Advanced R project
Authors: Islam Islamov 444601 and Leyla Ellazova 444831
University of Warsawi.islamov@student.uw.edu.pl and l.ellazova@student.uw.edu.pl
First, we will set the working directory and upload the dataset.
These columns are:
Type - Red or White
Fixed acidity
Volatile acidity
Citric acidity
Residual Sugar
Chlorides
Free sulfur dioxide
Total sulfur dioxide
Density
Acid base scale - pH
Sulphates
Alcohol
Quality ( on a scale of 3 to 9)
The main thing we would like to analyze is how the inputs affect the quality of the wine. Basically, we will try to make a prediction based on the level of inputs.
First we will take a look at our dataset and if needed we will omit the NA values.
## Rows: 6,497
## Columns: 13
## $ type <chr> "white", "white", "white", "white", "white", "whi…
## $ fixed.acidity <dbl> 7.0, 6.3, 8.1, 7.2, 7.2, 8.1, 6.2, 7.0, 6.3, 8.1,…
## $ volatile.acidity <dbl> 0.27, 0.30, 0.28, 0.23, 0.23, 0.28, 0.32, 0.27, 0…
## $ citric.acid <dbl> 0.36, 0.34, 0.40, 0.32, 0.32, 0.40, 0.16, 0.36, 0…
## $ residual.sugar <dbl> 20.70, 1.60, 6.90, 8.50, 8.50, 6.90, 7.00, 20.70,…
## $ chlorides <dbl> 0.045, 0.049, 0.050, 0.058, 0.058, 0.050, 0.045, …
## $ free.sulfur.dioxide <dbl> 45, 14, 30, 47, 47, 30, 30, 45, 14, 28, 11, 17, 1…
## $ total.sulfur.dioxide <dbl> 170, 132, 97, 186, 186, 97, 136, 170, 132, 129, 6…
## $ density <dbl> 1.0010, 0.9940, 0.9951, 0.9956, 0.9956, 0.9951, 0…
## $ pH <dbl> 3.00, 3.30, 3.26, 3.19, 3.19, 3.26, 3.18, 3.00, 3…
## $ sulphates <dbl> 0.45, 0.49, 0.44, 0.40, 0.40, 0.44, 0.47, 0.45, 0…
## $ alcohol <dbl> 8.8, 9.5, 10.1, 9.9, 9.9, 10.1, 9.6, 8.8, 9.5, 11…
## $ quality <dbl> 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 7, 5, 7, 6…## # A tibble: 6 × 13
## type fixed.ac…¹ volat…² citri…³ resid…⁴ chlor…⁵ free.…⁶ total…⁷ density pH
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 white 7 0.27 0.36 20.7 0.045 45 170 1.00 3
## 2 white 6.3 0.3 0.34 1.6 0.049 14 132 0.994 3.3
## 3 white 8.1 0.28 0.4 6.9 0.05 30 97 0.995 3.26
## 4 white 7.2 0.23 0.32 8.5 0.058 47 186 0.996 3.19
## 5 white 7.2 0.23 0.32 8.5 0.058 47 186 0.996 3.19
## 6 white 8.1 0.28 0.4 6.9 0.05 30 97 0.995 3.26
## # … with 3 more variables: sulphates <dbl>, alcohol <dbl>, quality <dbl>, and
## # abbreviated variable names ¹fixed.acidity, ²volatile.acidity, ³citric.acid,
## # ⁴residual.sugar, ⁵chlorides, ⁶free.sulfur.dioxide, ⁷total.sulfur.dioxideAs we can see there are some NA values in the columns given below.
We will omit the NAs, then rewrite it and then check if any NAs are left in our dataset.
After we are done with elimination of NA values we will now take a look at our dataset once again.
