545-51 project
anil jhanwar
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#load required packages/libraries
library(caTools)
library(ggplot2)
#nnet packege is required for multinomial regression
#install.packages("nnet")
library(nnet)
#install.packages("corrplot")
library(corrplot)## corrplot 0.84 loaded#car package is used for using VIF
library(car)## Loading required package: carDatawine_quality<-read.csv("winequality-red.csv",header = TRUE, sep = ",")
dim(wine_quality)## [1] 1599 12#so there are 1599 rows in the data and there are 12 columns (variables)#*********Exploratroy Data Analysis************
#analysing data type of all the variables
str(wine_quality)## 'data.frame': 1599 obs. of 12 variables:
## $ 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 ...#Checking for Missing data/Null Values
#Out of 1599 following number of rwos has complete cases i.e data with no null values in any rows
wine_quality[!which(complete.cases(wine_quality[,all.vars(wine_quality)])),]## [1] fixed.acidity volatile.acidity citric.acid
## [4] residual.sugar chlorides free.sulfur.dioxide
## [7] total.sulfur.dioxide density pH
## [10] sulphates alcohol quality
## <0 rows> (or 0-length row.names)#1599 - this shows that none of the rows have values
cor(wine_quality)## fixed.acidity volatile.acidity citric.acid
## fixed.acidity 1.00000000 -0.256130895 0.67170343
## volatile.acidity -0.25613089 1.000000000 -0.55249568
## citric.acid 0.67170343 -0.552495685 1.00000000
## residual.sugar 0.11477672 0.001917882 0.14357716
## chlorides 0.09370519 0.061297772 0.20382291
## free.sulfur.dioxide -0.15379419 -0.010503827 -0.06097813
## total.sulfur.dioxide -0.11318144 0.076470005 0.03553302
## density 0.66804729 0.022026232 0.36494718
## pH -0.68297819 0.234937294 -0.54190414
## sulphates 0.18300566 -0.260986685 0.31277004
## alcohol -0.06166827 -0.202288027 0.10990325
## quality 0.12405165 -0.390557780 0.22637251
## residual.sugar chlorides free.sulfur.dioxide
## fixed.acidity 0.114776724 0.093705186 -0.153794193
## volatile.acidity 0.001917882 0.061297772 -0.010503827
## citric.acid 0.143577162 0.203822914 -0.060978129
## residual.sugar 1.000000000 0.055609535 0.187048995
## chlorides 0.055609535 1.000000000 0.005562147
## free.sulfur.dioxide 0.187048995 0.005562147 1.000000000
## total.sulfur.dioxide 0.203027882 0.047400468 0.667666450
## density 0.355283371 0.200632327 -0.021945831
## pH -0.085652422 -0.265026131 0.070377499
## sulphates 0.005527121 0.371260481 0.051657572
## alcohol 0.042075437 -0.221140545 -0.069408354
## quality 0.013731637 -0.128906560 -0.050656057
## total.sulfur.dioxide density pH
## fixed.acidity -0.11318144 0.66804729 -0.68297819
## volatile.acidity 0.07647000 0.02202623 0.23493729
## citric.acid 0.03553302 0.36494718 -0.54190414
## residual.sugar 0.20302788 0.35528337 -0.08565242
## chlorides 0.04740047 0.20063233 -0.26502613
## free.sulfur.dioxide 0.66766645 -0.02194583 0.07037750
## total.sulfur.dioxide 1.00000000 0.07126948 -0.06649456
## density 0.07126948 1.00000000 -0.34169933
## pH -0.06649456 -0.34169933 1.00000000
## sulphates 0.04294684 0.14850641 -0.19664760
## alcohol -0.20565394 -0.49617977 0.20563251
## quality -0.18510029 -0.17491923 -0.05773139
## sulphates alcohol quality
## fixed.acidity 