STM1001: Computer Lab 10B Solutions
Data Science Module
Topic 10B: Machine Learning I
Example R code solutions for the Data Science Module Computer Lab 10B, which uses the caret R package (Kuhn et al. 2021) and Portuguese wine data obtained from UCI Machine Learning Repository (2009) (originally collected by Cortez et al. (2009)), are presented below.
This computer lab is designed to run alongside the content in the Introduction to Machine Learning in R supplement. It might be helpful to have this material open as you look through these solutions.
1 Preparations
1.1 Load Required Packages
# Install packages
install.packages("caret", "magrittr", "rpart.plot")
# Load packages
library(caret)
library(rpart.plot)1.2 Wine Data
No answer required.
1.3
Example R code for loading the red wine data is shown below:
red_wine <- read.csv(file = "winequality_red.csv", header = T)1.4 Aim
red_wine$quality <- as.factor(red_wine$quality)2 Data Visualisation
2.1
The head function provides an overview of the different variables. The summary function provides information on the spread of observed values for each variable, and the dim function tells us that we have observations for 1599 wine samples.
head(red_wine)## fixed.acidity volatile.acidity citric.acid residual.sugar chlorides
## 1 7.4 0.70 0.00 1.9 0.076
## 2 7.8 0.88 0.00 2.6 0.098
## 3 7.8 0.76 0.04 2.3 0.092
## 4 11.2 0.28 0.56 1.9 0.075
## 5 7.4 0.70 0.00 1.9 0.076
## 6 7.4 0.66 0.00 1.8 0.075
## free.sulfur.dioxide total.sulfur.dioxide density pH sulphates alcohol
## 1 11 34 0.9978 3.51 0.56 9.4
## 2 25 67 0.9968 3.20 0.68 9.8
## 3 15 54 0.9970 3.26 0.65 9.8
## 4 17 60 0.9980 3.16 0.58 9.8
## 5 11 34 0.9978 3.51 0.56 9.4
## 6 13 40 0.9978 3.51 0.56 9.4
## quality
## 1 5
## 2 5
## 3 5
## 4 6
## 5 5
## 6 5summary(red_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 density
## Min. :0.01200 Min. : 1.00 Min. : 6.00 Min. :0.9901
## 1st Qu.:0.07000 1st Qu.: 7.00 1st Qu.: 22.00 1st Qu.:0.9956
## Median :0.07900 Median :14.00 Median : 38.00 Median :0.9968
## Mean :0.08747 Mean :15.87 Mean : 46.47 Mean :0.9967
## 3rd Qu.:0.09000 3rd Qu.:21.00 3rd Qu.: 62.00 3rd Qu.:0.9978
## Max. :0.61100 Max. :72.00 Max. :289.00 Max. :1.0037
## pH sulphates alcohol quality
## Min. :2.740 Min. :0.3300 Min. : 8.40 3: 10
## 1st Qu.:3.210 1st Qu.:0.5500 1st Qu.: 9.50 4: 53
## Median :3.310 Median :0.6200 Median :10.20 5:681
## Mean :3.311 Mean :0.6581 Mean :10.42 6:638
## 3rd Qu.:3.400 3rd Qu.:0.7300 3rd Qu.:11.10 7:199
## Max. :4.010 Max. :2.0000 Max. :14.90 8: 18dim(red_wine)## [1] 1599 122.2
We notice that the majority of quality scores are either 5 or 6. Very few scores of 3 or 8 are recorded - this might make it difficult to accurately predict such scores.
plot(red_wine$quality)
2.3
As we can see from the featurePlot box plots, the free.sulfur.dioxide and total.sulfur.dioxide have much larger values than the other feature variables and lead to the box plot being relatively uninformative.
featurePlot(x = red_wine[, -12],
y = red_wine$quality,
plot = "box")
2.4
Example R code is provide below:
featurePlot(x = red_wine[, -c(6, 7, 12)],
y = red_wine$quality,
plot = "box")
Many of the box plots are still not informative - we will try to address this in the next section.
3 Pre-Processing
3.1
No answer required.
3.2
nearZeroVar(red_wine, saveMetrics = T, freqCut = 2, uniqueCut = 5)## freqRatio percentUnique zeroVar nzv