## Rows: 6,463
## Columns: 13
## $ type <chr> "white", "white", "white", "white", "white", "whi…
## $ fixed.acidity <dbl> 7.0, 6.3, 8.1, 7.2, 7.2, 8.1, 6.2, 7.0, 6.3, 8.1,…
## $ volatile.acidity <dbl> 0.27, 0.30, 0.28, 0.23, 0.23, 0.28, 0.32, 0.27, 0…
## $ citric.acid <dbl> 0.36, 0.34, 0.40, 0.32, 0.32, 0.40, 0.16, 0.36, 0…
## $ residual.sugar <dbl> 20.70, 1.60, 6.90, 8.50, 8.50, 6.90, 7.00, 20.70,…
## $ chlorides <dbl> 0.045, 0.049, 0.050, 0.058, 0.058, 0.050, 0.045, …
## $ free.sulfur.dioxide <dbl> 45, 14, 30, 47, 47, 30, 30, 45, 14, 28, 11, 17, 1…
## $ total.sulfur.dioxide <dbl> 170, 132, 97, 186, 186, 97, 136, 170, 132, 129, 6…
## $ density <dbl> 1.0010, 0.9940, 0.9951, 0.9956, 0.9956, 0.9951, 0…
## $ pH <dbl> 3.00, 3.30, 3.26, 3.19, 3.19, 3.26, 3.18, 3.00, 3…
## $ sulphates <dbl> 0.45, 0.49, 0.44, 0.40, 0.40, 0.44, 0.47, 0.45, 0…
## $ alcohol <dbl> 8.8, 9.5, 10.1, 9.9, 9.9, 10.1, 9.6, 8.8, 9.5, 11…
## $ quality <dbl> 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 7, 5, 7, 6…Since we need to know what quality of wine is most common, we will need to check the frequency of quality types.
Another way of checking it, but with numbers
## .
## 3 4 5 6 7 8 9
## 30 214 2128 2820 1074 192 5Both in barplot and in our table we can see that the most common once are wines with quality types from 5 to 7.
If this is not enough we can look at them as percentages too (you can round to however much you want).
## .
## 3 4 5 6 7 8 9
## 0.005 0.033 0.329 0.436 0.166 0.030 0.001We will need to take a look at all variables and how big is the relation between them and quality of wine.
First we will do simple barplots that will show what happens when we add more or less of each component.
blue - alcohol
ph - red
sulphates - green
density - purple
res.sugar - orange
fx.acid - pink
vol.acid - darkred
cit.acid - orange
chlorides - lightred
fr.sulfur - orange
tot.sulfur - darkgreen
This will arrange all the barplots created earlier
Let’s check this assumption with Pearson’s correlation test.
We will need to rewrite our quality and type variables as numeric, since we had some errors earlier.
There are 2 main ways of doing so, one will directly show us the relation of all variables to each other, and the other will show us the relation with only Quality and the rest of variables.
quality_cor <- cor(wine[, colnames(wine) != "quality"],
wine$quality)
quality_cor## [,1]
## type -0.11918495
## fixed.acidity -0.07617378
## volatile.acidity -0.26667748
## citric.acid 0.08492614
## residual.sugar -0.03465378
## chlorides -0.20055317
## free.sulfur.dioxide 0.05492413
## total.sulfur.dioxide -0.04159801
## density -0.30444677
## pH 0.01840276
## sulphates 0.03905364
## alcohol 0.44463687For the last time we will also look at Pearson’s correlation plot
and we can see that the results are pretty much the same with the numbers we got above(look at quality correlation with other variables)
This function will divide our wine into qualities and see how many are there of each. It is made as an addition to see basically a bigger picture of our outliers.
Now for the Outliers
## [1] "fixed.acidity"
## [1] "volatile.acidity"
## [1] "citric.acid"
## [1] "residual.sugar"
## [1] "chlorides"
## [1] "free.sulfur.dioxide"
## [1] "total.sulfur.dioxide"
## [1] "density"
## [1] "pH"
## [1] "sulphates"
## [1] "alcohol"
## [1] "quality"Function for Outliers and their elimination.
It is made to avoid the problems with the quality of our predictions later on.
After function
We will take a look at the outliers again.
As we can see this time there are no outliers thanks to our function.