0.183005664 -0.06166827 0.12405165
## volatile.acidity -0.260986685 -0.20228803 -0.39055778
## citric.acid 0.312770044 0.10990325 0.22637251
## residual.sugar 0.005527121 0.04207544 0.01373164
## chlorides 0.371260481 -0.22114054 -0.12890656
## free.sulfur.dioxide 0.051657572 -0.06940835 -0.05065606
## total.sulfur.dioxide 0.042946836 -0.20565394 -0.18510029
## density 0.148506412 -0.49617977 -0.17491923
## pH -0.196647602 0.20563251 -0.05773139
## sulphates 1.000000000 0.09359475 0.25139708
## alcohol 0.093594750 1.00000000 0.47616632
## quality 0.251397079 0.47616632 1.00000000corrplot(cor(wine_quality), type="lower")
#multiple histograms
#hist(wine_quality[,1], xlim=c(0, 3500), breaks=seq(0, 3500, 100), main=colnames[i], probability=TRUE, col="gray", border="white")
colnames <- dimnames(wine_quality)[[2]]
par(mfrow=c(1,1))
for(i in 1:2){
hist(wine_quality[,i], main=colnames(wine_quality)[i], probability=TRUE, col="orange", border="white")
}
tranformed_wine_quality<-wine_quality
tranformed_wine_quality$alcohol<-log(log(tranformed_wine_quality$alcohol))
tranformed_wine_quality$free.sulfur.dioxide<-log(tranformed_wine_quality$free.sulfur.dioxide)
tranformed_wine_quality$total.sulfur.dioxide<-log(tranformed_wine_quality$total.sulfur.dioxide)
set.seed(1234)
split = sample.split(wine_quality$quality, SplitRatio = 0.8)
training_set = subset(tranformed_wine_quality, split == TRUE)
test_set = subset(tranformed_wine_quality, split == FALSE)
model1 = lm(formula = quality ~ .,
data = training_set)
summary_model1<-summary(model1)
summary_model1##
## Call:
## lm(formula = quality ~ ., data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.32368 -0.36012 -0.07567 0.46699 2.11979
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 28.75778 24.16304 1.190 0.234208
## fixed.acidity 0.05035 0.02914 1.728 0.084240 .
## volatile.acidity -1.10739 0.13369 -8.283 3.02e-16 ***
## citric.acid -0.21544 0.16165 -1.333 0.182854
## residual.sugar 0.01758 0.01673 1.051 0.293453
## chlorides -1.53106 0.54256 -2.822 0.004849 **
## free.sulfur.dioxide 0.12564 0.04419 2.843 0.004535 **
## total.sulfur.dioxide -0.15365 0.04485 -3.426 0.000633 ***
## density -27.89910 24.41961 -1.142 0.253467
## pH -0.25230 0.21223 -1.189 0.234733
## sulphates 0.89879 0.13048 6.888 8.89e-12 ***
## alcohol 6.45504 0.75699 8.527 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6558 on 1266 degrees of freedom
## Multiple R-squared: 0.344, Adjusted R-squared: 0.3383
## F-statistic: 60.35 on 11 and 1266 DF, p-value: < 2.2e-16# Predicting the Test set results
y_pred = predict(model1, newdata = test_set)
y_actual<-test_set$quality
train_MSE = mean((model1$residuals)^2)
train_MSE## [1] 0.4260819#Test set MSE
MSPE<-mean((y_actual - y_pred) ^ 2)
MSPE## [1] 0.3921996df<-as.data.frame(cbind(y_actual,y_pred))
library(ggplot2)
ggplot(data=df,aes(x=as.factor(y_actual), y=y_pred))+geom_boxplot()
#applying variable selection using backward elimination
model2 = lm(formula = quality ~ .,
data = training_set)
summary_model2<-summary(model2)
summary_model2##
## Call:
## lm(formula = quality ~ ., data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.32368 -0.36012 -0.07567 0.46699 2.11979
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 28.75778 24.16304 1.190 0.234208