## fixed.acidity 1.175439 6.0037523 FALSE FALSE
## volatile.acidity 1.021739 8.9430894 FALSE FALSE
## citric.acid 1.941176 5.0031270 FALSE FALSE
## residual.sugar 1.190840 5.6910569 FALSE FALSE
## chlorides 1.200000 9.5684803 FALSE FALSE
## free.sulfur.dioxide 1.326923 3.7523452 FALSE FALSE
## total.sulfur.dioxide 1.194444 9.0056285 FALSE FALSE
## density 1.028571 27.2670419 FALSE FALSE
## pH 1.017857 5.5659787 FALSE FALSE
## sulphates 1.014706 6.0037523 FALSE FALSE
## alcohol 1.349515 4.0650407 FALSE FALSE
## quality 1.067398 0.3752345 FALSE FALSEnearZeroVar(red_wine, saveMetrics = F, freqCut = 2, uniqueCut = 5)## integer(0)3.3
None of the feature variables are flagged as exceeding our specified cut-off values.
The citric acid feature variable has the highest freqRatio value, at 1.94, and also has the lowest percentUnique value (5.003) of the feature variables (just missing our specified cut-off).
Neither of these values are too alarming - it should be ok to leave the citric acid feature variable in our data set for the time being.
We conclude that there do not appear to be any problematic variables.
3.4
base_cor <- cor(red_wine[, -12])
base_cor## fixed.acidity volatile.acidity citric.acid residual.sugar
## fixed.acidity 1.00000000 -0.256130895 0.67170343 0.114776724
## volatile.acidity -0.25613089 1.000000000 -0.55249568 0.001917882
## citric.acid 0.67170343 -0.552495685 1.00000000 0.143577162
## residual.sugar 0.11477672 0.001917882 0.14357716 1.000000000
## chlorides 0.09370519 0.061297772 0.20382291 0.055609535
## free.sulfur.dioxide -0.15379419 -0.010503827 -0.06097813 0.187048995
## total.sulfur.dioxide -0.11318144 0.076470005 0.03553302 0.203027882
## density 0.66804729 0.022026232 0.36494718 0.355283371
## pH -0.68297819 0.234937294 -0.54190414 -0.085652422
## sulphates 0.18300566 -0.260986685 0.31277004 0.005527121
## alcohol -0.06166827 -0.202288027 0.10990325 0.042075437
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## fixed.acidity 0.093705186 -0.153794193 -0.11318144
## volatile.acidity 0.061297772 -0.010503827 0.07647000
## citric.acid 0.203822914 -0.060978129 0.03553302
## residual.sugar 0.055609535 0.187048995 0.20302788
## chlorides 1.000000000 0.005562147 0.04740047
## free.sulfur.dioxide 0.005562147 1.000000000 0.66766645
## total.sulfur.dioxide 0.047400468 0.667666450 1.00000000
## density 0.200632327 -0.021945831 0.07126948
## pH -0.265026131 0.070377499 -0.06649456
## sulphates 0.371260481 0.051657572 0.04294684
## alcohol -0.221140545 -0.069408354 -0.20565394
## density pH sulphates alcohol
## fixed.acidity 0.66804729 -0.68297819 0.183005664 -0.06166827
## volatile.acidity 0.02202623 0.23493729 -0.260986685 -0.20228803
## citric.acid 0.36494718 -0.54190414 0.312770044 0.10990325
## residual.sugar 0.35528337 -0.08565242 0.005527121 0.04207544
## chlorides 0.20063233 -0.26502613 0.371260481 -0.22114054
## free.sulfur.dioxide -0.02194583 0.07037750 0.051657572 -0.06940835
## total.sulfur.dioxide 0.07126948 -0.06649456 0.042946836 -0.20565394
## density 1.00000000 -0.34169933 0.148506412 -0.49617977
## pH -0.34169933 1.00000000 -0.196647602 0.20563251
## sulphates 0.14850641 -0.19664760 1.000000000 0.09359475
## alcohol -0.49617977 0.20563251 0.093594750 1.00000000extreme_cor <- sum(abs(base_cor[upper.tri(base_cor)]) > .999)
extreme_cor## [1] 0summary(base_cor[upper.tri(base_cor)])## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.68298 -0.09942 0.04295 0.02285 0.16576 0.671703.5
The largest negative correlation value is -0.68297819, between pH and fixed.acidity.
The largest positive correlation value is 0.67170343, between citric.acid and fixed.acidity.
These correlation values are not too large in magnitude, so do not seem too problematic.
3.6
