R Markdown Guide for AST 232 Exams

§ 1What is R Markdown

R Markdown is a plain text file (.Rmd) that mixes three things: normal prose written in Markdown, R code inside "chunks" that runs when you knit the file, and math or tables. When you press Knit in RStudio, the file compiles into a polished PDF, HTML, or Word document with your code, its output, and your interpretation all in one place.

What a knitted output looks like

You write prose, followed by a code chunk. When knitted, the reader sees:

1. Your prose, rendered normally.
2. The R code itself, in a grey box (like the code blocks on this page).
3. The output of that code (numbers, tables, plots) right underneath.
4. Your interpretation, back in prose.

§ 2One Time Setup

Everything you need ships with RStudio. Only a small install step is needed the first time.

# In the R console, once per machine
install.packages(c("rmarkdown", "knitr"))

# For PDF output, you also need a LaTeX distribution.
# The lightweight option that just works everywhere:
install.packages("tinytex")
tinytex::install_tinytex()   # run once, takes 5-10 minutes

§ 3Anatomy of an .Rmd File

Every R Markdown document has three parts, always in this order.

---
title: "AST 232 Final Exam Solutions"
author: "Your Name, Roll 12345"
date: "2026-08-10"
output: pdf_document
---

# Introduction

Prose goes here. Write in **bold** and *italic*
just like in normal Markdown.

## Question 1

The next block is an R code chunk. Everything between the triple
backticks runs when we knit.

```{r q1-anova}
data(iris)
model <- aov(Sepal.Length ~ Species, data = iris)
summary(model)
```

Interpretation of the ANOVA goes here, again in prose.

• The YAML header at the top (between the two --- lines) tells knitr what to build and how.
• The body is Markdown prose plus math.
• The chunks are R code fenced by ```{r} and ```. Give each chunk a short name (like q1-anova) to help debugging.

§ 4The YAML Header

Only three fields matter for exam submissions: title, author, and output.

---
title:  "AST 232 Final Exam Solutions"
author: "K.M. Tanvir, Roll 20221234"
date:   "2026-08-10"
output: pdf_document
---

Any of pdf_document, html_document, or word_document works. If knitting fails on your machine for any reason, submit the raw .Rmd file itself; it will still be graded.

output:
  pdf_document:
    toc: true
    number_sections: true

§ 5Text Formatting

The body is plain Markdown. Everything below works in every knitted output.

§ 6R Code Chunks

A chunk starts with ```{r} and ends with ```, each on its own line. Everything between runs as R code.

```{r q1-solution}
# Compute the sex ratio
M <- 157500
F <- 162500
SR <- M / F * 100
round(SR, 2)
```

When knitted, the reader sees the code (in a grey box), then the output [1] 96.92. If a chunk produces a plot, the plot appears inline.

§ 7Chunk Options Cheat Sheet

Options go inside the curly braces after r, comma separated: ```{r my-chunk, echo=FALSE, message=FALSE}. The most useful ones:

Global defaults for the whole document

Set once at the top of the document with a setup chunk, then every later chunk inherits the defaults.

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  echo    = TRUE,       # show code by default
  message = FALSE,      # hide package chatter
  warning = FALSE,      # hide warnings from the reader
  fig.width  = 6,
  fig.height = 4,
  fig.align  = "center"
)
```

§ 8Inline R Code

Sometimes you want a single R value in the middle of a sentence. Wrap it in `r ... ` (backtick, r, space, code, backtick).

The mean rice yield was `r `round(mean(rice$yield), 2)` Mg/ha,
with a sample standard deviation of `r `round(sd(rice$yield), 2)`.

When knitted this reads as: "The mean rice yield was 4.78 Mg/ha, with a sample standard deviation of 0.66." No manual copy paste.

§ 9Nice Tables with knitr::kable

Plain R output like an ANOVA table prints as monospaced text, which reads fine but is not publication grade. knitr::kable() renders any data frame as a formatted table.