## fixed.acidity 0.05035 0.02914 1.728 0.084240 .
## volatile.acidity -1.10739 0.13369 -8.283 3.02e-16 ***
## citric.acid -0.21544 0.16165 -1.333 0.182854
## residual.sugar 0.01758 0.01673 1.051 0.293453
## chlorides -1.53106 0.54256 -2.822 0.004849 **
## free.sulfur.dioxide 0.12564 0.04419 2.843 0.004535 **
## total.sulfur.dioxide -0.15365 0.04485 -3.426 0.000633 ***
## density -27.89910 24.41961 -1.142 0.253467
## pH -0.25230 0.21223 -1.189 0.234733
## sulphates 0.89879 0.13048 6.888 8.89e-12 ***
## alcohol 6.45504 0.75699 8.527 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6558 on 1266 degrees of freedom
## Multiple R-squared: 0.344, Adjusted R-squared: 0.3383
## F-statistic: 60.35 on 11 and 1266 DF, p-value: < 2.2e-16#backward selection
step(model2,direction="backward",trace=FALSE)##
## Call:
## lm(formula = quality ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol, data = training_set)
##
## Coefficients:
## (Intercept) volatile.acidity chlorides
## 1.6635 -1.0370 -1.7453
## free.sulfur.dioxide total.sulfur.dioxide pH
## 0.1382 -0.1732 -0.4685
## sulphates alcohol
## 0.8664 6.9831#
#forward selection
min.model = lm(quality ~ 1, data=training_set)
formula <- formula(lm(quality~.,training_set))
fwd.model = step(min.model, direction='forward', scope=formula)## Start: AIC=-549.49
## quality ~ 1
##
## Df Sum of Sq RSS AIC
## + alcohol 1 176.568 653.51 -853.14
## + volatile.acidity 1 124.551 705.53 -755.26
## + sulphates 1 61.663 768.42 -646.14
## + citric.acid 1 46.230 783.85 -620.73
## + density 1 20.577 809.50 -579.57
## + total.sulfur.dioxide 1 18.190 811.89 -575.81
## + fixed.acidity 1 14.558 815.52 -570.11
## + chlorides 1 13.155 816.93 -567.91
## + pH 1 3.455 826.63 -552.82
## <none> 830.08 -549.49
## + free.sulfur.dioxide 1 0.422 829.66 -548.14
## + residual.sugar 1 0.251 829.83 -547.88
##
## Step: AIC=-853.14
## quality ~ alcohol
##
## Df Sum of Sq RSS AIC
## + volatile.acidity 1 75.259 578.25 -1007.50
## + sulphates 1 39.091 614.42 -929.97
## + citric.acid 1 27.306 626.21 -905.69
## + pH 1 23.036 630.48 -897.00
## + fixed.acidity 1 20.741 632.77 -892.36
## + density 1 4.334 649.18 -859.64
## + total.sulfur.dioxide 1 1.609 651.90 -854.29
## <none> 653.51 -853.14
## + chlorides 1 0.157 653.36 -851.45
## + free.sulfur.dioxide 1 0.064 653.45 -851.26
## + residual.sugar 1 0.014 653.50 -851.17
##
## Step: AIC=-1007.5
## quality ~ alcohol + volatile.acidity
##
## Df Sum of Sq RSS AIC
## + sulphates 1 17.1337 561.12 -1043.9
## + fixed.acidity 1 5.4840 572.77 -1017.7
## + pH 1 5.4751 572.78 -1017.7
## + density 1 1.6162 576.64 -1009.1
## + total.sulfur.dioxide 1 1.5266 576.73 -1008.9
## <none> 578.25 -1007.5
## + citric.acid 1 0.4164 577.84 -1006.4
## + chlorides 1 0.0649 578.19 -1005.6
## + free.sulfur.dioxide 1 0.0145 578.24 -1005.5
## + residual.sugar 1 0.0000 578.25 -1005.5
##
## Step: AIC=-1043.94
## quality ~ alcohol + volatile.acidity + sulphates
##
## Df Sum of Sq RSS AIC
## + chlorides 1 3.3055 557.82 -1049.5
## + pH 1 3.2298 557.89 -1049.3
## + fixed.acidity 1 3.1696 557.95 -1049.2
## + total.sulfur.dioxide 1 2.8727 558.25 -1048.5
## <none> 561.12 -1043.9
## + density 1 0.1386 560.98 -1042.3
## + free.sulfur.dioxide 1 0.0287 561.09 -1042.0
## + citric.acid 1 0.0129 561.11 -1042.0
## + residual.sugar 1 0.0002 561.12 -1041.9
##
## Step: AIC=-1049.49
## quality ~ alcohol + volatile.acidity + sulphates + chlorides
##
## Df Sum of Sq RSS AIC
## + pH 1 4.6363 553.18 -1058.2
## + fixed.acidity 1 3.6451 554.17 -1055.9
## + total.sulfur.dioxide 1 2.9941 554.82 -1054.4
## <none> 557.82 -1049.5
## + density 1 0.2467 557.57 -1048.1
## + citric.acid 1 0.0784 557.74 -1047.7
## + free.sulfur.dioxide 1 0.0516 557.76 -1047.6
## + residual.sugar 1 0.0276 557.79 -1047.5
##
## Step: AIC=-1058.16
## quality ~ alcohol + volatile.acidity + sulphates + chlorides +
## pH
##
## Df Sum of Sq RSS AIC
## + total.sulfur.dioxide 1 2.61560 550.56 -1062.2
## <none> 553.18 -1058.2
## + citric.acid 1 0.72663 552.45 -1057.8
## + fixed.acidity 1 0.44308 552.74 -1057.2
## + free.sulfur.dioxide 1 0.00168 553.18 -1056.2
## + density 1 0.00071 553.18 -1056.2
## + residual.sugar 1 0.00044 553.18 -1056.2
##
## Step: AIC=-1062.22
## quality ~ alcohol + volatile.acidity + sulphates + chlorides +
## pH + total.sulfur.dioxide
##
## Df Sum of Sq RSS AIC
## + free.sulfur.dioxide 1 4.3778 546.19 -1070.4
## <none> 550.56 -1062.2
## + citric.acid 1 0.5565 550.01 -1061.5
## + fixed.acidity 1 0.1770 550.39 -1060.6
## + residual.sugar 1 0.0738 550.49 -1060.4
## + density 1 0.0028 550.56 -1060.2
##
## Step: AIC=-1070.42
## quality ~ alcohol + volatile.acidity + sulphates + chlorides +
## pH + total.sulfur.dioxide + free.sulfur.dioxide
##
## Df Sum of Sq RSS AIC
## <none> 546.19 -1070.4
## + fixed.acidity 1 0.289937 545.90 -1069.1
## + citric.acid 1 0.175559 546.01 -1068.8
## + residual.sugar 1 0.088065 546.10 -1068.6
## + density 1 0.025579 546.16 -1068.5#results
#quality ~ alcohol + volatile.acidity + sulphates + total.sulfur.dioxide + chlorides + pH + free.sulfur.dioxide
#
#################
model3<-lm(formula = quality ~ volatile.acidity + chlorides + free.sulfur.dioxide + total.sulfur.dioxide + pH + sulphates + alcohol, data = training_set)
summary_model3<-summary(model3)
summary_model3##
## Call:
## lm(formula = quality ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol, data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.24794 -0.37109 -0.06992 0.47185 2.12950
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.66354 0.56919 2.923 0.003532 **
## volatile.acidity -1.03698 0.11354 -9.133 < 2e-16 ***
## chlorides -1.74533 0.52507 -3.324 0.000913 ***
## free.sulfur.dioxide 0.13818 0.04331 3.190 0.001455 **
## total.sulfur.dioxide -0.17320 0.04296 -4.032 5.86e-05 ***
## pH -0.46853 0.13231 -3.541 0.000413 ***
## sulphates 0.86638 0.12565 6.895 8.45e-12 ***
## alcohol 6.98311 0.49435 14.126 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6558 on 1270 degrees of freedom
## Multiple R-squared: 0.342, Adjusted R-squared: 0.3384
## F-statistic: 94.3 on 7 and 1270 DF, p-value: < 2.2e-16vif(model3)## volatile.acidity chlorides free.sulfur.dioxide
## 1.232230 1.251374 2.638836
## total.sulfur.dioxide pH sulphates
## 2.752512 1.232092 1.262575
## alcohol
## 1.287294# VIF values for all the variables are < 2 , this shows the multicolinarity problem doesn't seem to be affcting our model
y_pred3 = predict(model3, newdata = test_set)
y_actual3<-test_set$quality
#MSE
train_MSE3 = mean((model3$residuals)^2)
MSPE3<-mean((y_actual3 - y_pred3) ^ 2)#THis is the 2nd set of models where we would consider dependent variable as a ordinal variable (categorical variable)
#Hence liner regression approach will not work.