Using the the findCorrelation function to identify highly correlated feature variables to remove from our data set would depend on what we term an acceptable level of correlation. If we are happy with correlations of magnitude 0.69 and under, then we do not need to run this function.
If we would like to set the maximum acceptable correlation magnitude to e.g. 0.67, then the findCorrelation function would identify the fixed.acidity feature variable for removal.
Note: For the remainder of this lab, we will assume no feature variables needed to be removed.
3.7
centre_scale <- preProcess(red_wine[, -12],
method = c("center", "scale"))
red_wine_updated <- predict(centre_scale, red_wine)3.8
If we compare the original data to the updated data, we see that the feature variable values are now scaled and centred.
head(red_wine)## fixed.acidity volatile.acidity citric.acid residual.sugar chlorides
## 1 7.4 0.70 0.00 1.9 0.076
## 2 7.8 0.88 0.00 2.6 0.098
## 3 7.8 0.76 0.04 2.3 0.092
## 4 11.2 0.28 0.56 1.9 0.075
## 5 7.4 0.70 0.00 1.9 0.076
## 6 7.4 0.66 0.00 1.8 0.075
## free.sulfur.dioxide total.sulfur.dioxide density pH sulphates alcohol
## 1 11 34 0.9978 3.51 0.56 9.4
## 2 25 67 0.9968 3.20 0.68 9.8
## 3 15 54 0.9970 3.26 0.65 9.8
## 4 17 60 0.9980 3.16 0.58 9.8
## 5 11 34 0.9978 3.51 0.56 9.4
## 6 13 40 0.9978 3.51 0.56 9.4
## quality
## 1 5
## 2 5
## 3 5
## 4 6
## 5 5
## 6 5head(red_wine_updated)## fixed.acidity volatile.acidity citric.acid residual.sugar chlorides
## 1 -0.5281944 0.9615758 -1.391037 -0.45307667 -0.24363047
## 2 -0.2984541 1.9668271 -1.391037 0.04340257 0.22380518
## 3 -0.2984541 1.2966596 -1.185699 -0.16937425 0.09632273
## 4 1.6543385 -1.3840105 1.483689 -0.45307667 -0.26487754
## 5 -0.5281944 0.9615758 -1.391037 -0.45307667 -0.24363047
## 6 -0.5281944 0.7381867 -1.391037 -0.52400227 -0.26487754
## free.sulfur.dioxide total.sulfur.dioxide density pH sulphates
## 1 -0.46604672 -0.3790141 0.55809987 1.2882399 -0.57902538
## 2 0.87236532 0.6241680 0.02825193 -0.7197081 0.12891007
## 3 -0.08364328 0.2289750 0.13422152 -0.3310730 -0.04807379
## 4 0.10755844 0.4113718 0.66406945 -0.9787982 -0.46103614
## 5 -0.46604672 -0.3790141 0.55809987 1.2882399 -0.57902538
## 6 -0.27484500 -0.1966174 0.55809987 1.2882399 -0.57902538
## alcohol quality
## 1 -0.9599458 5
## 2 -0.5845942 5
## 3 -0.5845942 5
## 4 -0.5845942 6
## 5 -0.9599458 5
## 6 -0.9599458 53.9
The featurePlot box plots are now more informative, compared to those created in 2.3. For all variables, we are now able to see more clearly how the feature variables’ values differ across the different quality scores.
We observe that for several feature variables (sulphates, chlorides, volatile.acidity and residual.sugar) there are more extreme observations for quality scores of 5 and 6 than for the other scores.
featurePlot(x = red_wine_updated[, -12],
y = red_wine_updated$quality,
plot = "box")
3.10
featurePlot(x = red_wine_updated[, -12],
y = red_wine_updated$quality,
plot = "pairs",
auto.key = list(columns = 6))
We observe that for most pairs the data is too closely clumped to clearly distinguish between the quality ratings. Perhaps our machine learning model can help.
3.11 Training and Validation Data
Example R code is provided below.
Please note that the data partitioning into training or validation categories is random to an extent, so your results from this point onwards may differ slightly to those presented in the subsequent question solutions, since your training and validation data sets will most likely contain slightly different sets of observations.
set.seed(1650)
wine_train_index <- createDataPartition(red_wine_updated$quality,
p = 0.8,
list = FALSE, times = 1) 3.12
red_wine_train <- red_wine_updated[wine_train_index, ]
