HWKmdHTMLonly.Rmd

---
title: "Homework with **rmarkdown** and **knitr**"
author: "Alan T. Arnholt"
date: '`r Sys.Date()`'
output: html_document
bibliography:
- References/PackagesUsed.bib
- References/Main.bib
---

```{r, label = "setup", echo = FALSE, results= 'hide', message = FALSE, warning = FALSE}
knitr::opts_chunk$set(fig.show = 'as.is', fig.height = 6, fig.align = "center", 
                      fig.width = 6, prompt = FALSE, highlight = TRUE, 
                      tidy = FALSE, warning = FALSE, message = FALSE, 
                      echo = FALSE, tidy.opts=list(blank = TRUE, width.cutoff= 65))
# Lists of R packages used
PackagesUsed <- c("PASWR2", "ggplot2", "knitr", "MASS", "DT", "lattice", "rmarkdown")
# Write bib information
knitr::write_bib(PackagesUsed, file = "./References/PackagesUsed.bib")
# Load packages
lapply(PackagesUsed, library, character.only = TRUE)
```

This document assumes you are using the [Rstudio](https://www.rstudio.com/) [IDE](https://www.rstudio.com/products/RStudio/).
The best way to obtain this document and examine all the files associated with the project is to: 

1. [Fork](https://help.github.com/articles/fork-a-repo/) this repository to your own [GitHub](https://github.com/) account.
2. Clone the forked repository into a local RStudio [project](https://support.rstudio.com/hc/en-us/articles/200526207-Using-Projects).  

To clone the repository, you will need a recent version of [Git](http://git-scm.com/) installed on your machine. This [video](https://www.youtube.com/watch?v=YxZ8J2rqhEM) shows how to clone a repository using the RStudio [IDE](https://www.rstudio.com/products/RStudio/).  Several features from [Pandoc](http://pandoc.org/) [@Pandoc2015], **rmarkdown** [@R-rmarkdown], and **knitr** [@R-knitr] are illustrated in the document including numerous **knitr** chunk options (both local and global) which are fully documented [online](http://yihui.name/knitr/options/).  [Rstudio](https://www.rstudio.com/) has a great "[cheat sheet](https://www.rstudio.com/wp-content/uploads/2015/02/rmarkdown-cheatsheet.pdf)" for writing R markdown documents.  Further information about R markdown can be found [online](http://rmarkdown.rstudio.com/).  This document shows `R` code in the answers only when specifically directed in the question; however, all `R` code used in the document is visible in an **R-Code Appendix**.  The [YAML](http://yaml.org/) for this document is written as:

```
---
title: "Homework with **rmarkdown** and **knitr**"
author: "Alan T. Arnholt"
date: '`r Sys.Date()`'
output: html_document
bibliography:
- References/PackagesUsed.bib
- References/Main.bib
---
```

To add a bibliography to your document, you will need to create one or more `*.bib` files and add the YAML entry `bibliography: PathTo/file.bib` or use a list as above for multiple `*.bib` files.  The **knitr** function `write_bib()` [@R-knitr] is used to create *automagically* a `*.bib` file of the `R` packages used in this document and store the file in `./References/PackagesUsed.bib` (See the **R-Code Appendix**).  The two entries in `./References/Main.bib` were created by hand.  The citation management system [Zotero](https://www.zotero.org/) can create `BibTeX` files. This [4 minute video](https://www.youtube.com/watch?v=erTi298SX_w&list=PLJBNI3mCp9g0wsSDK111qgimqVF1dwPXO) illustrates how to store bibliographic information using Zotero, and the following [2 minute video](https://www.youtube.com/watch?v=ixUF3BN_KOA&list=PLJBNI3mCp9g0wsSDK111qgimqVF1dwPXO&index=3) shows how to export the bibliographic information from Zotero to a `BibTeX` file.  Inline $\LaTeX{}$ equations and display equations are placed between single and double `$` symbols, respectively.  To learn more about $\LaTeX{}$ see online resources such as [https://en.wikibooks.org/wiki/LaTeX](https://en.wikibooks.org/wiki/LaTeX).  If you need help with how to write a symbol in $\LaTeX{}$, you can draw the symbol at this [site](http://detexify.kirelabs.org/classify.html) and $\LaTeX{}$ code corresponding to the user drawn symbol will appear.

