The goal is to predict the type of wine based on the following variables: fixed acidity, volatile acidity, citric acid, residual sugar, chlorides, free sulfur dioxide, total sulfur dioxide, density, pH, sulphates and alcohol. Use these prediction techniques:
- Logistic regression
- Lasso logistic regression
- Linear discriminant analysis
- Quadratic discriminant analysis
- Naïve Bayes estimation
- K nearest neighbor
- Support vector machine
Type: wine type (red or white)
- Fixed acidity
- Volatile acidity
- Citric acid
- Residual sugar
- Chlorides
- Free sulfur dioxide
- Total sulfur dioxide
- Density
- pH
- Sulfates
- Alcohol: content of alcohol (%)
- Quality: wine quality (on a scale from 1 to 7)
Logistic Regression
## 'data.frame': 6497 obs. of 13 variables:
## $ type : Factor w/ 2 levels "red","white": 1 1 1 1 1 1 1 1 1 1 ...
## $ 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 ...
There is a class imbalance between wine types of 25-75%
##
## red white
## 0.2461136 0.7538864
##
## Call:
## glm(formula = type ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + sulphates + alcohol, family = binomial(), data = WineQ)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -5.7226 0.0009 0.0172 0.0538 5.9404
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.628e+03 1.199e+02 13.577 < 2e-16 ***
## volatile.acidity -6.605e+00 9.863e-01 -6.697 2.13e-11 ***
## citric.acid 2.875e+00 1.078e+00 2.667 0.00765 **
## residual.sugar 8.679e-01 8.615e-02 10.074 < 2e-16 ***
## chlorides -2.447e+01 3.818e+00 -6.408 1.48e-10 ***
## free.sulfur.dioxide -6.531e-02 1.340e-02 -4.874 1.10e-06 ***
## total.sulfur.dioxide 5.326e-02 4.914e-03 10.838 < 2e-16 ***
## density -1.619e+03 1.192e+02 -13.583 < 2e-16 ***
## sulphates -3.413e+00 1.203e+00 -2.836 0.00456 **
## alcohol -1.685e+00 2.256e-01 -7.466 8.25e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 7250.98 on 6496 degrees of freedom
## Residual deviance: 431.55 on 6487 degrees of freedom
## AIC: 451.55
##
## Number of Fisher Scoring iterations: 9
The variance inflation factor values are all below 10
## volatile.acidity citric.acid residual.sugar
## 1.487405 1.379847 1.641885
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## 1.289718 1.991048 2.006098
## density sulphates alcohol
## 4.020209 1.331723 3.473617
Compute the anti-logs of the coefficients.
## (Intercept) volatile.acidity citric.acid
## Inf 1.353286e-03 1.771751e+01
## residual.sugar chlorides free.sulfur.dioxide
## 2.381968e+00 2.367387e-11 9.367807e-01
## total.sulfur.dioxide density sulphates
## 1.054705e+00 0.000000e+00 3.293905e-02
## alcohol
## 1.854897e-01
Predict probability for Good or Bad credit
## 1 2 3 4 5
## 0.0001161913 0.0001505137 0.0002565461 0.0087953858 0.0001161913
## 6
## 0.0001717464
Predict “red” or “white” wine.