red_wine_validate <- red_wine_updated[-wine_train_index, ]4 Fitting a Decision Tree Machine Learning Model
Please note that we run the set.seed(1650) command prior to training the decision tree model, so that the results discussed here are accurate regardless of the number of times this document is generated. If you do not set a seed prior to training your models, your results may appear slightly different.
4.1 Decision Tree
set.seed(1650)
red_wine_decision_tree <- train(quality ~ .,
data = red_wine_train,
method = "rpart")
red_wine_decision_tree## CART
##
## 1282 samples
## 11 predictor
## 6 classes: '3', '4', '5', '6', '7', '8'
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 1282, 1282, 1282, 1282, 1282, 1282, ...
## Resampling results across tuning parameters:
##
## cp Accuracy Kappa
## 0.01221167 0.5737107 0.3033509
## 0.02374491 0.5657458 0.2697084
## 0.25237449 0.4719068 0.1116919
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.01221167.As we can see, the best accuracy achieved was only 57.37%, which is not much better than randomly guessing.
4.1.1
rpart.plot(red_wine_decision_tree$finalModel)
4.1.2
No answer required.
5 Validating Results
5.1
# Load magrittr package for piping
library(magrittr)
# count number of observations in validation data
validation_numbers <- dim(red_wine_validate)[1]
# Use the fitted model to predict quality values given the validation data
predict_red_wine_decision_tree <- predict(red_wine_decision_tree,
newdata =red_wine_validate)
# When run, the code below gives us the percentage of correct predictions
dec_tree_accuracy <- sum(predict_red_wine_decision_tree == red_wine_validate$quality) /
validation_numbers %>% round(2) * 100
dec_tree_accuracy## [1] 52.050475.2
We observe that the accuracy of the model using the validation data is only 52.05%, which is much lower than the 57.37% accuracy achieved using the training data. It would appear that our model may not perform as well as we anticipated, when presented with new data. This highlights the importance of cross-validating your machine learning models.
That’s everything. Next week we will continue our machine learning work.
References
Cortez, P., A. Cerdeira, F. Almeida, T. Matos, and J. Reis. 2009. “Modeling Wine Preferences by Data Mining from Physicochemical Properties.” Decision Support Systems 47 (4): 547–53.
Kuhn, M., J. Wing, S. Weston, A. Williams, C. Keefer, A. Engelhardt, T. Cooper, et al. 2021. caret: Classification and Regression Training. https://cran.r-project.org/web/packages/caret/index.html.
Thulin, M. 2021. Modern Statistics with R: From Wrangling and Exploring Data to Inference and Predictive Modelling.
UCI Machine Learning Repository. 2009. “Wine Quality Data Set[.csv File].” 2009. https://archive.ics.uci.edu/ml/datasets/Wine+Quality.
These notes have been prepared by Rupert Kuveke. Please note that some of the content in these notes has been developed from content in Thulin (2021). The copyright for the material in these notes resides with the authors named above, with the Department of Mathematical and Physical Sciences and with La Trobe University. Copyright in this work is vested in La Trobe University including all La Trobe University branding and naming. Unless otherwise stated, material within this work is licensed under a Creative Commons Attribution-Non Commercial-Non Derivatives License BY-NC-ND.
---
title: "STM1001: Computer Lab 10B Solutions"
output:
  bookdown::html_document2: 
    toc: true
    toc_float: true
    code_download: true
    theme: readable
    code_folding: show
bibliography: STM1001_DS_CL_references.bib 
link-citations: yes
---