levels(as.factor(wine_quality$quality))## [1] "3" "4" "5" "6" "7" "8"#as demonstrated above the categtical variable quality has 6 difference levels 3-8
#So logistic regression will not be able to classify all 6 classes at the same time as logistic regression is more suitable for a binary classification
#Hence here we will employ""
#multinomal logistic regression model
training_set$quality<-as.factor(training_set$quality)
test_set$quality<-as.factor(test_set$quality)
training_set[-12] = scale(training_set[-12])
test_set[-12] = scale(test_set[-12])
glm.fit=multinom(quality~., data=training_set)## # weights: 78 (60 variable)
## initial value 2289.868602
## iter 10 value 1627.470969
## iter 20 value 1265.644460
## iter 30 value 1200.448243
## iter 40 value 1173.063818
## iter 50 value 1165.296391
## iter 60 value 1164.000887
## iter 70 value 1163.949313
## final value 1163.948594
## convergedsummary(glm.fit)## Call:
## multinom(formula = quality ~ ., data = training_set)
##
## Coefficients:
## (Intercept) fixed.acidity volatile.acidity citric.acid residual.sugar
## 4 6.409809 2.7804077 -1.962018 -2.0060549 0.52195799
## 5 9.640708 1.1679273 -2.358993 -1.8293426 -0.16062131
## 6 9.784926 1.7279007 -2.794595 -2.1042224 -0.04392396
## 7 7.556765 2.1228349 -3.216412 -2.1038674 0.28582991
## 8 3.876369 0.5254109 -2.381461 -0.8180732 -0.52986416
## chlorides free.sulfur.dioxide total.sulfur.dioxide density pH
## 4 0.2315770 -0.8875621 2.022564 -3.450494 0.1357967
## 5 0.2229732 -0.4098571 2.362025 -2.212443 -1.1050954
## 6 0.1688509 -0.1782503 1.925406 -2.525190 -0.9280915
## 7 -0.2995520 0.2370099 1.280785 -2.664251 -0.7888335
## 8 -1.1164822 -0.4406022 1.483864 -2.291996 -1.9452987
## sulphates alcohol
## 4 -0.1287139 1.176349
## 5 0.2459895 1.506625
## 6 0.6102799 2.171551
## 7 1.0508378 2.844505
## 8 1.1513499 3.516117
##
## Std. Errors:
## (Intercept) fixed.acidity volatile.acidity citric.acid residual.sugar
## 4 2.040605 1.592743 0.6835868 0.9033522 0.4649719
## 5 2.033815 1.545408 0.6796741 0.8656888 0.4429749
## 6 2.033773 1.548275 0.6833376 0.8690179 0.4455230
## 7 2.040150 1.562479 0.7000762 0.8845010 0.4556881
## 8 2.183888 1.745202 0.8051351 1.0136004 0.6728811
## chlorides free.sulfur.dioxide total.sulfur.dioxide density pH
## 4 0.4938235 0.9811067 1.032053 1.379101 0.9984517
## 5 0.4488041 0.9635862 1.010962 1.341338 0.9801278
## 6 0.4522850 0.9656934 1.013241 1.344430 0.9820645
## 7 0.4944618 0.9797889 1.029682 1.360104 0.9935244
## 8 0.7970266 1.1121433 1.163382 1.512250 1.1187153
## sulphates alcohol
## 4 0.9041114 0.9645808
## 5 0.8617125 0.9312921
## 6 0.8630185 0.9344517
## 7 0.8679310 0.9467140
## 8 0.8940197 1.0827069
##
## Residual Deviance: 2327.897
## AIC: 2447.897#Prediction
y_pred_multinom<-predict(glm.fit, test_set, "probs")
a1<-data.frame(y_pred_multinom)
colnames(a1)<-c(3:8)
b1 <- fitted(glm.fit)
c1<-as.data.frame(matrix(0,ncol=1,nrow=nrow(a1)))
for(i in 1:nrow(a1)){
c1[i,1]<-colnames(a1[which.max(a1[i,])])
}
table(c1)## c1
## 3 4 5 6 7
## 1 1 154 148 17cm1<-table(test_set$quality,c1[,1])
cm1##
## 3 4 5 6 7
## 3 0 0 1 1 0
## 4 0 0 8 3 0
## 5 1 1 104 29 1
## 6 0 0 38 86 4
## 7 0 0 3 27 10
## 8 0 0 0 2 2accuracy1<- (cm1[1,1]+cm1[2,2]+cm1[3,3]+cm1[4,4]+cm1[5,5])/sum(cm1)
accuracy1## [1] 0.623053t1111<-as.data.frame(cbind(test_set$quality,c1[,1]))
str(t1111)## 'data.frame': 321 obs. of 2 variables:
