008620235
## total.sulfur.dioxide -4.693951e-03 -0.001835208
## density -6.031362e+01 24.551294539
## pH -7.894637e-01 -0.037842600
## sulphates 6.920661e-01 1.140602768
## alcohol 2.242512e-01 0.328144192anova(fit) # anova table ## Analysis of Variance Table
##
## Response: quality
## Df Sum Sq Mean Sq F value Pr(>F)
## fixed.acidity 1 16.04 16.038 38.1924 8.132e-10 ***
## volatile.acidity 1 143.57 143.573 341.9062 < 2.2e-16 ***
## citric.acid 1 0.02 0.024 0.0581 0.809535
## residual.sugar 1 0.16 0.158 0.3764 0.539600
## chlorides 1 13.06 13.062 31.1057 2.868e-08 ***
## free.sulfur.dioxide 1 2.97 2.974 7.0828 0.007861 **
## total.sulfur.dioxide 1 30.09 30.093 71.6631 < 2.2e-16 ***
## density 1 61.31 61.310 146.0054 < 2.2e-16 ***
## pH 1 7.15 7.154 17.0358 3.859e-05 ***
## sulphates 1 55.70 55.697 132.6366 < 2.2e-16 ***
## alcohol 1 45.67 45.672 108.7643 < 2.2e-16 ***
## Residuals 1587 666.41 0.420
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1vcov(fit) # covariance matrix for model parameters ## (Intercept) fixed.acidity volatile.acidity
## (Intercept) 4.492100e+02 4.253152e-01 3.303414e-01
## fixed.acidity 4.253152e-01 6.733247e-04 -1.562945e-04
## volatile.acidity 3.303414e-01 -1.562945e-04 1.466552e-02
## citric.acid 3.235398e-02 -1.272831e-03 9.543695e-03
## residual.sugar 1.893780e-01 1.677641e-04 4.364326e-05
## chlorides 7.606468e-01 2.538893e-03 -1.340534e-02
## free.sulfur.dioxide -3.813607e-03 -6.205116e-06 4.347546e-05
## total.sulfur.dioxide 1.103784e-03 4.381638e-06 -1.889492e-05
## density -4.583128e+02 -4.409095e-01 -3.364363e-01
## pH 2.234170e+00 3.572150e-03 -6.183079e-04
## sulphates 5.983606e-01 4.511465e-04 2.899835e-03
## alcohol -4.258940e-01 -3.734381e-04 -2.530845e-04
## citric.acid residual.sugar chlorides
## (Intercept) 3.235398e-02 1.893780e-01 7.606468e-01
## fixed.acidity -1.272831e-03 1.677641e-04 2.538893e-03
## volatile.acidity 9.543695e-03 4.364326e-05 -1.340534e-02
## citric.acid 2.166083e-02 -1.179444e-04 -1.627310e-02
## residual.sugar -1.179444e-04 2.250629e-04 6.822396e-05
## chlorides -1.627310e-02 6.822396e-05 1.757984e-01
## free.sulfur.dioxide 5.192585e-05 -4.120402e-06 -5.328066e-05
## total.sulfur.dioxide -2.841887e-05 -3.968613e-07 4.283090e-05
## density -2.737179e-02 -1.931659e-01 -8.508338e-01
## pH 9.654568e-04 9.458076e-04 1.856139e-02
## sulphates -4.468331e-04 3.443137e-04 -1.680336e-02
## alcohol -5.825858e-04 -1.994800e-04 1.025390e-03
## free.sulfur.dioxide total.sulfur.dioxide
## (Intercept) -3.813607e-03 1.103784e-03
## fixed.acidity -6.205116e-06 4.381638e-06
## volatile.acidity 4.347546e-05 -1.889492e-05
## citric.acid 5.192585e-05 -2.841887e-05
## residual.sugar -4.120402e-06 -3.968613e-07
## chlorides -5.328066e-05 4.283090e-05
## free.sulfur.dioxide 4.714508e-06 -1.048949e-06
## total.sulfur.dioxide -1.048949e-06 5.310452e-07
## density 4.013057e-03 -1.241979e-03
## pH -5.726739e-05 2.707286e-05
## sulphates -1.339587e-05 -2.754751e-06
## alcohol 1.503270e-06 1.610225e-06
## density pH sulphates
## (Intercept) -4.583128e+02 2.234170e+00 5.983606e-01
## fixed.acidity -4.409095e-01 3.572150e-03 4.511465e-04
## volatile.acidity -3.364363e-01 -6.183079e-04 2.899835e-03
## citric.acid -2.737179e-02 9.654568e-04 -4.468331e-04
## residual.sugar -1.931659e-01 9.458076e-04 3.443137e-04
## chlorides -8.508338e-01 1.856139e-02 -1.680336e-02
## free.sulfur.dioxide 4.013057e-03 -5.726739e-05 -1.339587e-05
## total.sulfur.dioxide -1.241979e-03 2.707286e-05 -2.754751e-06
## density 4.679910e+02 -2.371814e+00 -6.134005e-01
## pH -2.371814e+00 3.670955e-02 2.817249e-03
## sulphates -6.134005e-01 2.817249e-03 1.307306e-02
## alcohol 4.330216e-01 -2.638799e-03 -8.744756e-04
## alcohol
## (Intercept) -4.258940e-01
## fixed.acidity -3.734381e-04
## volatile.acidity -2.530845e-04
## citric.acid -5.825858e-04
## residual.sugar -1.994800e-04
## chlorides 1.025390e-03
## free.sulfur.dioxide 1.503270e-06
## total.sulfur.dioxide 1.610225e-06
## density 4.330216e-01
## pH -2.638799e-03
## sulphates -8.744756e-04
## alcohol 7.013803e-04—– Machine Learning —— Phase 2 ——–
## 2. Data Processing ---- Setting the scene for further analysis ---- Phase 2 --------
## 2.1. Preliminaries ----
Wine <- read.csv("Wine.csv")
train <- read.csv('Wine.csv', stringsAsFactors = FALSE, header = FALSE)
test <- read.csv('Wine.csv', stringsAsFactors = FALSE, skip = 1, header = FALSE)
adult <- rbind(train, test)
names( adult ) <- c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides',
'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates',
'alcohol', 'quality')
# 2.2 Data Cleaning ----
summarizeColumns(adult)## 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 7str( adult )## '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" ...View(adult)
#View(test)
#View(Wine)
## Free onwards