<style>
#TOC {
  background: url("https://www.latrobe.edu.au/_media/la-trobe-api/v5/img/logo.svg");
  background-size: contain;
  padding-top: 80px !important;
  background-repeat: no-repeat;
}
</style>

### Data Science Module {-}

### Topic 10B: Machine Learning I {-}

<br>

Example R code solutions for the [Data Science Module Computer Lab 10B](https://rpubs.com/LTU_STM1001/DSMCL10_S), which uses the `caret` R package [@caret] and Portuguese wine data obtained from @UCIWine (originally collected by @wine), are presented below.

This computer lab is designed to run alongside the content in the [Introduction to Machine Learning in R supplement](https://bookdown.org/rehk/stm1001_dsm_t1_introduction_to_machine_learning_in_r/). It might be helpful to have this material open as you look through these solutions.

<br>

# Preparations {#prep}

## Load Required Packages {#load}

```{r class.source = "fold-show", eval = F, echo = T, warning = F, message = F}
# Install packages
install.packages("caret", "magrittr", "rpart.plot")

# Load packages
library(caret)
library(rpart.plot)
```

```{r class.source = "fold-show", eval = T, include = F}
# Specify required packages
ml_packages <- c("caret", "magrittr", "rpart.plot")
# Install missing packages
install.packages(setdiff(ml_packages, rownames(installed.packages())))
# Load all packages
lapply(ml_packages, library, character.only = TRUE)
```

## Wine Data

No answer required.

##

Example R code for loading the red wine data is shown below:

```{r class.source = "fold-show", eval = T, include = F}
red_wine <- read.csv(file = "data/winequality_red.csv", header = T)
```

```{r class.source = "fold-show", eval = F, echo = T, warning = F, message = F}
red_wine <- read.csv(file = "winequality_red.csv", header = T)
```

## Aim

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F}
red_wine$quality <- as.factor(red_wine$quality)
```

# Data Visualisation {#dataviz}

##

The `head` function provides an overview of the different variables. The `summary` function provides information on the spread of observed values for each variable, and the `dim` function tells us that we have observations for 1599 wine samples.

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F}
head(red_wine)
summary(red_wine)
dim(red_wine)
```

##

We notice that the majority of quality scores are either 5 or 6. Very few scores of 3 or 8 are recorded - this might make it difficult to accurately predict such scores.

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F}
plot(red_wine$quality)
```

## {#featureplots}

As we can see from the `featurePlot` box plots, the `free.sulfur.dioxide` and `total.sulfur.dioxide` have much larger values than the other feature variables and lead to the box plot being relatively uninformative.

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F, fig.dim = c(8, 8)}
featurePlot(x = red_wine[, -12], 
            y = red_wine$quality, 
            plot = "box")
```

##

Example R code is provide below:

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F, fig.dim = c(8, 8)}
featurePlot(x = red_wine[, -c(6, 7, 12)], 
            y = red_wine$quality, 
            plot = "box")
```

Many of the box plots are still not informative - we will try to address this in the next section.

# Pre-Processing {#prepro}

##

No answer required.

##

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F}
nearZeroVar(red_wine, saveMetrics = T, freqCut = 2, uniqueCut = 5)
nearZeroVar(red_wine, saveMetrics = F, freqCut = 2, uniqueCut = 5)
```
##

None of the feature variables are flagged as exceeding our specified cut-off values.

The `citric acid` feature variable has the highest `freqRatio` value, at 1.94, and also has the lowest `percentUnique` value (5.003) of the feature variables (just missing our specified cut-off).

Neither of these values are too alarming - it should be ok to leave the `citric acid` feature variable in our data set for the time being. 

We conclude that there do not appear to be any problematic variables.

##

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F}
base_cor <- cor(red_wine[, -12])
base_cor

extreme_cor <- sum(abs(base_cor[upper.tri(base_cor)]) > .999)
extreme_cor

summary(base_cor[upper.tri(base_cor)])
```

##

The largest negative correlation value is -0.68297819, between `pH` and `fixed.acidity`.
The largest positive correlation value is 0.67170343, between `citric.acid` and `fixed.acidity`.

These correlation values are not too large in magnitude, so do not seem too problematic.

## 

Using the the `findCorrelation` function to identify highly correlated feature variables to remove from our data set would depend on what we term an acceptable level of correlation. If we are happy with correlations of magnitude 0.69 and under, then we do not need to run this function.
If we would like to set the maximum acceptable correlation magnitude to e.g. 0.67, then the `findCorrelation` function would identify the `fixed.acidity` feature variable for removal.

*Note: For the remainder of this lab, we will assume no feature variables needed to be removed.*

##

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F}
centre_scale <- preProcess(red_wine[, -12], 
                           method = c("center", "scale"))
red_wine_updated <- predict(centre_scale, red_wine)
```

## 

If we compare the original data to the updated data, we see that the feature variable values are now scaled and centred.

