---
title: "Final project"
date: "2026-04-14"
output:
  bookdown::html_document2: default
  bookdown::pdf_document2: default
---

```{r setup, include=FALSE}
# Please do not show your code in the document unless it helps the
# reader understand something important.  Set include=FALSE to suppress
# R code.
library(tidyverse)
knitr::opts_chunk$set(echo = FALSE)
knitr::opts_chunk$set(fig.width=6, fig.height=4, fig.align="center") 
data("cars")
```



# Introduction

A short, high-level description of what you want to do,
how you do it, and what you find.


# Problem description

Ask your real-world question and describe why it's important. Bring in 
outside context as necessary.  Be specific about how someone
might use your results, either to gather more data, implement
a policy, or produce a useful tool.

You can cite papers like this: @belkin:2019:reconciling.


# Data

Describe where you got the data, and how it was collected.  Cite
published papers and websites.  Describe how its collection method
helps (or hurts) the ability to answer your real-world question.

You can use code quantities direclty in the text.  For example,
the `cars` dataset has `r nrow(cars)` rows.

## Including Plots

You can also embed plots, for example:

```{r carsplot, fig.cap="The cars data.", out.height="30%", echo=FALSE}
ggplot(cars) +
  geom_point(aes(x=speed, y=dist)) +
  xlab("Speed") + ylab("Distance") +
  ggtitle("Scatterplot of cars data")
```



You can refer to the plot as Figure \@ref(fig:carsplot).
Please make sure that all axes and other formatting are clearly labeled,
and that the figure annotations are roughly the same size as the document font
so they are readable.



Note that the `echo = FALSE` parameter was added to the code chunk to prevent 
printing of the R code that generated the plot.

# Methods

Describe how you will use your statistical model to answer your
real-world question.  Describe what assumptions are necessary
for your methods to provide an answer, and discuss whether
they are likely to hold in real life.   Say what tools you
use, and what statistical results you are relying on.

Math can look like this:
$$
\begin{equation}
\hat{\beta} = (X^T X)^{-1} X^T Y (\#eq:ols)
\end{equation}
$$

You can refer to Equation \@ref(eq:ols) in the text as well.

# Results

Discuss the actual numerical results in an easy-to-read
format.  Graphs are usually much better than tables of numbers.
Make sure you connect your quantitiative results back to
your assumptions and methods.


# Discussion

Put it all together.


# Bibilography



