---
title: 'Lab #5:  Regression Trees and Random Forests'
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
set.seed(24)
```

We will now analyze the dementia dataset using tree-based methods.

## Classification Trees

1. Load the `rpart` package
```{r}
```

2. Read in the dementia data "dementia2.csv" into a data frame called `dat`.
```{r}
```

3. Generate a table of the elements in the `Dementia` variable
```{r}
```

4. Fit a classification tree with `Dementia` as response and all other variables as predictors. Then run the `summary` command on the fitted tree. (Note that the `variable.importance` values are calculated only for the variables that were considered for surrogate or primary splits.)
```{r}
```

5. Plot the tree and add text indicating the splits.
```{r}
```

6. Install the `rpart.plot` package and load it. Plot the tree again using the `rpart.plot` function. Play with the `type` option and select the tree visualization that you prefer most.
```{r}
```

7. Select 200 rows at random to be the training set and call it `train`
```{r}
```

8. Build a classification tree on the training data where a split is attempted when the minimum number of observations is `minsplit = 10`. Call this tree `treeTrain`. Plot this tree and compare it to the one trained on all the data. How different are the two trees?
```{r}
```

9. Predict the classes of the test data based on the fitted tree to the training data
```{r}
```

10. Generate a table of the predicted vs. true values in the test data and calculate the classification accuracy
```{r}
```

11. Let's now use cross-validation results to prune the tree. The CV results from `rpart` are stored in the `cp` table. The `error` column corresponds to the training error, relative to the root node error. The `xerror` column corresponds to the (relative) CV error. Use the `printcp` command to display results and `plotcp` to visualize. 
```{r}
```

12. Prune the tree to a good value of $k$ that minimizes the `xerror` using the `prune` command. Plot the resulting tree. (The CP table can be accessed through the `cptable` attribute.)
```{r}
```

13. Generate the confusion matrix of the pruned tree for the test data. What is the test accuracy of the model?
```{r}
```

14. Compare the classification accuracy of the pruned tree to the unpruned tree. Did pruning help?
```{r}
```

## Random Forests

15. Install the `ranger` package
```{r}
```

16. Load the `ranger` package
```{r}
```

17. Fit a random forest to the training data using the `ranger` command. The out of bag (OOB) error estimate are a clever way that random forests gets honest error estimates (i.e. not over-fitted). What is the OOB error for the RF?
```{r}
```

18. Use your fitted RF to make predictions on the test dataset. What is the test error? How does it compare to OOB error?
```{r}
```

19. Let's try various values of `mtry` ranging from 1 to 50 in a loop. Record the accuracy results and make a plot.

```{r}
```

20. Make a plot of error rates in OOB vs. test set across values of `mtry`
```{r}
```

21. How does the OOB error compare to the test error? Would you prefer to rely on OOB or test set error?

```{r}
```

22. What do you think is a good choice for `mtry`?
```{r}
```