## 1 2 3 4 5 6
## "Red" "Red" "Red" "Red" "Red" "Red"
## pred
## Red White
## red 1579 20
## white 16 4882
Plot the ROC Curve
Calculate the area under the curve(AUC)
## An object of class "performance"
## Slot "x.name":
## [1] "None"
##
## Slot "y.name":
## [1] "Area under the ROC curve"
##
## Slot "alpha.name":
## [1] "none"
##
## Slot "x.values":
## list()
##
## Slot "y.values":
## [[1]]
## [1] 0.9960834
##
##
## Slot "alpha.values":
## list()
Validate
Compute the prediction accuracy on the test set
Estimate probabilities of Red or white
## 5 6 8 9 12
## 5.249033e-05 8.273912e-05 1.453147e-03 2.390208e-04 1.282373e-01
## 13
## 2.148350e-02
## 5 6 8 9 12 13
## "Red" "Red" "Red" "Red" "Red" "Red"
## pred
## Red White
## red 804 12
## white 8 2473
Build Roc Curve for Test set
Compute the test set area under the curve(AUC)
## An object of class "performance"
## Slot "x.name":
## [1] "None"
##
## Slot "y.name":
## [1] "Area under the ROC curve"
##
## Slot "alpha.name":
## [1] "none"
##
## Slot "x.values":
## list()
##
## Slot "y.values":
## [[1]]
## [1] 0.9949731
##
##
## Slot "alpha.values":
## list()
Lasso Logistic Regression
Lambda values are a power of 10
## [1] 1.000000e+10 7.390722e+09 5.462277e+09 4.037017e+09 2.983647e+09
## [6] 2.205131e+09 1.629751e+09 1.204504e+09 8.902151e+08 6.579332e+08
## [11] 4.862602e+08 3.593814e+08 2.656088e+08 1.963041e+08 1.450829e+08
## [16] 1.072267e+08 7.924829e+07 5.857021e+07 4.328761e+07 3.199267e+07
## [21] 2.364489e+07 1.747528e+07 1.291550e+07 9.545485e+06 7.054802e+06
## [26] 5.214008e+06 3.853529e+06 2.848036e+06 2.104904e+06 1.555676e+06
## [31] 1.149757e+06 8.497534e+05 6.280291e+05 4.641589e+05 3.430469e+05
## [36] 2.535364e+05 1.873817e+05 1.384886e+05 1.023531e+05 7.564633e+04
## [41] 5.590810e+04 4.132012e+04 3.053856e+04 2.257020e+04 1.668101e+04
## [46] 1.232847e+04 9.111628e+03 6.734151e+03 4.977024e+03 3.678380e+03
## [51] 2.718588e+03 2.009233e+03 1.484968e+03 1.097499e+03 8.111308e+02
## [56] 5.994843e+02 4.430621e+02 3.274549e+02 2.420128e+02 1.788650e+02
## [61] 1.321941e+02 9.770100e+01 7.220809e+01 5.336699e+01 3.944206e+01
## [66] 2.915053e+01 2.154435e+01 1.592283e+01 1.176812e+01 8.697490e+00
## [71] 6.428073e+00 4.750810e+00 3.511192e+00 2.595024e+00 1.917910e+00
## [76] 1.417474e+00 1.047616e+00 7.742637e-01 5.722368e-01 4.229243e-01
## [81] 3.125716e-01 2.310130e-01 1.707353e-01 1.261857e-01 9.326033e-02
## [86] 6.892612e-02 5.094138e-02 3.764936e-02 2.782559e-02 2.056512e-02
## [91] 1.519911e-02 1.123324e-02 8.302176e-03 6.135907e-03 4.534879e-03
## [96] 3.351603e-03 2.477076e-03 1.830738e-03 1.353048e-03 1.000000e-03
## [1] 0.03764936
Coefficients
## (Intercept) fixed.acidity pH
## 128.21039106 -0.10526325 -0.41664288
## volatile.acidity citric.acid residual.sugar
## -4.71524039 0.00000000 0.00000000
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## -8.85550824 0.00000000 0.02664162
