assignment_template.qmd

---
title: "MAST90084 Assignment X"
author: "Your Name (Student ID)"
date: last-modified
format:
  pdf:
    papersize: a4
    geometry:
      - margin=1in
knitr:
  opts_chunk:
    fig.align: "center"
    fig.width: 7
    fig.height: 4.5
---

```{r}
#| label: setup
# Reproducibility
library(conflicted)
library(tidyverse)
set.seed(1) # CHANGE TO YOUR STUDENT ID
```

## Simple simulation + ggplot example

```{r}
#| label: sim-ggplot-example
# Simulate basic data
n <- 100
x <- rnorm(n, mean = 0, sd = 1)
y <- 2 + 0.8 * x + rnorm(n, mean = 0, sd = 1)
sim_data <- tibble(x = x, y = y) |>
    arrange(x)

sim_data

# Plot with ggplot2
ggplot(sim_data, ggplot2::aes(x = x, y = y)) +
    geom_point(alpha = 0.7) +
    geom_smooth(method = "lm", se = TRUE) +
    labs(
        title = "Simulated data with linear trend",
        x = "x",
        y = "y"
    ) +
    theme_minimal()
```

## LaTeX examples (quick reference)

Use `equation` for one numbered equation.

\begin{equation}
\label{eq:single}
\hat{\theta} = \arg\max_{\theta} \; \ell(\theta)
\end{equation}

Use `split` inside `equation` when one equation is too long and needs line breaks,
or has a flow of equals signs.

\begin{equation}
\label{eq:split}
\begin{split}
\log L(\beta)
&= \sum_{i=1}^n \left\{ y_i x_i^T\beta - \log\left(1 + e^{x_i^T\beta}\right) \right\} \\
&\quad - \frac{\lambda}{2}\,\beta^T\beta\\
&= \sum_{i=1}^n \left\{ y_i x_i^T\beta - \log\left(1 + e^{x_i^T\beta}\right) \right\} - \frac{\lambda}{2}\,\beta^T\beta
\end{split}
\end{equation}

Use `gather` for multiple equations that are centered and not aligned at symbols.

\begin{gather}
\label{eq:gather-a}
\mathbb{E}[X] = \mu \\
\label{eq:gather-b}
\mathrm{Var}(X) = \sigma^2
\end{gather}

Use `align` for multiple equations aligned at `=` (or another symbol via `&`).

\begin{align}
\Pr(Y=1\mid x)
&= \frac{e^{\eta}}{1 + e^{\eta}}, \quad\text{for } \eta = x^T\beta \\
\log\left(\frac{\Pr(Y=1\mid x)}{1-\Pr(Y=1\mid x)}\right)
&= x^T\beta
\end{align}

You can reference these using `Equation \ref{eq:single}`.

## Question 1

### (a)

Write your answer here.

```{r}
#| label: q1a-code
#| eval: false
# Code for Question 1(a)
```

### (b)

Write your answer here.

```{r}
#| label: q1b-code
#| eval: false
# Code for Question 1(b)
```

\clearpage

## Question 2

### (a)

Write your answer here.

```{r}
#| label: q2a-code
#| eval: false
# Code for Question 2(a)
```

### (b)

Write your answer here.

```{r}
#| label: q2b-code
#| eval: false
# Code for Question 2(b)
```

\clearpage

## Question 3

### (a)

Write your answer here.

```{r}
#| label: q3a-code
#| eval: false
# Code for Question 3(a)
```

### (b)

Write your answer here.

```{r}
#| label: q3b-code
#| eval: false
# Code for Question 3(b)
```

\clearpage

## Question 4

### (a)

Write your answer here.

```{r}
#| label: q4a-code
#| eval: false
# Code for Question 4(a)
```

### (b)

Write your answer here.

```{r}
#| label: q4b-code
#| eval: false
# Code for Question 4(b)
```