```{r anova-table}
model <- aov(yield ~ treat, data = rice)
knitr::kable(
  summary(model)[[1]],
  digits  = 3,
  caption = "ANOVA table for the rice fertilizer trial"
)
```

§ 10Plots and Figures

Every base R plot inside a chunk lands in the knitted output automatically. No ggsave or file handling needed.

```{r yield-boxplot, fig.width=6, fig.height=4, fig.cap="Yield by fertilizer"}
boxplot(yield ~ treat, data = rice,
        col = "#dbeafe", border = "#2563eb",
        xlab = "Fertilizer", ylab = "Yield (Mg/ha)")
```

Two things to remember:

• The chunk name (here yield-boxplot) becomes the filename of the generated figure.
• Set fig.width and fig.height per chunk for anything unusual. Default globals cover 95% of cases.

§ 11Math Equations

Math uses LaTeX syntax and renders beautifully in every output format. Two flavours:

• Inline: wrap in single dollar signs. $\bar{y} = \frac{1}{n}\sum_{i=1}^n y_i$ renders as an inline equation.
• Display: wrap in double dollar signs on their own lines, for a centred equation on its own line.

The Fergany method computes the probability of dying as
$$
_nq_x = 1 - e^{-n \cdot {_nM_x}}
$$
so the survivors column follows from $l_{x+n} = l_x \cdot _np_x$
with $_np_x = 1 - {_nq_x}$.

§ 12Knitting to PDF, HTML, Word

Once the file is written, press the Knit button in RStudio (or Ctrl/Cmd + Shift + K). RStudio runs every chunk in order, then compiles the output.

§ 13Ready to Paste AST 232 Exam Template

Copy this into a new .Rmd file to start your exam. Change the header, replace the placeholders, and knit.

---
title: "AST 232 Final Exam Solutions"
author: "Your Name, Roll 20221234"
date: "`r format(Sys.Date())`"
output:
  pdf_document:
    toc: true
    number_sections: true
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  echo    = TRUE,
  message = FALSE,
  warning = FALSE,
  fig.width = 6, fig.height = 4, fig.align = "center"
)
```

# Question 1: Fertility measures for a district

## (a) Compute the Total Fertility Rate

```{r q1a}
age_group  <- c("15-19", "20-24", "25-29", "30-34",
                "35-39", "40-44", "45-49")
female_pop <- c(110000, 105000, 100000, 95000,
                85000,  75000,  65000)
births     <- c(8000, 15000, 11000, 7000,
                2200, 600,   100)
ASFR <- births / female_pop * 1000
TFR  <- 5 * sum(ASFR) / 1000
round(TFR, 3)
```

The Total Fertility Rate is `r `round(TFR, 2)` children per woman,
slightly above the replacement level of 2.10.

## (b) Interpretation

Write your interpretation here in normal prose.

# Question 2: Randomized Complete Block Design

## (a) Fit the ANOVA

```{r q2a}
# Type the data, fit the model, print the ANOVA
```

## (b) Tukey HSD

```{r q2b}
# TukeyHSD on the treatment factor
```

§ 14Common Issues and Fixes

"object 'x' not found" when knitting

You referred to a variable that was never defined in the file. Something you typed in the console works there but the knit session cannot see it. Put the definition in a chunk.

PDF fails to build with a LaTeX error

If TinyTeX is installed but the build fails, the missing LaTeX package usually installs itself the next time you knit. If the same error repeats, run tinytex::reinstall_tinytex() once.

Plot looks squished or overflows the page

Set fig.width and fig.height on the offending chunk. For a full page landscape figure try fig.width = 8, fig.height = 5.

Every knit prints "Attaching package: dplyr" and other noise

Add message = FALSE and warning = FALSE to your global setup chunk (see Section 7).

Special characters (Bangla, math) render as ????

Save the file as UTF 8 (File → Save with Encoding → UTF 8). For PDF, ensure the LaTeX engine supports the character set; for Bangla text prefer xelatex in the YAML: output: pdf_document: latex_engine: xelatex.

The knit button greys out

Close and reopen the .Rmd file. If the problem persists, save your work, restart RStudio, and try again.