## density sulphates alcohol
## -124.41186872 -2.65875795 0.00000000
## (Intercept) fixed.acidity pH
## 128.21039106 -0.10526325 -0.41664288
## volatile.acidity chlorides total.sulfur.dioxide
## -4.71524039 -8.85550824 0.02664162
## density sulphates
## -124.41186872 -2.65875795
Validate lasso logistic regression
## [1] 5.20977e-05
Predict probability for test set
## 1
## 1 0.0001267130
## 2 0.0001612888
## 4 0.0237603689
## 5 0.0001267130
## 8 0.0093942905
## 11 0.0199101880
## 1
## 1 "Red"
## 2 "Red"
## 4 "Red"
## 5 "Red"
## 8 "Red"
## 11 "Red"
Prediction accuracy
## [1] 0.7503791
## 12 x 1 sparse Matrix of class "dgCMatrix"
## 1
## (Intercept) 1.189542e+03
## fixed.acidity .
## pH -1.048479e+00
## volatile.acidity -6.506930e+00
## citric.acid 1.379715e+00
## residual.sugar 5.798524e-01
## chlorides -2.018809e+01
## free.sulfur.dioxide -2.706807e-02
## total.sulfur.dioxide 4.420857e-02
## density -1.181022e+03
## sulphates -3.970915e+00
## alcohol -9.786519e-01
Linear Discriminant Analysis
Standardized Coefficients
## Call:
## lda(type ~ fixed.acidity + pH + volatile.acidity + citric.acid +
## residual.sugar + chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + sulphates + alcohol, data = WineQ)
##
## Prior probabilities of groups:
## red white
## 0.2461136 0.7538864
##
## Group means:
## fixed.acidity pH volatile.acidity citric.acid residual.sugar
## red 8.319637 3.311113 0.5278205 0.2709756 2.538806
## white 6.854788 3.188267 0.2782411 0.3341915 6.391415
## chlorides free.sulfur.dioxide total.sulfur.dioxide density
## red 0.08746654 15.87492 46.46779 0.9967467
## white 0.04577236 35.30808 138.36066 0.9940274
## sulphates alcohol
## red 0.6581488 10.42298
## white 0.4898469 10.51427
##
## Coefficients of linear discriminants:
## LD1
## fixed.acidity 0.32334347
## pH 1.10607299
## volatile.acidity -3.06028749
## citric.acid 0.87495758
## residual.sugar 0.35118041
## chlorides -5.08835703
## free.sulfur.dioxide -0.01921302
## total.sulfur.dioxide 0.02006459
## density -910.43476356
## sulphates -0.86513227
## alcohol -0.82519241
## $class
## [1] red red red red red red red red red red red
## [12] red red red red red red red red red red red
## [23] red red red red red red red red red red red
## [34] red red red red red red red red red red red
## [45] red red red red red white red red red red red
## [56] red red red red red red red red red red red
## [67] red red red red red red red red red red red
## [78] red red red red red red red red red red red
## [89] red red red red red red red red red red red
## [100] red red red red red red red red red red red
## [111] red red red red red red red red red red red
## [122] red red red red red red red red red red red
## [133] red red red red red red red red red red red
## [144] red red red red red red red red red red red
## [155] red red red red red red red red red red red
## [166] red red red red red red red red red red red
## [177] red red red red red red red red red red red
## [188] red red red red red red red red red red red
## [199] red red red red red red red red red red red
## [210] red red red red red red red red red red red
## [221] red red red red red red red red red red red
## [232] red red red red red red red red red red red
## [243] red red red red red red red red red red red
## [254] red red red red red red red red red red red
## [265] red red red red red red red red red red red
## [276] red red red red red red red red red red red
## [287] red red red red red red red red red red red
## [298] red red red red red red red red red red red
## [309] red red red red red red red red red red red
## [320] red red red red red red red red red red red
## [331] red red red red red red red red red red red
## [342] red red red red red red red red red red red
## [353] red red white red red red red red red red red
## [364] red red red red red red red red red red red
## [375] red red red red red red red red red red red
## [386] red red red red red red red red red red red
## [397] red red red red red red red red red red red
## [408] red red red red red red red red red red red
## [419] red red red red red red red red red red red
## [430] red red red