Now dividing our dataset into train and test samples
train<-sample(nrow(wine)*0.8)Model selection
Model #1
##
## Call:
## lm(formula = quality ~ . - type, data = wine.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.82263 -0.46705 -0.01595 0.47189 2.21454
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.797e+01 1.658e+01 5.307 1.16e-07 ***
## fixed.acidity 7.352e-02 2.010e-02 3.657 0.000258 ***
## volatile.acidity -1.575e+00 1.007e-01 -15.633 < 2e-16 ***
## citric.acid -1.193e-01 9.589e-02 -1.244 0.213679
## residual.sugar 5.616e-02 6.589e-03 8.523 < 2e-16 ***
## chlorides 8.420e-01 7.658e-01 1.099 0.271641
## free.sulfur.dioxide 7.011e-03 8.277e-04 8.470 < 2e-16 ***
## total.sulfur.dioxide -2.238e-03 3.062e-04 -7.308 3.12e-13 ***
## density -8.768e+01 1.686e+01 -5.200 2.07e-07 ***
## pH 6.018e-01 9.934e-02 6.058 1.47e-09 ***
## sulphates 7.701e-01 9.388e-02 8.203 2.94e-16 ***
## alcohol 2.281e-01 2.210e-02 10.325 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7036 on 5158 degrees of freedom
## Multiple R-squared: 0.2937, Adjusted R-squared: 0.2922
## F-statistic: 195 on 11 and 5158 DF, p-value: < 2.2e-16Now we wil check the multicollinearity, with the help of VIF - Variance inflation factor
In case if VIF>10 then there is multicollinearity
Multicollinearity is the occurrence of high intercorrelations among two or more independent variables in a multiple regression model. Multicollinearity can lead to skewed or misleading results when a researcher or analyst attempts to determine how well each independent variable can be used most effectively to predict or understand the dependent variable in a statistical model.
## fixed.acidity volatile.acidity citric.acid
## 3.210615 1.382746 1.264477
## residual.sugar chlorides free.sulfur.dioxide
## 10.666093 1.794805 1.893137
## total.sulfur.dioxide density pH
## 2.063821 25.473683 2.390585
## sulphates alcohol
## 1.296809 7.589321Model #2
##
## Call:
## lm(formula = quality ~ . - type - density, data = wine.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8244 -0.4625 -0.0147 0.4741 2.1760
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.7953023 0.3130057 5.736 1.03e-08 ***
## fixed.acidity -0.0061888 0.0130377 -0.475 0.635033
## volatile.acidity -1.7116528 0.0974729 -17.560 < 2e-16 ***
## citric.acid -0.1380128 0.0960665 -1.437 0.150881
## residual.sugar 0.0243940 0.0024759 9.853 < 2e-16 ***
## chlorides -0.6291021 0.7134665 -0.882 0.377951
## free.sulfur.dioxide 0.0072712 0.0008283 8.778 < 2e-16 ***
## total.sulfur.dioxide -0.0021759 0.0003067 -7.094 1.48e-12 ***
## pH 0.2536861 0.0735765 3.448 0.000569 ***
## sulphates 0.5842631 0.0870327 6.713 2.11e-11 ***
## alcohol 0.3289874 0.0106208 30.976 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7053 on 5159 degrees of freedom
## Multiple R-squared: 0.29, Adjusted R-squared: 0.2887
## F-statistic: 210.8 on 10 and 5159 DF, p-value: < 2.2e-16## fixed.acidity volatile.acidity citric.acid
## 1.343780 1.288256 1.262688
## residual.sugar chlorides free.sulfur.dioxide
## 1.498266 1.549887 1.886203
## total.sulfur.dioxide pH sulphates
## 2.060714 1.304795 1.108922
## alcohol
## 1.744393Yes, we can see that now residual.sugar is not having same issue as before, but let’s try to exclude it too.
##
## Call:
## lm(formula = quality ~ . - type - density - residual.sugar, data = wine.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.71967 -0.46329 -0.02265 0.49174 2.07290
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.6826048 0.3025477 8.867 < 2e-16 ***
