(Another) introduction to R

It’s Memorial Day and my dissertation defense is tomorrow. This week I’m phoning in my blog.

I had the opportunity to teach a short course last week that was part of a larger workshop focused on ecosystem restoration. A fellow grad student and I taught a session on Excel and R for basic data analysis. I insisted on teaching the R portion given my intense hatred for Excel. I wanted to share the slides I presented for the workshop since most of my blogs haven’t been very helpful for beginners. Consider this material my contribution to the already expansive collection of online resources for learning R.

Our short course provided a background to basic data analysis, an introduction using Excel, and an introduction using R. We used a simulated dataset to evaluate the success of a hypothetical ecosystem restoration (produced by my colleague, S. Berg). The dataset provided information on the abundance of redwing blackbirds at a restored plot and a reference plot at each of three sites over a six year period. Our analyses focused on comparing mean abundances between restoration and reference sites (t-tests) and an evaluation of abundance over time (regression). The stats are understandably basic but they should be useful for beginning R users.

The first presentation was a general introduction to R (my hopeless attempt to get people excited) and the second was an introduction to R for data analysis. I’ve uploaded the dataset if anyone is interested trying the analyses on their own. I’ve also included my LaTeX code for the true geeks.

Enjoy!

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\documentclass[xcolor=svgnames]{beamer} \usetheme{Boadilla} \usecolortheme[named=ForestGreen]{structure} \usepackage{graphicx} \usepackage[final]{animate} %\usepackage[colorlinks=true,urlcolor=blue,citecolor=blue,linkcolor=blue]{hyperref} \usepackage{breqn} \usepackage{xcolor} \usepackage{booktabs} \usepackage{tikz} \usetikzlibrary{shadows,arrows,positioning} \usepackage[noae]{Sweave} \definecolor{links}{HTML}{2A1B81} \hypersetup{colorlinks,linkcolor=links,urlcolor=links} \usepackage{pgfpages} %\pgfpagesuselayout{4 on 1}[letterpaper, border shrink = 5mm, landscape] \tikzstyle{block} = [rectangle, draw, text width=7em, text centered, rounded corners, minimum height=3em, minimum width=7em, top color = white, bottom color=green!30,  drop shadow] \begin{document} \SweaveOpts{concordance=TRUE} \title[R for Data Analysis]{\includegraphics[width=0.07\textwidth]{Rlogo.jpg} \hspace{0.2em} for Data Analysis} \author[M. Beck and S. Berg]{Marcus W. Beck \and Sergey Berg} \institute[UofM]{Department of Fisheries, Wildlife, and Conservation Biology \\ University of Minnesota, Twin Cities} \date{May 21, 2013} \titlegraphic{ \centerline{ \begin{tikzpicture}   \node[fill=white,draw] at (0,0) {\includegraphics[width=0.6\textwidth]{peeper.jpg}}; \end{tikzpicture}} } %%%%%% \begin{frame} \vspace{-0.3in} \titlepage \end{frame} \section{Background} %%%%%% \begin{frame}{What you'll learn about \hspace{0.2em}\includegraphics[width=0.07\textwidth]{Rlogo.jpg}} \setbeamercovered{again covered={\opaqueness<1->{25}}} \onslide<1-> \begin{itemize} \itemsep20pt \item Data organization \item Data exploration and visualization \begin{itemize} \item Common functions \item Graphing tools \end{itemize} \item Data analysis and hypothesis testing \begin{itemize} \item Common functions \item Evaluation of output \item Graphing tools \\~\\ \end{itemize} \end{itemize} \pause \Large \centerline{\emph{Interactive! Interrupt me!