## $ V1: Factor w/ 6 levels "1","2","3","4",..: 3 3 3 4 4 3 2 4 3 3 ...
## $ V2: Factor w/ 5 levels "3","4","5","6",..: 3 3 3 3 3 3 3 4 3 3 ...library(caret)## Loading required package: latticex1<-rep(0,6)
cm1##
## 3 4 5 6 7
## 3 0 0 1 1 0
## 4 0 0 8 3 0
## 5 1 1 104 29 1
## 6 0 0 38 86 4
## 7 0 0 3 27 10
## 8 0 0 0 2 2t1111<-cbind(cm1, x1)
t1111<-data.frame(cbind(cm1, x1))
#ggplot(data = t1111, aes(x=V1, y=V2, fill=value)) + geom_tile()
#plot(confusionMatrix$t1111)
qplot(quality, c1[,1], data=test_set, colour= quality, geom = c( "jitter", "abline"), main = "predicted vs. observed in validation data", xlab = "Observed Classe", ylab = "Predicted Classe")
#here we achieve an accuracy of 63.22 % on classification models with 6 categories of dependent variable
#this classification accuracy is much better than randomly clasifing the data into 6 classses which will have the accuracy
#percentage euqlas 100%/6 = 16.66% (approaximately)#2nd multinomial logit model with selected variables
wine_quality<-read.csv("winequality-red.csv",header = TRUE, sep = ",")
training_set$quality<-as.factor(training_set$quality)
test_set$quality<-as.factor(test_set$quality)
# Feature Scaling
training_set[-12] = scale(training_set[-12])
test_set[-12] = scale(test_set[-12])
multinom_model2=multinom(quality ~ fixed.acidity + volatile.acidity + residual.sugar +
free.sulfur.dioxide + density + pH + sulphates + alcohol,
data = training_set)## # weights: 60 (45 variable)
## initial value 2289.868602
## iter 10 value 1495.391682
## iter 20 value 1262.920575
## iter 30 value 1215.052357
## iter 40 value 1197.663219
## iter 50 value 1196.101548
## iter 60 value 1196.039980
## final value 1196.039912
## converged#summary(multinom_model2)
#Prediction
multinom_prob2<-predict(multinom_model2, test_set, "probs")
df_multinom_prob2<-data.frame(multinom_prob2)
colnames(df_multinom_prob2)<-c(3:8)
df_class_2<-as.data.frame(matrix(0,ncol=1,nrow=nrow(df_multinom_prob2)))
for(i in 1:nrow(df_multinom_prob2)){
df_class_2[i,1]<-colnames(df_multinom_prob2[which.max(df_multinom_prob2[i,])])
}
table(df_class_2)## df_class_2
## 4 5 6 7
## 1 164 141 15cm2<-table(test_set$quality,df_class_2[,1])
cm2##
## 4 5 6 7
## 3 0 1 1 0
## 4 0 8 3 0
## 5 1 106 29 0
## 6 0 47 78 3
## 7 0 2 28 10
## 8 0 0 2 2accuracy2<- (cm2[2,1]+cm2[3,2]+cm2[4,3]+cm2[5,4])/sum(cm2)
accuracy2## [1] 0.6043614#here the acuracy is 59.81%
# by using the selected variable there is not any imprvement in classifciation accuracy, however the accuracy is slightly decresed.#plots for visualizationpar(mfrow=c(4,3))
for(i in 1:12){
hist(wine_quality[,i], main=colnames(wine_quality)[i], probability=TRUE, col="orange", border="white")
}
par(mfrow=c(1,1))
for(i in 1:2){
hist(wine_quality[,i], main=colnames(wine_quality)[i], probability=TRUE, col="orange", border="white")
}
colnames(wine_quality)[11]## [1] "alcohol"hist(wine_quality[,11], main=colnames(wine_quality)[11], probability=TRUE, col="orange", border="white")
qplot(quality, c1[,1], data=test_set, colour= quality, geom = c( "jitter", "abline"), size=4,main = "predicted vs. observed in validation data", xlab = "Observed Classe", ylab = "Predicted Classe")
#hypotheis test
#null hypothesis: the alcohol content does not make any difference in quality of wine
#alternative hypothesis: the quality of wine is different for differnt alcohal level
x1<-wine_quality$alcohol[wine_quality$quality<=5]
x2<-wine_quality$alcohol[wine_quality$quality>5]
t.test(x1, x2)##
## Welch Two Sample t-test
##
## data: x1 and x2
## t = -19.782, df = 1516.8, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1.020622 -0.836479
## sample estimates:
## mean of x mean of y
## 9.926478 10.855029#test result
#pvalye isless than signifciant threshold, it impliies that we can reject null. This established that alcohol content has an impact on the quality of wineIncluding Plots
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