red red red red red red red red
## [441] red red red red red red red red red red red
## [452] red red red red red red red red red red red
## [463] red red red red red red red red red red red
## [474] red red red red red red red red red red red
## [485] red red red red red red red red red red white
## [496] red red red red red red red red red red red
## [507] red red red red red red red red red red red
## [518] red red red red red red red red red red red
## [529] red red red red red red red red red red red
## [540] red red red red red red red red red red red
## [551] red red red red red red red red red red red
## [562] red red red red red red red red red red red
## [573] red red red red red red red red red red red
## [584] red red red red red red red red white red red
## [595] red red red red red red red red red red red
## [606] red red red red red red red red red red red
## [617] red red red red red red red red red red red
## [628] red red red red red red red red red red red
## [639] red red red red red red red red red red red
## [650] white red red red red red red red red red red
## [661] red red red red red red red red red red red
## [672] red red red red red red red red red red red
## [683] red red red red red red red red red red red
## [694] red red red red red red red red red red red
## [705] red red red red red red red red red red red
## [716] red red red red red red red red red red red
## [727] red red red red red red red red red red red
## [738] red red red red red red red red red red red
## [749] red red red red red red red red red red red
## [760] red red red red red red red red red red red
## [771] red red red red red red red red red red red
## [782] red red red red red red red red red red red
## [793] red red red red red red red red red red red
## [804] red red red red red red red red red red red
## [815] red red red red red red red red red red red
## [826] red red red red red red red red red red red
## [837] white white red red red red red red red red red
## [848] red red red red red red red red red red red
## [859] red red red red red red red red red red red
## [870] red red red red red red red red red red red
## [881] red red red red red red red red red red red
## [892] red red red red red red red red red red red
## [903] red red red red red red red red red red red
## [914] red red red red red red red red red red red
## [925] red red red red red red red red red red red
## [936] red red red red red red red red red red red
## [947] red red red red red red red red red red red
## [958] red red red red red red red red red red red
## [969] red red red red red red red red red red red
## [980] red red red red red red red red red red red
## [991] red red red red red red red red red red red
## [1002] red red red red red red red red red red red
## [1013] red red red red red white white red red red red
## [1024] red red red red red red red red red red red
## [1035] red red red red red red red red red red red
## [1046] red red red red red red red red red red red
## [1057] red red red red red red red red red red red
## [1068] red red red red red red red red red red red
## [1079] red white red white red red red red red red red
## [1090] red red red red red red red red red red red
## [1101] red red red red red red red red red red red
## [1112] red red red white red red red red red red red
## [1123] red red red red red red red red red white red
## [1134] red red red red red red red red red red red
## [1145] red red red red red red red red red red red
## [1156] red red red red red red red red red red red
## [1167] red red red red red red red red red red red
## [1178] red red red red red red red red red red red
## [1189] red red red red red red red red red red red
## [1200] red red red red red red red red red red red
## [1211] red red red red red red red red red red red
## [1222] red red red red red red red red red red red
## [1233] red white red white red red red red red red red
## [1244] red white red red red red red red red red red
## [1255] red red red red red red red red red red red
## [1266] red red red red red red red red red red red
## [1277] red red red red red red red red red red red
## [1288] red red red red red red red red red red red
## [1299] red red red red red red red red red red red
## [1310] red red red red red red red red red red red
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## [1409] red red red red red red red red red red red