## fixed.acidity -0.0120800 0.0131447 -0.919 0.3581
## volatile.acidity -1.6333069 0.0980482 -16.658 < 2e-16 ***
## citric.acid -0.0987875 0.0968734 -1.020 0.3079
## chlorides -1.5600749 0.7137347 -2.186 0.0289 *
## free.sulfur.dioxide 0.0082906 0.0008294 9.995 < 2e-16 ***
## total.sulfur.dioxide -0.0016461 0.0003048 -5.401 6.92e-08 ***
## pH 0.1293863 0.0731585 1.769 0.0770 .
## sulphates 0.5437645 0.0877411 6.197 6.19e-10 ***
## alcohol 0.2929845 0.0100648 29.110 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7119 on 5160 degrees of freedom
## Multiple R-squared: 0.2767, Adjusted R-squared: 0.2754
## F-statistic: 219.3 on 9 and 5160 DF, p-value: < 2.2e-16## fixed.acidity volatile.acidity citric.acid
## 1.340954 1.279682 1.260520
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## 1.522702 1.856773 1.997376
## pH sulphates alcohol
## 1.266432 1.106449 1.537899
### We can see the Density and residual sugar are higher than 10 as well
as alcohol being very close but not more then 10. ### Now we will make a
regression model
and now here we will need our quality as numeric that we already did earlier
##
## 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.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.82263 -0.46705 -0.01595 0.47189 2.21454
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.797e+01 1.658e+01 5.307 1.16e-07 ***
## fixed.acidity 7.352e-02 2.010e-02 3.657 0.000258 ***
## volatile.acidity -1.575e+00 1.007e-01 -15.633 < 2e-16 ***
## citric.acid -1.193e-01 9.589e-02 -1.244 0.213679
## residual.sugar 5.616e-02 6.589e-03 8.523 < 2e-16 ***
## chlorides 8.420e-01 7.658e-01 1.099 0.271641
## free.sulfur.dioxide 7.011e-03 8.277e-04 8.470 < 2e-16 ***
## total.sulfur.dioxide -2.238e-03 3.062e-04 -7.308 3.12e-13 ***
## density -8.768e+01 1.686e+01 -5.200 2.07e-07 ***
## pH 6.018e-01 9.934e-02 6.058 1.47e-09 ***
## sulphates 7.701e-01 9.388e-02 8.203 2.94e-16 ***
## alcohol 2.281e-01 2.210e-02 10.325 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7036 on 5158 degrees of freedom
## Multiple R-squared: 0.2937, Adjusted R-squared: 0.2922
## F-statistic: 195 on 11 and 5158 DF, p-value: < 2.2e-16Now for the prediction of test data set
## 1 2 3 4 5 6
## 6.397178 5.132746 5.981751 6.117660 5.351733 6.435004## 1 2 3 4 5 6
## 7 6 6 7 6 7Now for the Confusion Matrix
A confusion matrix, also known as an error matrix, is a specific table layout that allows visualization of the performance of an algorithm.
## actual
## predicted 3.5 4 5 6 7 7.5
## 5 2 24 94 26 1 0
## 6 11 136 1350 1337 252 46
## 7 7 17 177 910 640 135
## 8 0 0 0 2 3 0Now for the Accuracy of our model(linear in our case)
## [1] 0.2451663The accuracy for our model is onluy 24,5%, meaning that we shoukd try out other models too, in order to get better results.
Now let’s dod a logistic regression
polr() - will be used to fit ordinal logistic regression
Ordinal Logistic Regression - a statistical test used to predict a single ordered categorical variable using one or more other variables.
## fixed.acidity volatile.acidity citric.acid
## 1.864147e+02 2.364436e+06 1.574669e+05
## residual.sugar chlorides free.sulfur.dioxide
## 1.701527e+00 8.862709e+06 2.358498e+00
## total.sulfur.dioxide density pH
## 2.920313e+00 6.314801e+06 5.529830e+04
## sulphates alcohol
## 4.263106e+05 4.426875e+02## Call:
## polr(formula = quality2 ~ . - type - quality, data = wine.train,
## Hess = TRUE)
##
## Coefficients:
## Value Std. Error t value
## fixed.acidity 0.062229 0.0361248 1.7226
## volatile.acidity -3.910251 0.2652338 -14.7427
## citric.acid -0.060066 0.2697742 -0.2227
## residual.sugar 0.083250 0.0078619 10.5890
## chlorides -3.223162 0.0265041 -121.6101
## free.sulfur.dioxide 0.019672 0.0025386 7.7490
## total.sulfur.dioxide -0.007446 0.0008519 -8.7413
## density -54.537856 0.4666007 -116.8834
## pH 0.825945 0.2248289 3.6737
## sulphates 2.341744 0.2487452 9.4142
## alcohol 0.848126 0.0302951 27.9954
##
## Intercepts:
## Value Std. Error t value
## 3.5|4 -48.4024 0.4766 -101.5664
## 4|5 -46.2365 0.4763 -97.0719
## 5|6 -43.0830 0.4822 -89.3482
## 6|7 -40.4748 0.4923 -82.2216
## 7|7.5 -38.1278 0.5036 -75.7077
##
## Residual Deviance: 9835.458
## AIC: 9867.458Stepwise regression is a procedure we can use to build a regression model from a set of predictor variables by entering and removing predictors in a stepwise manner into the model until there is no statistically valid reason to enter or remove any more.
