% Example of Literate Programming for Presentations
%
% James Keirstead
% AcademicProductivity.com
% 25 August 2009
%
% Published at http://www.academicproductivity.com/2009/literate-programming-for-talks


\title{Linear regression}
\author{James Keirstead}

\begin{document}

\begin{frame}
 \maketitle
\end{frame}

In this talk, I will be demonstrating how to create a simple linear regression model in R.


The first step is to create some data.  Let's assume we have a simple function, $f(x)$ where $y = x + \epsilon$ and the error term, $\epsilon$, is normally distributed with $\mu = 0$ and $\sigma = 1$.

% The following is an R code block that creates the x and y data series.  It will not be visible in either the article or the slides.

<<echo=FALSE>>=
x <- 1:100
y <- x + rnorm(100,0,1)
@ 

Now that we've created our data set, let's inspect it.

\begin{frame}{Our data set}
<<echo=FALSE,fig=TRUE>>=
plot(x,y)
@ 
\end{frame}

Looks pretty linear! We can then perform the linear regression in R.  %Note that this code will be shown in the lecture notes but not on the slides.

<<>>=
lm <- lm(y~x)
@ 

The results of the linear regression show that the model is significant with an adjusted $r^2$ value of \Sexpr{round(summary(lm)$adj.r.squared,4)}.

\begin{frame}{Results of linear regression}
<<echo=FALSE>>=
summary(lm)
@ 
\end{frame}


\end{document}