## [1420] red red red red red red red red red red red
## [1431] red red red red red red red red red red red
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## [1453] red red red red white red red red red red red
## [1464] red red red red red red red red red red red
## [1475] red red red red red red red red red red red
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## [1508] red red red red red red white red red red red
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## [1530] red red red red red red red red red red red
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## [1563] red red red red red red red red red red red
## [1574] red white red red red red red red red red red
## [1585] red red red red red red red red red red red
## [1596] red red red red white white white white white white white
## [1607] white white white white white white white white white white white
## [1618] white white white white white white white white white white white
## [1629] white white white white white white white white white white white
## [1640] white white white white white white white white white white white
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## [1926] white white white white white white white white white white white
## [1937] white white white white white white white white white white white
## [1948] white white white white white white white white white white white
## [1959] white white white white white white white white white white white
## [1970] white white white white white white white white white white white
## [1981] white white white white white white white white white white white
## [1992] white white white white white white white white white white white
## [2003] white white white white white white white white white white white
## [2014] white white white white white white white white white white white
## [2025] white white white white white white white white white white white
## [2036] white white white white white white white white white white white
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## [2179] white white white white white white white white white white white
## [2190] white white white white white white white white white white white
## [2201] white white white white white white white white red white white
## [2212] white white white white white white white white white white white
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## [2399] white white white white white white white white white white white
## [2410] white white white white white white white white white white white
## [2421] white white white white white white white white white red white
## [2432] white white red white white white white white white white white
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## [2542] white white white white white white red white white white white
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## [5501] red white white white white white white white white white white
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## [5930] white white white white white white white white white white white
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## [5985] white white white white white white white white white white white
## [5996] white white white white white white white white white white white
## [6007] white white white white white white white white white white white
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## [6084] white white white white white white white white white white white