We can look at AIC to see which model is better.
## Start: AIC=9867.46
## quality2 ~ (type + fixed.acidity + volatile.acidity + citric.acid +
## residual.sugar + chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol + quality) - type - quality
##
## Df AIC
## - citric.acid 1 9865.5
## - fixed.acidity 1 9866.7
## - density 1 9867.3
## <none> 9867.5
## - chlorides 1 9867.6
## - pH 1 9874.8
## - residual.sugar 1 9889.6
## - free.sulfur.dioxide 1 9925.6
## - total.sulfur.dioxide 1 9935.4
## - sulphates 1 9939.6
## - volatile.acidity 1 10043.0
## - alcohol 1 10110.0
##
## Step: AIC=9865.51
## quality2 ~ fixed.acidity + volatile.acidity + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df AIC
## - fixed.acidity 1 9864.8
## - density 1 9865.4
## <none> 9865.5
## - chlorides 1 9865.7
## - pH 1 9873.4
## - residual.sugar 1 9887.9
## - free.sulfur.dioxide 1 9927.5
## - total.sulfur.dioxide 1 9935.8
## - sulphates 1 9937.6
## - volatile.acidity 1 10074.0
## - alcohol 1 10112.1
##
## Step: AIC=9864.76
## quality2 ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + density + pH + sulphates + alcohol
##
## Df AIC
## - density 1 9863.4
## <none> 9864.8
## - chlorides 1 9866.5
## - pH 1 9871.9
## - residual.sugar 1 9897.0
## - free.sulfur.dioxide 1 9922.5
## - total.sulfur.dioxide 1 9934.4
## - sulphates 1 9935.8
## - volatile.acidity 1 10087.8
## - alcohol 1 10299.9
##
## Step: AIC=9863.38
## quality2 ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df AIC
## <none> 9863.4
## - chlorides 1 9866.8
## - pH 1 9870.0
## - free.sulfur.dioxide 1 9922.1
## - residual.sugar 1 9926.4
## - total.sulfur.dioxide 1 9933.0
## - sulphates 1 9942.0
## - volatile.acidity 1 10100.7
## - alcohol 1 10686.4## 3.5 4 5 6 7 7.5
## 1 0.0034958339 0.026215106 0.38870771 0.4884762 0.08336730 0.009737883
## 2 0.0024425598 0.018482504 0.31336385 0.5374827 0.11433514 0.013893214
## 3 0.0056867196 0.041860549 0.49224197 0.4009690 0.05324613 0.005995643
## 4 0.0054847109 0.040442226 0.48481471 0.4079567 0.05508533 0.006216353
## 5 0.0015331478 0.011692345 0.22626316 0.5705221 0.16801640 0.021972862
## 6 0.0005624501 0.004325692 0.09858348 0.5062952 0.33247412 0.057759013Training data set Accuracy
## [1] 6 6 5 5 6 6
## Levels: 3.5 4 5 6 7 7.5Confusion matrix for train data set
## predicted
## Actual 3.5 4 5 6 7 7.5
## 3.5 0 0 13 8 0 0
## 4 0 0 87 62 1 0
## 5 0 0 859 623 8 0
## 6 0 0 420 1422 130 2
## 7 0 0 55 526 171 0
## 7.5 0 0 10 81 47 0Let’s check the accuracy once again
## [1] 0.5418785We can see that the accuracy is almost doubled from previous time, now it is 54,4%.
Now we will need to also do it for test sample.