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F}
head(red_wine)
head(red_wine_updated)
```

##

The `featurePlot` box plots are now more informative, compared to those created in \@ref(featureplots). For all variables, we are now able to see more clearly how the feature variables' values differ across the different `quality` scores.

We observe that for several feature variables (`sulphates`, `chlorides`, `volatile.acidity` and `residual.sugar`) there are more extreme observations for `quality` scores of 5 and 6 than for the other scores.

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F, fig.dim = c(8,8), cache = T}
featurePlot(x = red_wine_updated[, -12], 
            y = red_wine_updated$quality, 
            plot = "box")
```

##

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F, fig.dim = c(8,8), cache = T}
featurePlot(x = red_wine_updated[, -12], 
            y = red_wine_updated$quality, 
            plot = "pairs",
            auto.key = list(columns = 6))
```

We observe that for most pairs the data is too closely clumped to clearly distinguish between the quality ratings. Perhaps our machine learning model can help.

## Training and Validation Data

Example R code is provided below. 

**Please note that the data partitioning into training or validation categories is random to an extent, so your results from this point onwards may differ slightly to those presented in the subsequent question solutions, since your training and validation data sets will most likely contain slightly different sets of observations.**


```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F}
set.seed(1650)
wine_train_index <- createDataPartition(red_wine_updated$quality, 
                                        p = 0.8, 
                                        list = FALSE, times = 1) 
```

##

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F}
red_wine_train <- red_wine_updated[wine_train_index, ]
red_wine_validate <- red_wine_updated[-wine_train_index, ]
```

# Fitting a Decision Tree Machine Learning Model {#fit}

Please note that we run the `set.seed(1650)` command prior to training the decision tree model, so that the results discussed here are accurate regardless of the number of times this document is generated. If you do not set a seed prior to training your models, your results may appear slightly different.

## Decision Tree

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F, cache = T}
set.seed(1650)
red_wine_decision_tree <- train(quality ~ .,
                            data = red_wine_train,
                            method = "rpart")
red_wine_decision_tree
```

As we can see, the best accuracy achieved was only 57.37%, which is not much better than randomly guessing.

###

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F, fig.dim = c(8,6)}
rpart.plot(red_wine_decision_tree$finalModel)
```

###

No answer required.

# Validating Results

##

```{r class.source = "fold-show", eval = T, echo = T, warning = F, message = F}
# Load magrittr package for piping
library(magrittr)

# count number of observations in validation data
validation_numbers <- dim(red_wine_validate)[1]

# Use the fitted model to predict quality values given the validation data
predict_red_wine_decision_tree <- predict(red_wine_decision_tree, 
                                          newdata =red_wine_validate)
# When run, the code below gives us the percentage of correct predictions
dec_tree_accuracy <- sum(predict_red_wine_decision_tree == red_wine_validate$quality) / 
                     validation_numbers %>% round(2) * 100

dec_tree_accuracy
```

##

We observe that the accuracy of the model using the validation data is only 52.05%, which is much lower than the 57.37% accuracy achieved using the training data. It would appear that our model may not perform as well as we anticipated, when presented with new data. This highlights the importance of cross-validating your machine learning models.


<br>

#### That's everything. Next week we will continue our machine learning work. #### {-}

<br>

# References {- #Ref}
<div id="refs"></div>

<br>

<font color = "grey">
These notes have been prepared by Rupert Kuveke. Please note that some of the content in these notes has been developed from content in @ModStat. The copyright for the material in these notes resides with the authors named above, with the Department of Mathematical and Physical Sciences and with La Trobe University. Copyright in this work is vested in La Trobe University including all La Trobe University branding and naming. Unless otherwise stated, material within this work is licensed under a Creative Commons Attribution-Non Commercial-Non Derivatives License 
<a href = "https://creativecommons.org/licenses/by-nc-nd/4.0/CC" target="_blank"> BY-NC-ND. </a>
</font>