}} \end{frame} \section{Data organization} %%%%%% \begin{frame}[fragile]{Data organization} We'll use the same dataset we used in Excel, replicating the analyses\\~\\ First we have to import the data into our R `workspace' \\~\\ \pause The workspace is a group of R objects that are loaded for our current session \\~\\ Data are loaded into the workspace by importing (or making within R) and assigning them to a variable (object) with a name of our choosing\\~\\ We can see what's loaded in our workspace:\\~\\ \pause <<echo=true>>= a<-c(1,2) ls() @ \end{frame} %%%%%% \begin{frame}[fragile]{Data organization} \onslide<+->{Import the data following this workflow:}\\~\\ \begin{center} \begin{tikzpicture}[node distance=2.5cm, auto, >=stealth]     \onslide<2->{     \node[block] (a) {1. Open data in Excel and clean};}     \onslide<3->{     \node[block] (b)  [right of=a, node distance=4.2cm] {2. Save data in `.csv' format};     \draw[->] (a) -- (b);}     \onslide<4->{     \node[block] (c)  [right of=b, node distance=4.2cm]  {3. Import in R using 'read.csv'};     \draw[->] (b) -- (c);} \end{tikzpicture} \end{center} \begin{columns}[t] \onslide<2->{ \begin{column}{0.33\textwidth} \begin{itemize} \item Column names should be simple \item Ensure all data will be easy to read \end{itemize} \end{column}} \onslide<3->{ \begin{column}{0.33\textwidth} \begin{itemize} \item File, Save as .csv \item Creates a comma separated file that looks like a spreadsheet \item One spreadsheet at a time \end{itemize} \end{column}} \onslide<4->{ \begin{column}{0.33\textwidth} \begin{itemize} \item header = T \item See ?read.csv for list of function options \item Remember to assign a name \end{itemize} \end{column}} \end{columns} \end{frame} %%%%%% \begin{frame}[fragile,shrink]{Data organization} If the data are a text file... open the text file, how are the columns separated? \begin{itemize} \item comma \item tabs \item space \item arbitrary character\\~\\ \end{itemize} \pause Use the read.table function and identify the column delimiter: <<echo=true>>= setwd('C:/Documents/monitoring_workshop') ls() dat<-read.table('RWBB Survey.txt',sep='\t',header=T) ls() @ \end{frame} %%%%%% \begin{frame}[fragile]{Data organization} Now that the data are in our workspace, let's explore!\\~\\ \pause Did the data import correctly (rarely a problem)?\\~\\ <<echo=true,eval=false>>= head(dat) #or tail(dat) @ \scriptsize <<echo=false>>= head(dat) #or tail(dat) @ \end{frame} \section{Data exploration} %%%%%% \begin{frame}[fragile]{Data exploration} What object class is the data? <<>>= class(dat) @ \pause What are the dimensions of the data frame? <<>>= dim(dat) nrow(dat) ncol(dat) @ The data contain \Sexpr{nrow(dat)} rows and \Sexpr{ncol(dat)} columns, is this correct? \end{frame} %%%%%% \begin{frame}[fragile]{Data exploration} Can we get a summary of the data frame? \pause <<>>= summary(dat) @ \end{frame} %%%%%% \begin{frame}[fragile]{Data exploration} Individual summmaries of variables are also possible\\~\\ How do we obtain variables of interest? \small <<>>= names(dat) @ \pause \normalsize We can get a variable directly using \$ or via indexing with [,] \small <<>>= dat$Temperature dat[,'Temperature'] #same as dat[,7] @ \end{frame} %%%%%% \begin{frame}[fragile]{Data exploration} Just as we had summaries of the data frame, we can get summaries of individual variables <<>>= summary(dat$Temperature) @ \pause Or more simplistically... <<>>= mean(dat$Temperature) range(dat$Temperature) unique(dat$Temperature) @ \end{frame} %%%%%% \begin{frame}[fragile]{Data exploration} Note that the classes of our variables affect how R functions interpet them\\~\\ For example, the summary function returns different information...\\~\\ \small <<>>= class(dat$Temperature) summary(dat$Temperature) class(dat$SiteName) summary(dat$SiteName) @ \end{frame} %%%%%% \begin{frame}[fragile,t]{Data exploration} What about site-specific evaluations?  What if we want to look at the temperature only at Kelly?\\~\\ <<>>= Kelly<-subset(dat, dat$SiteName=='Kelly') @ \vspace{0.2in} We've created a new object in our workspace that is our original data frame with sites only from Kelly\\~\\ \pause <<>>= dim(Kelly) Kelly$SiteName @ \end{frame} %%%%%% \begin{frame}[fragile,t]{Data exploration} What about site-specific evaluations?  What if we want to look at the temperature only at Kelly?\\~\\ <<>>= Kelly<-subset(dat, dat$SiteName=='Kelly') @ \vspace{0.2in} Now we can evaluate the temperature, for example, only at Kelly\\~\\ <<>>= mean(Kelly$Temperature) #this is the same as all sites @ \end{frame} %%%%%% \begin{frame}[fragile]{Data exploration} What abour our restoration project?  