---
title: "Homework 06 Solutions"
pagetitle: "Homework 06 Solutions"
body-classes: "lecture-page practice-page"
format:
  html:
    html-math-method: mathml
    page-layout: full
    toc: true
    toc-location: body
    toc-title: "On this page"
    toc-depth: 2
    code-fold: true
    code-summary: "Show the solution code"
---

## Question 1: Compare KNN and logistic regression

### Original question

Use [breast-cancer.csv](data/breast-cancer.csv), which contains 569 cases from the [Wisconsin Diagnostic Breast Cancer dataset](https://archive.ics.uci.edu/dataset/17/breast%2Bcancer%2Bwisconsin%2Bdiagnostic). Predict `y` (1 for malignant and 0 for benign) using `mean_radius`, `mean_texture`, and `mean_smoothness`.

Set a random seed and randomly split the observations into 70% training and 30% test data. Use the same split for every model. Standardize the predictors using the training means and standard deviations, and apply the same transformations to the test data.

Fit ordinary logistic regression with an intercept and no penalty, and KNN with Euclidean distance, equal neighbor weights, and

$$
k\in\{5,15,25,35,45\}.
$$

Using the estimated probabilities for `y = 1` on the test data, plot all six ROC curves in one figure and report their AUC values. Which of the six fitted models do you prefer? Give a brief justification based on your results.

### Solution

To be added.

## Question 2: Training and test ROC curves

### Original question

Use the same data, training/test split, and standardization as in Question 1. Fit KNN with Euclidean distance, equal neighbor weights, and

$$
k\in\{1,3,5,10,20\}.
$$

Use each fitted model to estimate probabilities for both the training and test observations. For training predictions, include each observation itself among its $k$ nearest neighbors.

For each $k$, use a separate panel to show the training and test ROC curves together. Report both AUC values.

Explain the difference between training and test performance and how it changes with $k$. In particular, explain what happens at $k=1$ and why training performance may not reflect performance on new observations.

### Solution

To be added.

## Question 3: To be added

### Original question

To be added.

### Solution

To be added.

## Question 4

No solution can be provided for Question 4.

## Question 5: To be added

### Original question

To be added.

### Solution

To be added.