Confusion MAtrix for test daat set
## actual
## predicted 3.5 4 5 6 7 7.5
## 3.5 0 0 0 0 0 0
## 4 0 0 0 0 0 0
## 5 4 42 389 175 26 5
## 6 5 21 246 615 220 37
## 7 0 1 3 56 76 17
## 7.5 0 0 0 0 0 0Accuracy is again not that high, only 23%.
## [1] 0.238674Binomial Logistic Regression Model
Basically we divided the quality column to two parts 5 or higher and lower than 5
Split into new train and test for Binomial Logistic regression
Now we will use the glm function to run our logistic regression model
## Start: AIC=4658.44
## category ~ (type + fixed.acidity + volatile.acidity + citric.acid +
## residual.sugar + chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol + quality + quality2) -
## type - quality - quality2
##
## Df Deviance AIC
## - fixed.acidity 1 4634.4 4656.4
## - density 1 4634.5 4656.5
## - pH 1 4634.6 4656.6
## - chlorides 1 4634.8 4656.8
## <none> 4634.4 4658.4
## - citric.acid 1 4637.9 4659.9
## - residual.sugar 1 4647.9 4669.9
## - free.sulfur.dioxide 1 4673.2 4695.2
## - total.sulfur.dioxide 1 4686.0 4708.0
## - sulphates 1 4699.7 4721.7
## - volatile.acidity 1 4818.9 4840.9
## - alcohol 1 4827.3 4849.3
##
## Step: AIC=4656.45
## category ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 4634.6 4654.6
## - pH 1 4634.7 4654.7
## - chlorides 1 4634.9 4654.9
## <none> 4634.4 4656.4
## - citric.acid 1 4638.0 4658.0
## - residual.sugar 1 4659.0 4679.0
## - free.sulfur.dioxide 1 4673.2 4693.2
## - total.sulfur.dioxide 1 4686.0 4706.0
## - sulphates 1 4701.3 4721.3
## - volatile.acidity 1 4821.8 4841.8
## - alcohol 1 4932.1 4952.1
##
## Step: AIC=4654.56
## category ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - pH 1 4634.7 4652.7
## - chlorides 1 4635.2 4653.2
## <none> 4634.6 4654.6
## - citric.acid 1 4639.0 4657.0
## - free.sulfur.dioxide 1 4673.7 4691.7
## - total.sulfur.dioxide 1 4687.7 4705.7
## - residual.sugar 1 4693.1 4711.1
## - sulphates 1 4710.0 4728.0
## - volatile.acidity 1 4851.3 4869.3
## - alcohol 1 5212.7 5230.7
##
## Step: AIC=4652.72
## category ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## sulphates + alcohol
##
## Df Deviance AIC
## - chlorides 1 4635.4 4651.4
## <none> 4634.7 4652.7
## - citric.acid 1 4640.2 4656.2
## - free.sulfur.dioxide 1 4674.3 4690.3
## - total.sulfur.dioxide 1 4688.3 4704.3
## - residual.sugar 1 4693.6 4709.6
## - sulphates 1 4714.4 4730.4
## - volatile.acidity 1 4851.3 4867.3
## - alcohol 1 5218.6 5234.6
##
## Step: AIC=4651.39
## category ~ volatile.acidity + citric.acid + residual.sugar +
## free.sulfur.dioxide + total.sulfur.dioxide + sulphates +
## alcohol
##
## Df Deviance AIC
## <none> 4635.4 4651.4
## - citric.acid 1 4641.5 4655.5
## - free.sulfur.dioxide 1 4674.4 4688.4
## - total.sulfur.dioxide 1 4689.7 4703.7
## - residual.sugar 1 4697.3 4711.3
## - sulphates 1 4715.8 4729.8
## - volatile.acidity 1 4906.4 4920.4
## - alcohol 1 5408.9 5422.9Prediction - Train set
## 1 2 3 4 5 6
## 0.4819976 0.5904504 0.5904504 0.6415135 0.4819976 0.7518595## 1 2 3 4 5 6
## -0.07204056 0.36582745 0.36582745 0.58193944 -0.07204056 1.10855417## 1 2 3 4 5 6
## 0.4819976 0.5904504 0.5904504 0.6415135 0.4819976 0.7518595Categorize the set into Good and Bad wine
Confusion matrix for training set
## actual
## predicted 0 1
## Bad 964 462
## Good 696 2402## [1] 0.7440318Confusion Matrix - test set
## actual
## predicted 0 1
## Bad quality 386 177
## Good quality 326 1050## [1] 0.7405879