## [6095] white white white white white white white white white white white
## [6106] white white white white white white white white white white white
## [6117] white white white white white white white white white white white
## [6128] white white white white white white white white white white white
## [6139] white white white white white white white white white white white
## [6150] white white white white white white white white white white white
## [6161] white white white white white white white white white white white
## [6172] white white white white white white white white white white white
## [6183] white white white white white white white white white white white
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## [6205] white white white white white white white white white white white
## [6216] white white white white white white white white white white white
## [6227] white white white white white white white white white white white
## [6238] white white white white white white white white white white white
## [6249] white white white white white white white white white white white
## [6260] white white white white white white white white white white white
## [6271] white white white white white white white white white white white
## [6282] white white white white white white white white white white white
## [6293] white white white white white white white white white white white
## [6304] white white white white white white white white white white white
## [6315] white white white white white white white white white white white
## [6326] white white white white white white white white white white white
## [6337] white white white white white white white white white white white
## [6348] white white white white white white white white white white white
## [6359] white white white white white white white white white white white
## [6370] white white white white white white white white white white white
## [6381] white white white white white white white white white white white
## [6392] white white white white white white white white white white white
## [6403] white white white white white white white white white white white
## [6414] white white white white white white white white white white white
## [6425] white white white white white white white white white white white
## [6436] white white white white white white white white white white white
## [6447] white white white white white white white white white white white
## [6458] white white white white white white white white white white white
## [6469] white white white white white white white white white white white
## [6480] white white white white white white white white white white white
## [6491] white white white white white white white
## Levels: red white
##
## $posterior
## red white
## 1 1.000000e+00 1.589343e-10
## 2 1.000000e+00 6.349806e-10
## 3 1.000000e+00 1.689005e-09
## 4 9.996938e-01 3.061677e-04
## 5 1.000000e+00 1.589343e-10
## 6 1.000000e+00 4.362155e-10
## 7 9.999826e-01 1.744070e-05
## 8 9.999868e-01 1.324428e-05
## 9 1.000000e+00 3.575187e-08
## 10 9.998099e-01 1.900898e-04
## 11 9.999178e-01 8.222106e-05
## 12 9.998099e-01 1.900898e-04
## 13 9.982707e-01 1.729295e-03
## 14 1.000000e+00 4.146272e-11
## 15 9.999998e-01 2.316851e-07
## 16 9.999995e-01 4.685444e-07
## 17 9.997655e-01 2.344708e-04
## 18 1.000000e+00 1.726798e-11
## 19 9.999936e-01 6.431525e-06
## 20 1.000000e+00 1.077697e-08
## 21 9.669194e-01 3.308059e-02
## 22 9.999998e-01 1.946699e-07
## 23 9.999997e-01 3.402050e-07
## 24 9.997622e-01 2.377705e-04
## 25 9.999993e-01 7.080173e-07
## 26 9.999005e-01 9.953388e-05
## 27 9.999918e-01 8.187986e-06
## 28 9.999997e-01 3.402050e-07
## 29 1.000000e+00 1.044604e-09
## 30 1.000000e+00 1.401615e-08
## 31 9.999871e-01 1.291859e-05
## 32 1.000000e+00 6.097321e-11
## 33 9.997737e-01 2.262969e-04
## 34 9.998563e-01 1.437184e-04
## 35 9.988851e-01 1.114926e-03
## 36 1.000000e+00 8.971593e-10
## 37 1.000000e+00 6.160976e-12
## 38 9.999976e-01 2.366454e-06
## 39 1.000000e+00 3.792685e-09
## 40 9.999553e-01 4.466003e-05
## 41 9.999553e-01 4.466003e-05
## 42 9.999995e-01 5.350912e-07
## 43 1.000000e+00 1.775363e-13
## 44 1.000000e+00 8.012498e-11
## 45 9.999999e-01 6.631127e-08
## 46 9.999806e-01 1.941891e-05
## 47 9.999990e-01 1.048672e-06
## 48 9.998978e-01 1.021929e-04
## 49 9.999414e-01 5.856386e-05
## 50 2.173965e-01 7.826035e-01
## 51 1.000000e+00 2.996943e-08
## 52 9.999861e-01 1.393237e-05
## 53 9.999719e-01 2.805505e-05
## 54 6.759983e-01 