---
title: "Lab 4"
author: "STAT 302"
date: "Due Date Here"
output: html_document
---

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

*If you collaborated with anyone, you must include "Collaborated with: FIRSTNAME LASTNAME" at the top of your lab!*

For this lab, note that there are tidyverse methods to perform cross-validation in R (see the `rsample` package). However, your goal is to understand and be able to implement the algorithm "by hand", meaning  that automated procedures from the `rsample` package, or similar packages, will not be accepted.

To begin, load in the popular `penguins` data set from the package `palmerpenguins`.

```{r}
library(palmerpenguins)
data(package = "palmerpenguins")
```

## Part 1. k-Nearest Neighbors Cross-Validation (10 points)

Our goal here is to predict output class `species` using covariates `bill_length_mm`, `bill_depth_mm`, `flipper_length_mm`, and `body_mass_g`.
All your code should be within a function `my_knn_cv`.

**Input:**

  * `train`: input data frame
  * `cl`: true class value of your training data
  * `k_nn`: integer representing the number of neighbors
  * `k_cv`: integer representing the number of folds
  
*Please note the distinction between `k_nn` and `k_cv`!*

**Output:** a list with objects

  * `class`: a vector of the predicted class $\hat{Y}_{i}$ for all observations
  * `cv_err`: a numeric with the cross-validation misclassification error


You will need to include the following steps:

* Within your function, define a variable `fold` that randomly assigns observations to folds $1,\ldots,k$ with equal probability. (*Hint: see the example code on the slides for k-fold cross validation*)
* Iterate through $i = 1:k$. 
  * Within each iteration, use `knn()` from the `class` package to predict the class of the $i$th fold using all other folds as the training data.
  * Also within each iteration, record the prediction and the misclassification rate (a value between 0 and 1 representing the proportion of observations that were classified **incorrectly**).
* After you have done the above steps for all $k$ iterations, store the vector `class` as the output of `knn()` with the full data as both the training and the test data, and the value `cv_error` as the average misclassification rate from your cross validation.

**Submission:** To prove your function works, apply it to the `penguins` data. Predict output class `species` using covariates `bill_length_mm`, `bill_depth_mm`, `flipper_length_mm`, and `body_mass_g`. Use $5$-fold cross validation (`k_cv = 5`). Use a table to show the `cv_err` values for 1-nearest neighbor and 5-nearest neighbors (`k_nn = 1` and `k_nn = 5`). Comment on which value had lower CV misclassification error and which had lower training set error (compare your output `class` to the true class, `penguins$species`).

## Part 2. Random Forest Cross-Validation (10 points)

Now, we will predict output `body_mass_g` using covariates `bill_length_mm`, `bill_depth_mm`, and `flipper_length_mm`.
All your code should be within a function `my_rf_cv`.

**Input:**

  * `k`: number of folds

**Output:**

  * a numeric with the cross-validation error
  
Your code will look very similar to Part 1! You will need the following steps: 

* Within your function, define a variable `fold` within the `penguins` data that randomly assigns observations to folds $1,\ldots,k$ with equal probability. (*Hint: see the example code on the slides for k-fold cross validation*)
* Iterate through $i = 1:k$. 
  * Within each iteration, define your training data as all the data not in the $i$th fold.
  * Also within each iteration, use `randomForest()` from the `randomForest` package to train a random forest model with $100$ trees to predict `body_mass_g` using covariates `bill_length_mm`, `bill_depth_mm`, and `flipper_length_mm`. <br>
*Hint: `randomForest()` takes formula input. Your code here will probably look something like: *
`MODEL <- randomForest(body_mass_g ~ bill_length_mm + bill_depth_mm + flipper_length_mm, data = TRAINING_DATA, ntree = 100)`
  * Also within each iteration, predict the `body_mass_g` of the $i$th fold which was not used as training data. <br>
  *Hint: predicting with `randomForest()` works similar to `lm()`. Your code here will probably looks something like: *
  `PREDICTIONS <- predict(MODEL, TEST_DATA[, -1])`
  *where we remove the first column, `body_mass_g` from our test data.*
  * Also within each iteration, evaluate the MSE, the average squared difference between predicted `body_mass_g` and true `body_mass_g`.
* Return the average MSE across all $k$ folds.

**Submission:** 
To prove your function works, apply it to the `penguins` data. Predict `body_mass_g` using covariates `bill_length_mm`, `bill_depth_mm`, and `flipper_length_mm`.
Run your function with $5$-fold cross validation (`k = 5`) and report the CV MSE.
