---
title: "Assignment Title"
author: "Your Name"
date: "`r Sys.Date()`"
format:
  typst: 
    number-sections: false 
    margin: 
      top: 1in 
      right: 1.25in 
      bottom: 1in 
      left: 0.5in 
    fontsize: 11pt 
    page-breaks-before: 1 
    page-breaks-after: 1  
    page-size: letter 
    page-number: true 
    fig-width: 7  # Adjust the width as needed
    fig-height: 5  # Adjust the height as needed
    tbl-cap-location: top 
    fig-cap-location: bottom
---

# Introduction

This assignment covers the key concepts and methods for [insert topic here]. The purpose is to demonstrate the understanding of the techniques discussed in the lectures and their application to real data sets.

::: {.callout-note}
Replace `[insert topic here]` with a brief description of the assignment's main objective.
:::

# Problem 1: [Problem Title]

## Question

Clearly state the question or problem that you are solving. Provide any given information, data, or equations.

## Solution

1. **Mathematical Formulas:**

Typeset your mathematical formulas using LaTeX. For example:

$$
\hat{\beta} = (X'X)^{-1} X'Y
$$

2. **R Code for Calculation:**

Use R code to perform any necessary calculations or data analysis:

```{r}
#| label: fig-problem1-plot
# Example R code to generate a plot for Problem 1
library(ggplot2)
data <- data.frame(x = c(1, 2, 3, 4, 5), y = c(2, 4, 3, 5, 7))
ggplot(data, aes(x = x, y = y)) +
    geom_point() +
    geom_smooth(method = "lm", se = FALSE, color = "blue") +
    labs(
        title = "Scatter Plot with Regression Line for Problem 1",
        x = "Independent Variable",
        y = "Dependent Variable"
    )
```

3. **Interpretation:**

Interpret the results of your analysis. For example, explain what the estimated coefficients represent and how they relate to the problem context.

::: {.callout-note}
Provide a clear explanation of the steps taken and their relevance to the solution.
:::

# Problem 2: [Problem Title]

## Question

Provide a detailed description of the problem, including any given information.

## Solution

1. **Handwritten Calculations:**

If you need to show any hand calculations, write them clearly and legibly, then scan or take a high-quality picture of your work. Embed the scanned image in your document:

```markdown
![Handwritten Calculation for Problem 2](path/to/your/image.png){ width=60% }
```

2. **R Code for Analysis:**

Include R code for any analysis required:

```{r}
#| label: fig-problem2-plot
# Example R code for creating a histogram
hist(data$x, main = "Histogram of X Values", xlab = "X Values", col = "lightblue", border = "black")
```

# Conclusion

Summarize the findings from each problem. Reflect on the results and any challenges encountered during the assignment.

::: {.callout-note}
Discuss any additional insights gained from completing the assignment.
:::

# Additional Instructions

- Ensure all R code chunks are labeled appropriately (`fig-` for figures, `tbl-` for tables).
- Make sure that all figures, tables, and equations are correctly referenced in the text.
- Remember to proofread your assignment before submission to check for clarity, accuracy, and formatting consistency.

::: {.callout-note}
Follow these instructions to complete your assignment in the correct format.
:::

## Include he following code for diagnostic and reproducibility purposes:

```{r}
sessionInfo()
```