**Note: The [RStudio](https://www.rstudio.com/) [IDE](https://www.rstudio.com/products/RStudio/) will populate most entries for the YAML; however, you will need manually to add the `bibliography` entry.**

## Code chunks

1.  The first code chunk named `setup` has local options `echo = FALSE`, `results= 'hide'`, `message = FALSE`, and `warning = FALSE`.  These options have the chunk execute without echoing the code, displaying any results, messages, or warnings in the console.  The global options for the document are defined with `knitr::opts_chunk$set()` (shown below). After the global options are defined, a character vector (`PackagesUsed`) is created with the names of the packages used in this document.  The bibliographic information for the packages is automatically written to a file with the `write_bib()` function. Last, the packages are loaded and attached.  If your installation does not have any of the packages referenced in `PackagesUsed`, you should install the missing packages using the function `install.packages()`.

```
knitr::opts_chunk$set(fig.show = 'as.is', fig.height = 6, fig.align = "center", 
                      fig.width = 6, prompt = FALSE, highlight = TRUE, 
                      tidy = FALSE, warning = FALSE, message = FALSE, 
                      echo = FALSE, tidy.opts=list(blank = TRUE, width.cutoff= 65))
# Lists of R packages used
PackagesUsed <- c("PASWR2", "ggplot2", "knitr", "MASS", "DT", "lattice", "rmarkdown")
# Write bib information
knitr::write_bib(PackagesUsed, file = "./References/PackagesUsed.bib")
# Load packages
lapply(PackagesUsed, library, character.only = TRUE)
```

Note: The chunk option `fig.align = "center"` should be omitted if you want to create either a PDF or Word document from the R markdown file.

2. The second code chunk named `load` uses the local options `echo = TRUE`, `comment = NA`, and `prompt = TRUE`. The `echo = TRUE` overwrites the global option `echo = FALSE` and echoes all `R` code and output to the console.  The option `comment = NA` removes the default comment (`##`), and the option `prompt = TRUE` displays the `R` prompt symbol (`>`). 

3. The third code chunk named `datatable` uses the global options to create a Data Table.

4. The fourth code chunk named `partA` changes the height and width of the plot used in the graphics device from the global settings of 5 and 5, to 12 and 12 with the options `fig.height = 12`, and `fig.width = 12`.

5. The fifth code chunk named `partB` changes the height and width of the plot used in the graphics device from the global settings of 5 and 5, to 12 and 12 with the options `fig.height = 12`, and `fig.width = 12`.

6. The sixth code chunk named `partC` does not overwrite any of the global option setting.

7. The seventh code chunk named `partD` does not overwrite any of the global options.

8. The eighth code chunk named `partE` hides output send to the console with the local option `results = "hide"`.

9. The ninth code chunk named `tablestuff` uses the default global options.

10. The tenth code chunk named `appendix` shows all of the code used for all code chunks without evaluating the code with the options `echo = TRUE`, `ref.label = all_labels()`, and `eval = FALSE`.

11. The eleventh code chunk named `SessionInfo` uses the local option `echo = TRUE` to show the results of `sessionInfo()` in the console.

________________________________________________________________________


#### Modified question 2 from chapter 2 of [@PASWR2E] with brief answers.

Load `Cars93` from the **MASS** package [@R-MASS], and use the function `str()` on the `Cars93` data frame.  Create a Data Table using the **DT** package [@R-DT].

```{r, label = "load", echo = TRUE, comment = NA, prompt = TRUE}
library(MASS)  
str(Cars93)
```

The following is a Data Table created with the **DT** package. 
```{r, label = "datatable"}
# Create Data Table with datatable
DT::datatable(Cars93)
```

