This document assumes you are using the Rstudio IDE. The best way to obtain this document and examine all the files associated with the project is to:

1. Fork this repository to your own GitHub account.
2. Clone the forked repository into a local RStudio project.

To clone the repository, you will need a recent version of Git installed on your machine. This video shows how to clone a repository using the RStudio IDE. Several features from Pandoc (MacFarlane 2015), rmarkdown (Allaire et al. 2015), and knitr (Xie 2015) are illustrated in the document including numerous knitr chunk options (both local and global) which are fully documented online. Rstudio has a great "cheat sheet" for writing R markdown documents. Further information about R markdown can be found online. 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 for this document is written as:

---
title: "Homework with **rmarkdown** and **knitr**"
author: "Alan T. Arnholt"
date: '2015-07-21'
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() (Xie 2015) 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 can create BibTeX files. This 4 minute video illustrates how to store bibliographic information using Zotero, and the following 2 minute video 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. If you need help with how to write a symbol in LaTeX, you can draw the symbol at this site; and LaTeX code corresponding to the user drawn symbol will appear.

Notes:

1. The RStudio IDE will populate most entries for the YAML; however, you will need manually to add the bibliography entry.
2. To create a PDF document (you must have LaTeX installed) or a Word document, change the YAML entry output: html_document to output: pdf_document or output: word_document, respectively.
3. To define the styles in a Word document generated from R markdown see this video.

Code chunks

knitr::opts_chunk$set(fig.show = 'as.is', fig.height = 6,  
                      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)

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().

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 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.

4. The fourth 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.

5. The fifth code chunk named partC does not overwrite any of the global option setting.

6. The sixth code chunk named partD does not overwrite any of the global options.

7. The seventh code chunk named partE hides output send to the console with the local option results = "hide".

8. The eighth code chunk named tablestuff uses the default global options.

9. The ninth 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.

10. The tenth 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 (Ugarte, Militino, and Arnholt 2015) with brief answers.

Load Cars93 from the MASS package (Ripley 2015), and use the function str() on the Cars93 data frame.

> library(MASS)  
> str(Cars93)

'data.frame':   93 obs. of  27 variables:
 $ Manufacturer      : Factor w/ 32 levels "Acura","Audi",..: 1 1 2 2 3 4 4 4 4 5 ...
 $ Model             : Factor w/ 93 levels "100","190E","240",..: 49 56 9 1 6 24 54 74 73 35 ...
 $ Type              : Factor w/ 6 levels "Compact","Large",..: 4 3 1 3 3 3 2 2 3 2 ...
 $ Min.Price         : num  12.9 29.2 25.9 30.8 23.7 14.2 19.9 22.6 26.3 33 ...
 $ Price             : num  15.9 33.9 29.1 37.7 30 15.7 20.8 23.7 26.3 34.7 ...
 $ Max.Price         : num  18.8 38.7 32.3 44.6 36.2 17.3 21.7 24.9 26.3 36.3 ...
 $ MPG.city          : int  25 18 20 19 22 22 19 16 19 16 ...
 $ MPG.highway       : int  31 25 26 26 30 31 28 25 27 25 ...
 $ AirBags           : Factor w/ 3 levels "Driver & Passenger",..: 3 1 2 1 2 2 2 2 2 2 ...
 $ DriveTrain        : Factor w/ 3 levels "4WD","Front",..: 2 2 2 2 3 2 2 3 2 2 ...
 $ Cylinders         : Factor w/ 6 levels "3","4","5","6",..: 2 4 4 4 2 2 4 4 4 5 ...
 $ EngineSize        : num  1.8 3.2 2.8 2.8 3.5 2.2 3.8 5.7 3.8 4.9 ...
 $ Horsepower        : int  140 200 172 172 208 110 170 180 170 200 ...
 $ RPM               : int  6300 5500 5500 5500 5700 5200 4800 4000 4800 4100 ...
 $ Rev.per.mile      : int  2890 2335 2280 2535 2545 2565 1570 1320 1690 1510 ...
 $ Man.trans.avail   : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 1 1 1 1 ...
 $ Fuel.tank.capacity: num  13.2 18 16.9 21.1 21.1 16.4 18 23 18.8 18 ...
 $ Passengers        : int  5 5 5 6 4 6 6 6 5 6 ...
 $ Length            : int  177 195 180 193 186 189 200 216 198 206 ...
 $ Wheelbase         : int  102 115 102 106 109 105 111 116 108 114 ...
 $ Width             : int  68 71 67 70 69 69 74 78 73 73 ...
 $ Turn.circle       : int  37 38 37 37 39 41 42 45 41 43 ...
 $ Rear.seat.room    : num  26.5 30 28 31 27 28 30.5 30.5 26.5 35 ...
 $ Luggage.room      : int  11 15 14 17 13 16 17 21 14 18 ...
 $ Weight            : int  2705 3560 3375 3405 3640 2880 3470 4105 3495 3620 ...
 $ Origin            : Factor w/ 2 levels "USA","non-USA": 2 2 2 2 2 1 1 1 1 1 ...
 $ Make              : Factor w/ 93 levels "Acura Integra",..: 1 2 4 3 5 6 7 9 8 10 ...

