\documentclass{beamer}
\usepackage{graphicx}
\usepackage{Sweave}
\usepackage{hyperref}

\mode<presentation>
{
  \usetheme{CambridgeUS}
}

\usepackage[english]{babel}
\usepackage[latin1]{inputenc}
\usepackage{times}
\usepackage[T1]{fontenc}

\title{Analysis of your weight data}
\author{\href{http://www.mayin.org/ajayshah}{Ajay Shah}}

\begin{document}
\SweaveOpts{engine=R,eps=FALSE,keep.source=TRUE,results=hide,echo=FALSE,prefix.string=pix/pic}
\setkeys{Gin}{width=\textwidth}

<<start-off,results=verbatim>>=
library(ggplot2)
library(xtable)
system("mkdir pix")
calories.per.g <- 2.2*3.5             # TODO: Put in an exact number

d <- read.table("ans_data.text", col.names=c("date","w"))
d$w <- 1000*d$w
d$date <- as.Date(as.character(d$date))
d$time <- as.numeric(d$date-d$date[1])
@

\begin{frame}
  \titlepage
\end{frame}

\begin{frame}
  \frametitle{Scatterplot}
  \begin{center}
<<scatterplot,fig=TRUE,width=10>>=
print(ggplot(d, aes(date,w/1000)) +
      geom_point() +
      labs(x=NULL, y="Weight (kilos)") +
      scale_x_date(major="1 months", minor="7 days", format="%b %y"))
@
\end{center}
\end{frame}

\begin{frame}
  \frametitle{Simple OLS regression of weight (in grams) on time (in days)}
  \begin{center}
<<olsres,results=tex>>=
m <- lm(w ~ time, data=d)
imbalance <- (coef(m)[2] + c(-1.96,1.96)*summary(m)$coefficients[2,2]) * calories.per.g
imbalance.string <- sprintf("Imbalance = %.2f to %.2f kCal/day", imbalance[1], imbalance[2])
print(xtable(m),floating=FALSE)
@   
\end{center}
\end{frame}

\begin{frame}
  \frametitle{Scatterplot + overall OLS time trend}
  \begin{center}
<<lmpic,fig=TRUE,width=10>>=
print(ggplot(d, aes(date,w/1000)) +
      geom_point() +
      labs(x=NULL, y="Weight (kilos)") + 
      geom_smooth(method="lm") +
      opts(title=imbalance.string) +
      scale_x_date(major="1 months", minor="7 days", format="%b %y"))
@   
\end{center}
\end{frame}

\begin{frame}
  \frametitle{OLS spline estimation}
  \begin{center}
<<splinespic,fig=TRUE,width=10>>=
library(splines)
print(ggplot(d, aes(date,w/1000)) +
      geom_point() +
      labs(x=NULL, y="Weight (kilos)") + 
      stat_smooth(method="lm", formula = y ~ ns(x,4)) +
      opts(title = "Spline smoothing") +
      scale_x_date(major="1 months", minor="7 days", format="%b %y"))
@   
\end{center}
\end{frame}

<<setup-recent-width>>=
recentwidth <- 42                       # In the future, do this nicely
@ 

\begin{frame}
  \frametitle{Latest \Sexpr{recentwidth} days}
  \begin{center}
<<recentols,results=tex>>=
small <- subset(d, d$date > (tail(d$date,1) - recentwidth))
m <- lm(w ~ time, data=small)
imbalance <- (coef(m)[2] + c(-1.96,1.96)*summary(m)$coefficients[2,2]) * calories.per.g
imbalance.string <- sprintf("Imbalance = %.2f to %.2f kCal/day", imbalance[1], imbalance[2])
print(xtable(m),floating=FALSE)
@   
\end{center}
\end{frame}

\begin{frame}
  \frametitle{Scatterplot +  OLS time trend: Recent \Sexpr{recentwidth} days}
  \begin{center}
<<recentlmpic,fig=TRUE,width=10>>=
print(ggplot(small, aes(date,w/1000)) +
      geom_point() +
      labs(x=NULL, y="Weight (kilos)") + 
      geom_smooth(method="lm") +
      opts(title=imbalance.string) +
      scale_x_date(major="1 week", format="%d %b"))
@   
\end{center}
\end{frame}

\begin{frame}
  \frametitle{Density of imbalance per day (latest \Sexpr{recentwidth} days)}
  \begin{center}
<<bootdist,fig=TRUE,width=10>>=
library(boot)
sampleols <- function(dataset, indexes) {
  return(lm(w ~ time, data=dataset[indexes,])$coefficients[2])
}
b <- boot(d, sampleols, R=2000)
k <- density(b$t)
tmp <- data.frame(x=k$x*calories.per.g, y=k$y)
ci <- calories.per.g*boot.ci(b, type="basic")$basic[1,c(4,5)]
print(ggplot(tmp, aes(x, y)) +
      geom_line() +
      labs(x="Imbalance (kcal/day)", y="Density (through bootstrap)") +
      geom_vline(xintercept=ci[1]) +
      geom_vline(xintercept=ci[2])
      )
@ 
  
  \end{center}
\end{frame}

\begin{frame}
  \frametitle{Finding out more}

  See \href{http://www.mayin.org/ajayshah/MISC/weightloss.html}{http://www.mayin.org/ajayshah/MISC/weightloss.html}

\end{frame}

\begin{frame}
  \hfill\mbox{Thank you.}
\end{frame}

\end{document}