\documentclass[notitlepage]{article}
\usepackage{Math533}
\usepackage{listings}
\usepackage{numprint}

\lstloadlanguages{R}

\lstset{basicstyle=\ttfamily, numbers=none, literate={~} {$\sim$}{2}}

\begin{document}
\title{Using \texttt{knitr} to produce reports from \texttt{R} scripts}
\author{David A. Stephens}
\maketitle
\begin{abstract}
This document shows you how to use the \texttt{knitr} package in \texttt{R} or \texttt{RStudio}
to create pdf documents based on \texttt{R} scripts.
\end{abstract}

The file that created this pdf document is \texttt{knit-01-lm.Rnw}, or the 
equivalent file \texttt{RStudio-knit-01-lm.Rnw} for use in \texttt{RStudio}.

\bigskip

\begin{itemize}
\item Using \texttt{R}: when issuing the commands
\begin{lstlisting}
library(knitr)
knit('knit-01-lm.Rnw')
\end{lstlisting}
whilst running \texttt{R} in a folder containing the file \texttt{knit-01-lm.Rnw}, the code will 
produce a Latex file \texttt{knit-01-lm.tex} which can then be compiled using \texttt{pdflatex}.

\medskip

\item Using \texttt{RStudio}:  you can open the \texttt{RStudio-knit-01-lm.Rnw} file directly in \texttt{RStudio}, and compile
it using the `Compile pdf' button at the top of the R/Sweave script window that opens automatically when you click on
the \texttt{.Rnw} file.  Note that you should set the file to be compiled correctly by going to the
\[
\textit{Tools} \longrightarrow \textit{Global Options}
\]
pulldown menu, and hitting the Sweave symbol in the left-hand sidebar.  Then from the top pulldown menu
\textit{Weave Rnw files using} select the option `\texttt{knitr}'.

\end{itemize}

\bigskip

Here is a plot of the rocket propulsion data from the textbook, as studied in class:
%<<setup, echo=FALSE>>=
%library(knitr)
%knit_hooks$set(source = function(x, options) {
%    paste("\\begin{lstlisting}[numbers=left, firstnumber=last]\n", x, 
%        "\\end{lstlisting}\n", sep = "")
%})
%@

<<model,comment='+', fig.width=6, fig.height=4.5, fig.align='center'>>=
data.source<-"http://www.math.mcgill.ca/dstephens/Regression/Data/2-1-RocketProp.csv"
RocketProp<-read.csv(file=data.source)
names(RocketProp)<-c('i','Strength','Age')
x<-RocketProp$Age
y<-RocketProp$Strength
plot(x,y,pch=19,cex=0.6,xlab='Age',ylab='Shear Strength')
xmean<-mean(x)
ymean<-mean(y)
abline(v=xmean,h=ymean,lty=2)
@
The mean of the $x$ values is \Sexpr{xmean}, and the mean of the $y$ values is \Sexpr{ymean}.


<<pwc1,comment='+', fig.width=6.25, fig.height=4.75, fig.align='center'>>=
############################################
#Fit the simple linear regression using lm

fit.RP<-lm(y~x)
summary(fit.RP)
coef(fit.RP)
@

From this, we can deduce that the estimate of the intercept is $\widehat \beta_0=\Sexpr{coef(fit.RP)[1]}$, 
and the estimate of the slope is $\widehat \beta_1=\Sexpr{coef(fit.RP)[2]}$, that is, the line of best fit is
\[
y = \Sexpr{coef(fit.RP)[1]} + \Sexpr{coef(fit.RP)[2]} x
\]
However, this is reporting the estimates to too many decimal places: we can reduce that by using the \texttt{round}
function: for example \texttt{round(coef(fit.RP)[1],3)} gives the result to 3 decimal places.  We have
\[
y = \Sexpr{round(coef(fit.RP)[1],3)} + \Sexpr{round(coef(fit.RP)[2],3)} x.
\]
The line of best fit is good (see plot below).

\medskip

Here is an alternative way to use the \texttt{lm} function in \texttt{R}, by using 
the \texttt{data=RocketProp} argument; this allows you to call the variables by name 
in the command
\[
\texttt{fit.RP<-lm(Strength~Age,data=RocketProp)}
\]
<<hr,comment='+', fig.width=5.25, fig.height=4.25, fig.align='center'>>=
fit.RP<-lm(Strength~Age,data=RocketProp)
plot(x,y,pch=19,cex=0.6,xlab='Age',ylab='Shear Strength')
coef(fit.RP)
abline(coef(fit.RP),col='red')
title('Line of best fit for Rocket Propulsion Data')
@
\end{document}