---
title: "Dummy homework"
author: "Name, student number"
output:
  bookdown::pdf_document2:
    number_sections: no
    toc: no
---
Here is a simple R Markdown template for returning homework exercises. Notice that use of R Markdown is not compulsory.

- Template includes some basic examples about code blocks, equations, figures and cross-referencing.

- Rmd file can be compiled with the key combination Ctrl+Shift+K or by pressing the \texttt{Knit} button on R Studio interface.

- Code chunk can be inserted with the key combination Ctrl+Alt+I or by pressing the \texttt{Insert} button on R Studio interface.

- Equations work very similarly to LaTeX. However, cross-referencing differs significantly from LaTeX syntax.

- Notice that cross-referencing is not provided in base R Markdown. [\textcolor{blue}{Bookdown}](https://github.com/rstudio/bookdown) package provides output formats which enable cross-referencing.

- More information and examples about R Markdown can be found [\textcolor{blue}{here}](https://bookdown.org/yihui/rmarkdown/) and [\textcolor{blue}{here}](https://bookdown.org/yihui/rmarkdown-cookbook/).

# Dummy exercise 
## Code blocks 
Below is an example code block.

```{r}
emis <- read.table('emissions.txt', header = TRUE, sep = '\t', row.names = 1)
fit <- lm(NOx ~ ., data = emis)
head(emis)
```

## Equations and inline R code 
Value of the *coefficient of determination* is approximately $R^2 \approx$ `r round(summary(fit)$r.squared, 2)`. Previous value was actually computed with inline R command (see Rmd file)! Coefficient of determination can be calculated with the formula

$$
R^2 = 1 - \frac{SSE}{SST}.
$$

Additionally, one can have numbered equations and cross-reference them,
\begin{equation}
(\#eq:rsquared)
R^2 = 1 - \frac{SSE}{SST}.
\end{equation}
Coefficient of determination $R^2$ is calculated according to equation \@ref(eq:rsquared).

## Plotting
Notice that labeled text is quite useful for making clean figure captions (see Rmd file).

(ref:captionscatter) Scatter plot of variables.

```{r scatter, fig.cap='(ref:captionscatter)'}
pairs(emis, pch = 19, col = "midnightblue", gap = 0,
      upper.panel = NULL, cex.labels = 1)
```

Figure \@ref(fig:scatter) suggests that there is negative correlation between variables \texttt{NOx} and \texttt{Humidity}.