(a) Create density histograms for the variables `Min.Price`, `Max.Price`, `Weight`, and `Length` variables using a different color for each histogram.

```{r, label = "partA", fig.height = 12, fig.width = 12}
# Create graphs for part a
p1 <- ggplot(data = Cars93, aes(x = Min.Price, y = ..density..)) + 
  geom_histogram(fill = "green") + 
  theme_bw()
p2 <- ggplot(data = Cars93, aes(x = Max.Price, y = ..density..)) + 
  geom_histogram(fill = "pink") + 
  theme_bw()
p3 <- ggplot(data = Cars93, aes(x = Weight, y = ..density..)) + 
  geom_histogram(fill = "yellow") + 
  theme_bw()
p4 <- ggplot(data = Cars93, aes(x = Length, y = ..density..)) + 
  geom_histogram(fill = "lightblue") + 
  theme_bw()
multiplot(p1, p2, p3, p4, cols = 2)
```

(b) Superimpose estimated density curves over the histograms.

```{r, label = "partB", fig.height = 12, fig.width = 12}
# Create graphs for part b
p1 <- ggplot(data = Cars93, aes(x = Min.Price, y = ..density..)) + 
  geom_histogram(fill = "green") + 
  theme_bw() + 
  geom_density()
p2 <- ggplot(data = Cars93, aes(x = Max.Price, y = ..density..)) + 
  geom_histogram(fill = "pink") + 
  theme_bw() + 
  geom_density()
p3 <- ggplot(data = Cars93, aes(x = Weight, y = ..density..)) + 
  geom_histogram(fill = "yellow") + 
  theme_bw() + 
  geom_density()
p4 <- ggplot(data = Cars93, aes(x = Length, y = ..density..)) + 
  geom_histogram(fill = "lightblue") + 
  theme_bw() + 
  geom_density()
multiplot(p1, p2, p3, p4, cols = 2)
```

(c) Use the `bwplot()` function from **lattice** [@R-lattice] to create a box and whiskers plot of Price for every type of vehicle according to the drive train. Do you observe any differences between prices? *Rear wheel drive vehicles are generally more expensive than either 4WD or front wheel drive vehicles.*

```{r, label = "partC"}
# Graph for part c
bwplot(Price ~ DriveTrain, data = Cars93)
```

(d) Create a graph similar to the one created in (c) using functions from **ggplot2** [@R-ggplot2].

```{r, label = "partD"}
# Graph for part d
ggplot(data = Cars93, aes(x = DriveTrain, y = Price)) +
  geom_boxplot() +
  theme_bw()
```

(e) Create scatter plot of `Horsepower` versus `Weight`, and superimpose the least squares line from regressing `Horsepower` onto `Weight`.  Write out the least squares line and the theoretical least squares model.

```{r, label = "partE", results = "hide"}
# Graph for part e
ggplot(data = Cars93, aes(x = Weight, y = Horsepower)) + 
  geom_point() + 
  stat_smooth(method = "lm") + 
  theme_bw()
mod_lm <- lm(Horsepower ~ Weight, data = Cars93)
summary(mod_lm)
```

The least squares line from regressing `Horsepower` onto `Weight` is:
$\widehat{\text{Horsepower}} = `r coef(mod_lm)[1]` + `r coef(mod_lm)[2]`\times \text{Weight}.$
The theoretical model for least squares regression is:
$Y = \beta_0 + \beta_1 x + \epsilon$ where $\epsilon \sim N(0, \sigma^2).$

-------------------------------------------------------------------------------

Use the data frame `EPIDURALF` from the **PASWR2** package [@R-PASWR2], and create a table of the average weight of parturient women classified by `ease` and `treatment`.

```{r, label = "tablestuff"}
# Create requested table with kable
EPIDURALF$ease <- factor(EPIDURALF$ease, levels = c("Easy", "Difficult", "Impossible")) # levels in order of difficulty
TS <- with(data = EPIDURALF, {tapply(kg, list(ease, treatment), mean)})
DF <- data.frame(TS)
knitr::kable(DF, col.names = c("Hamstring Stretch", "Traditional Sitting"), caption = "Table: Mean weight (kg.) of parturient women classified by `ease` and `treatment`")
```

--------------------------------------------------------------------------

# R-Code Appendix

```{r, label = "appendix", echo = TRUE, ref.label = all_labels(), eval = FALSE}
```

It is always a good idea to include your `sessionInfo()`:

```{r, label = "SessionInfo", echo = TRUE}
sessionInfo()
```
--------------------------------------------------------------------------

# References