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

b. Superimpose estimated density curves over the histograms.

c. Use the bwplot() function from lattice (Sarkar 2015) 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.

d. Create a graph similar to the one created in (c) using functions from ggplot2 (Wickham and Chang 2015).

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.

The least squares line from regressing Horsepower onto Weight is: Horsepower_hat =  -57.7382032 + 0.0655947  × Weight. The theoretical model for least squares regression is: Y = β₀ + β₁x + ϵ where ϵ ∼ N(0, σ²).

---

Use the data frame EPIDURALF from the PASWR2 package (Arnholt 2014), and create a table of the average weight of parturient women classified by ease and treatment.

Table: Mean weight (kg.) of parturient women classified by ease and treatment

	Hamstring Stretch	Traditional Sitting
Easy	78.67000	79.40187
Difficult	92.66667	94.27451
Impossible	127.87500	113.61538

---

R-Code Appendix

knitr::opts_chunk$set(fig.show = 'as.is', fig.height = 6, 
                      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)
library(MASS)  
str(Cars93)
# 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)
# 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)
# Graph for part c
bwplot(Price ~ DriveTrain, data = Cars93)
# Graph for part d
ggplot(data = Cars93, aes(x = DriveTrain, y = Price)) +
  geom_boxplot() +
  theme_bw()
# 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)
# Create requested table with kable
# levels in order of difficulty
EPIDURALF$ease <- factor(EPIDURALF$ease, levels = c("Easy", "Difficult", "Impossible")) 
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`")
sessionInfo()

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

sessionInfo()

## R version 3.2.1 (2015-06-18)
## Platform: x86_64-unknown-linux-gnu (64-bit)
## Running under: Red Hat Enterprise Linux Server release 6.6 (Santiago)
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] rmarkdown_0.7   DT_0.1          MASS_7.3-40     knitr_1.10.5   
## [5] PASWR2_1.0      lattice_0.20-31 ggplot2_1.0.1  
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_0.11.6      magrittr_1.5     munsell_0.4.2    colorspace_1.2-6
##  [5] highr_0.5        stringr_1.0.0    plyr_1.8.3       tools_3.2.1     
##  [9] grid_3.2.1       gtable_0.1.2     e1071_1.6-4      htmltools_0.2.6 
## [13] class_7.3-12     yaml_2.1.13      digest_0.6.8     reshape2_1.4.1  
## [17] formatR_1.2      htmlwidgets_0.5  evaluate_0.7     labeling_0.3    
## [21] stringi_0.5-5    scales_0.2.5     proto_0.3-10

---

References

Allaire, JJ, Joe Cheng, Yihui Xie, Jonathan McPherson, Winston Chang, Jeff Allen, Hadley Wickham, and Rob Hyndman. 2015. Rmarkdown: Dynamic Documents for R. http://CRAN.R-project.org/package=rmarkdown.

Arnholt, Alan T. 2014. PASWR2: Probability and Statistics with R, Second Edition. http://CRAN.R-project.org/package=PASWR2.

MacFarlane, John. 2015. Pandoc: A Universal Document Converter. http://johnmacfarlane.net/pandoc/index.html.

Ripley, Brian. 2015. MASS: Support Functions and Datasets for Venables and Ripley’s MASS. http://CRAN.R-project.org/package=MASS.

Sarkar, Deepayan. 2015. Lattice: Lattice Graphics. http://CRAN.R-project.org/package=lattice.

Ugarte, María Dolores, Ana F. Militino, and Alan T. Arnholt. 2015. Probability and Statistics with R. Second. Boca Raton, FL: CRC Press.

Wickham, Hadley, and Winston Chang. 2015. Ggplot2: An Implementation of the Grammar of Graphics. http://CRAN.R-project.org/package=ggplot2.

Xie, Yihui. 2015. Knitr: A General-Purpose Package for Dynamic Report Generation in R. http://CRAN.R-project.org/package=knitr.