3.240017e-01
## 55 9.999150e-01 8.495165e-05
## 56 1.000000e+00 9.730664e-09
## 57 9.998606e-01 1.394416e-04
## 58 9.999999e-01 1.309875e-07
## 59 1.000000e+00 9.903008e-09
## 60 9.939207e-01 6.079343e-03
## 61 9.999927e-01 7.339608e-06
## 62 9.999291e-01 7.089966e-05
## 63 9.999997e-01 3.141111e-07
## 64 1.000000e+00 1.642649e-08
## 65 1.000000e+00 1.193928e-08
## 66 1.000000e+00 1.193928e-08
## 67 9.999998e-01 2.246404e-07
## 68 1.000000e+00 2.578815e-11
## 69 9.999887e-01 1.130083e-05
## 70 1.000000e+00 1.712122e-10
## 71 1.000000e+00 2.752181e-08
## 72 9.986031e-01 1.396862e-03
## 73 9.992131e-01 7.869218e-04
## 74 1.000000e+00 4.055817e-08
## 75 9.999862e-01 1.383735e-05
## 76 1.000000e+00 1.901182e-09
## 77 1.000000e+00 1.901182e-09
## 78 1.000000e+00 7.849221e-12
## 79 9.999960e-01 3.951291e-06
## 80 9.999926e-01 7.355946e-06
## 81 9.999638e-01 3.618325e-05
## 82 1.000000e+00 4.032461e-12
## 83 9.998280e-01 1.719505e-04
## 84 1.000000e+00 1.308822e-13
## 85 9.998110e-01 1.889854e-04
## 86 9.999996e-01 3.604089e-07
## 87 9.999998e-01 2.427274e-07
## 88 9.999962e-01 3.827026e-06
## 89 9.999512e-01 4.879875e-05
## 90 1.000000e+00 1.075734e-09
## 91 9.580865e-01 4.191345e-02
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## 1895 5.656969e-09 1.000000e+00
## 1896 1.102151e-08 1.000000e+00
## 1897 6.131264e-08 9.999999e-01
## 1898 1.150491e-07 9.999999e-01
## 1899 9.077203e-10 1.000000e+00
## 1900 2.592614e-04 9.997407e-01
## 1901 4.967531e-08 1.000000e+00
## 1902 2.592614e-04 9.997407e-01
## 1903 2.727311e-09 1.000000e+00
## 1904 2.642504e-08 1.000000e+00
## 1905 2.642504e-08 1.000000e+00
## 1906 8.690671e-08 9.999999e-01
## 1907 3.340087e-08 1.000000e+00
## 1908 9.954662e-10 1.000000e+00
## 1909 5.371073e-10 1.000000e+00
## 1910 7.543264e-06 9.999925e-01
## 1911 1.592671e-09 1.000000e+00
## 1912 2.907204e-06 9.999971e-01
## 1913 1.532438e-08 1.000000e+00
## 1914 8.780092e-09 1.000000e+00
## 1915 1.483834e-06 9.999985e-01
## 1916 2.220664e-10 1.000000e+00
## 1917 1.418178e-10 1.000000e+00
## 1918 1.570203e-10 1.000000e+00
## 1919 5.344308e-07 9.999995e-01
## 1920 5.002617e-06 9.999950e-01
## 1921 1.418178e-10 1.000000e+00
## 1922 2.220664e-10 1.000000e+00
## 1923 1.669042e-10 1.000000e+00
## 1924 1.026133e-09 1.000000e+00
## 1925 4.966388e-11 1.000000e+00
## 1926 2.913185e-13 1.000000e+00
## 1927 1.892629e-07 9.999998e-01
## 1928 1.713812e-11 1.000000e+00
## 1929 2.672207e-07 9.999997e-01
## 1930 2.102383e-07 9.999998e-01
## 1931 3.271260e-10 1.000000e+00
## 1932 1.273554e-08 1.000000e+00
## 1933 1.276820e-09 1.000000e+00
## 1934 5.520431e-09 1.000000e+00
## 1935 1.273554e-08 1.000000e+00
## 1936 1.550496e-09 1.000000e+00
## 1937 4.272308e-09 1.000000e+00
## 1938 1.909411e-04 9.998091e-01
## 1939 3.630692e-06 9.999964e-01
## 1940 9.927614e-10 1.000000e+00
## 1941 4.475729e-05 9.999552e-01
## 1942 1.016853e-09 1.000000e+00
## 1943 6.222499e-07 9.999994e-01
## 1944 2.367837e-07 9.999998e-01
## 1945 9.098663e-10 1.000000e+00
## 1946 3.181003e-06 9.999968e-01
## 1947 2.626033e-07 9.999997e-01
## 1948 2.868953e-07 9.999997e-01
## 1949 1.847943e-07 9.999998e-01
## 1950 3.118168e-09 1.000000e+00
## 1951 5.464282e-11 1.000000e+00
## 1952 1.908658e-08 1.000000e+00
## 1953 5.464282e-11 1.000000e+00
## 1954 5.500913e-13 1.000000e+00
## 1955 4.177843e-12 1.000000e+00
## 1956 4.177843e-12 1.000000e+00
## 1957 5.153114e-09 1.000000e+00
## 1958 1.015847e-08 1.000000e+00
## 1959 4.924178e-09 1.000000e+00
## 1960 1.028895e-10 1.000000e+00
## 1961 6.593808e-04 9.993406e-01
## 1962 1.205726e-09 1.000000e+00
## 1963 4.177843e-12 1.000000e+00
## 1964 4.097386e-08 1.000000e+00
## 1965 1.740383e-07 9.999998e-01
## 1966 1.816188e-07 9.999998e-01
## 1967 1.458187e-08 1.000000e+00
## 1968 2.714306e-09 1.000000e+00
## 1969 2.365371e-08 1.000000e+00
## 1970 1.458187e-08 1.000000e+00
## 1971 2.714306e-09 1.000000e+00
## 1972 3.771325e-05 9.999623e-01
## 1973 2.355288e-09 1.000000e+00
## 1974 1.308457e-08 1.000000e+00
## 1975 1.308457e-08 1.000000e+00
## 1976 3.913631e-09 1.000000e+00
## 1977 1.062007e-08 1.000000e+00
## 1978 8.400950e-10 1.000000e+00
## 1979 3.913631e-09 1.000000e+00
## 1980 1.062007e-08 1.000000e+00
