---
title: "FW 536 — R Markdown tutorial starter"
author: "Your Name Here"
date: "`r Sys.Date()`"
output:
  html_document:
    self_contained: true
    toc: true
    toc_depth: 3
    toc_float: true
    code_folding: show
    theme: cosmo
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  echo    = TRUE,    # show your code (graders will read it)
  message = FALSE,   # hide package start-up noise
  warning = FALSE,   # hide warnings (be careful — sometimes warnings matter!)
  fig.width = 6,
  fig.height = 4
)
```

# Welcome

This is a starter R Markdown file for FW 536. Open it in RStudio, click
**Knit** (the yarn-and-needles icon at the top of the editor), and confirm
that you get an HTML output. If you do, you're ready for the workshop.

If knitting fails, see the troubleshooting section of the
[R Markdown tutorial HTML](rmarkdown_tutorial.html) for common fixes.

# 1. A code chunk

Below is an R code chunk. When you knit, R executes the code and the
output appears beneath it.

```{r}
x <- rnorm(100, mean = 5, sd = 2)
mean(x)
sd(x)
```

# 2. A plot

```{r, fig.cap="Histogram of 100 draws from a Normal(5, 2) distribution."}
hist(x, breaks = 15, col = "steelblue", border = "white",
     main = "", xlab = "x")
abline(v = mean(x), col = "darkred", lwd = 2)
```

# 3. Inline R

You can also write code inline. The mean of `x` is `r round(mean(x), 2)`
and the standard deviation is `r round(sd(x), 2)`.

This is useful in problem-set answers: instead of hard-coding numbers in
your prose, compute them with inline R so they update automatically when
the data change.

# 4. Math

Inline math: the standardized score is $z_i = (x_i - \mu) / \sigma$.

Display math:

$$
P(\theta \mid y) \; = \; \frac{P(y \mid \theta)\, P(\theta)}{P(y)}
$$

# 5. Embedding a photo of hand-written work

For derivations that are faster on paper, photograph the page and embed
the image. Save the photo as `images/example.jpg` in the same folder as
this `.Rmd`.

```{r, echo=FALSE, eval=FALSE, out.width="60%", fig.cap="Hand-derivation of Problem N"}
knitr::include_graphics("images/example.jpg")
```

(Note: the chunk above has `eval=FALSE` so it doesn't fail when there's
no image. Once you save a real image, change to `eval=TRUE`.)

# 6. A small statistical example

Here's a complete worked example to confirm the rendering pipeline works:

```{r}
# Simulate a small Poisson regression
set.seed(2026)
n <- 80
x <- rnorm(n)
mu <- exp(0.5 + 0.4 * x)
y <- rpois(n, mu)

# Fit and summarize
fit <- glm(y ~ x, family = poisson)
coef(fit)
exp(coef(fit))            # multiplicative effect of a 1-unit increase in x
```

The intercept on the natural scale is approximately
`r round(exp(coef(fit)[1]), 2)`, and a one-unit increase in `x`
multiplies expected `y` by approximately
`r round(exp(coef(fit)[2]), 2)`.

# 7. Submitting your work

1. Knit this file to HTML (Ctrl/Cmd-Shift-K, or the **Knit** button).
2. Confirm that `rmarkdown_tutorial_starter.html` appears in the same
   folder as the `.Rmd`.
3. Upload the `.html` to the Canvas assignment.

Tip — always **Restart R** (Session menu) and re-knit from a fresh
session before submitting, to catch bugs that depend on hidden console
state.