## 1981 2.615025e-10 1.000000e+00
## 1982 2.228929e-08 1.000000e+00
## 1983 2.355288e-09 1.000000e+00
## 1984 7.834243e-11 1.000000e+00
## 1985 1.308457e-08 1.000000e+00
## 1986 6.692111e-12 1.000000e+00
## 1987 7.529152e-11 1.000000e+00
## 1988 1.896920e-08 1.000000e+00
## 1989 1.195980e-09 1.000000e+00
## 1990 1.195980e-09 1.000000e+00
## 1991 1.093517e-05 9.999891e-01
## 1992 4.847178e-06 9.999952e-01
## 1993 2.610611e-08 1.000000e+00
## 1994 2.245929e-08 1.000000e+00
## 1995 1.772796e-08 1.000000e+00
## 1996 2.667125e-07 9.999997e-01
## 1997 3.064665e-07 9.999997e-01
## 1998 1.319826e-09 1.000000e+00
## 1999 7.257595e-09 1.000000e+00
## 2000 3.064665e-07 9.999997e-01
## 2001 2.245929e-08 1.000000e+00
## 2002 2.285708e-05 9.999771e-01
## 2003 1.599957e-13 1.000000e+00
## 2004 3.718552e-11 1.000000e+00
## 2005 1.772796e-08 1.000000e+00
## 2006 1.131340e-09 1.000000e+00
## 2007 1.387066e-06 9.999986e-01
## 2008 3.449066e-09 1.000000e+00
## 2009 2.667125e-07 9.999997e-01
## 2010 5.898993e-10 1.000000e+00
## 2011 5.871917e-07 9.999994e-01
## 2012 1.295952e-07 9.999999e-01
## 2013 1.295952e-07 9.999999e-01
## 2014 5.898993e-10 1.000000e+00
## 2015 5.871917e-07 9.999994e-01
## 2016 4.350275e-08 1.000000e+00
## 2017 1.064773e-10 1.000000e+00
## 2018 4.350275e-08 1.000000e+00
## 2019 3.960565e-07 9.999996e-01
## 2020 7.002215e-11 1.000000e+00
## 2021 2.304673e-12 1.000000e+00
## 2022 3.172464e-12 1.000000e+00
## 2023 3.172464e-12 1.000000e+00
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## 2027 2.479290e-11 1.000000e+00
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## 2029 1.121674e-10 1.000000e+00
## 2030 2.479290e-11 1.000000e+00
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## 2032 1.076190e-10 1.000000e+00
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## 6491 1.964558707
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## 6496 2.145127349
## 6497 2.380341627
## [1] red red red red red red
## Levels: red white
## class
## red white
## red 1580 19
## white 16 4882
Accuracy
## [1] 0.9946129
Validate Linear Discriminant Analysis
Predict on the test set
List of predicted values
## [1] red red red red red red
## Levels: red white
Accuracy
## [1] 0.9951471
Quadratic Discriminant Analysis
Correctly classified cases
## [1] red red red red red red
## Levels: red white
Accuracy
## [1] 0.9861475
Validate the Quadratic Discriminant Analysis
Compute prediction accuracy on the test set
Accuracy
## [1] 0.9860479
Naive Bayes
##
## Naive Bayes Classifier for Discrete Predictors
##
## Call:
## naiveBayes.default(x = X, y = Y, laplace = laplace)
##
## A-priori probabilities:
## Y
## red white
## 0.2446875 0.7553125
##
## Conditional probabilities:
## fixed.acidity
## Y [,1] [,2]
## red 8.352746 1.7266127
## white 6.860612 0.8486221
##
## pH
## Y [,1] [,2]
## red 3.310307 0.1510446
## white 3.188084 0.1513797
##
## volatile.acidity
## Y [,1] [,2]
## red 0.5259195 0.1759740
## white 0.2780761 0.1030328
##
## citric.acid
## Y [,1] [,2]
## red 0.2756705 0.1904068
## white 0.3342325 0.1172442
##
## residual.sugar
## Y [,1] [,2]
## red 2.610983 1.522160
## white 6.386926 5.125251
##
## chlorides
## Y [,1] [,2]
## red 0.08749553 0.04238467
## white 0.04527844 0.02071325
##
## free.sulfur.dioxide
## Y [,1] [,2]
## red 15.63729 10.11209
## white 35.33719 16.77666
##
## total.sulfur.dioxide
## Y [,1] [,2]
## red 46.08174 31.54761
## white 138.96959 43.29990
##
## density
## Y [,1] [,2]
## red 0.9968298 0.001873513
## white 0.9940263 0.003091514
##
## sulphates
## Y [,1] [,2]
## red 0.6576628 0.159616
## white 0.4910674 0.114619
##
## alcohol
## Y [,1] [,2]
## red 10.42925 1.049367
## white 10.52375 1.239292
Predicted values
## [1] red red red red red red
## Levels: red white
## pred
## red white
## red 788 28
## white 53 2428
Accuracy
## [1] 0.9860479
KNN
find optimal “k” value of 5.
##
## Parameter tuning of 'knn.wrapper':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## k
## 1
##
## - best performance: 0.0575
Standardize the predictors for the knn model.
Accuracy
## [1] 0.9909008
Suport Vector Machine
Accuracy
## [1] 0.9942372
Find the best cost value.(4)
## cost
## 1 4