Aren't we comparing the abundances of breeding birds between restored and reference sites? \\~\\ Let's start with our reference sites... <<>>= ref<-dat$Reference summary(ref) #or summary(dat$Reference) @ \pause Now the restored sites... <<>>= rest<-dat$Restoration summary(rest) @ \end{frame} \section{Data visualization} %%%%%% \begin{frame}[fragile]{Data visualization} Textual summaries of our data are nice, but we should also visualize: \begin{itemize} \item How are our data distributed? \item Are there any outliers or extreme observations? \item How do our variables compare (to a reference, to one another, over time, etc.)?\\~\\ \end{itemize} \pause R has many built in functions for data exploration and plotting \begin{itemize} \item hist - plots a histogram (binned densities of continuous values) \item qqplot - comparison of a variable to a normal distribution \item barplot - for bar plots... \item plot - bivariate comparison of two variables \item Much, much more... \end{itemize} \end{frame} %%%%%% \begin{frame}[fragile]{Data visualization} Let's examine the distribution of abundances for the breeding birds at our reference site\\~\\ \begin{columns} \begin{column}{0.6\textwidth} <<hist_ref,fig=true,width=6,height=5,include=false>>= hist(ref) #or hist(dat$Reference) @ \begin{center} \includegraphics[width=\textwidth,trim=0in 0in 0.3in 0.3in]{R_for_data_analysis-hist_ref.pdf} \end{center} \end{column} \begin{column}{0.4\textwidth} \pause 14 of our reference sites have abundances between 0--5 breeding birds \end{column} \end{columns} \end{frame} %%%%%% \begin{frame}[fragile]{Data visualization} How does it compare to our restoration site?\\~\\ \begin{columns} \begin{column}{0.6\textwidth} <<hist_rest,fig=true,width=6,height=5,include=false>>= hist(rest) #or hist(dat$Restoration) @ \begin{center} \includegraphics[width=\textwidth,trim=0in 0in 0.3in 0.3in]{R_for_data_analysis-hist_rest.pdf} \end{center} \end{column} \begin{column}{0.4\textwidth} \pause Six of our reference sites have abundances between 10--15 breeding birds \end{column} \end{columns} \end{frame} %%%%%% \begin{frame}[fragile]{Data visualization} Now that we've seen the distribution, how can we compare directly?\\~\\ <<box,fig=true,width=6,height=5,include=false>>= boxplot(ref,rest) @ \begin{columns} \begin{column}{0.6\textwidth} \begin{center} \includegraphics[width=\textwidth,trim=0in 0in 0.3in 0.3in]{R_for_data_analysis-box.pdf} \end{center} \end{column} \begin{column}{0.4\textwidth} \pause Let's make it look better... \end{column} \end{columns} \end{frame} %%%%%% \begin{frame}[fragile]{Data visualization} Now that we've seen the distribution, how can we compare directly?\\~\\ <<box2,fig=true,width=6,height=5,include=false>>= boxplot(ref,rest,names=c('Reference','Restoration'),     ylab='Bird abundance',col=c('lightblue','lightgreen'),     main='Comparison of abundances between sites') @ \begin{columns} \begin{column}{0.6\textwidth} \pause \begin{center} \includegraphics[width=\textwidth,trim=0in 0in 0.3in 0.3in]{R_for_data_analysis-box2.pdf} \end{center} \end{column} \begin{column}{0.4\textwidth} \pause Dark line is median, box is 25$^{th}$ to 75$^{th}$ quartile (or IQR), whiskers are 1.5 $\times$ IQR\\~\\ Beyond can be considered outliers... \end{column} \end{columns} \end{frame} %%%%%% \begin{frame}[fragile]{Data visualization} What's going on with the outlier at our reference site?  How can we identify it? \\~\\ We can use the boxplot function for the dirty work...\\~\\ \pause <<>>= myplot<-boxplot(ref,rest) myplot$out @ \vspace{0.2in} This gives us the actual value, now we need to find it in our data frame \\~\\ \pause <<>>= outlier<-myplot$out out.row<-which(ref==outlier) out.row #this is the row number @ \end{frame} %%%%%% \begin{frame}[fragile]{Data visualization} <<eval=false>>= dat[out.row,] #same as dat[8,] @ \scriptsize <<echo=false>>= dat[out.row,] #same as dat[8,] @ \vspace{0.2in} \normalsize Now we know that our outlier was from Kelly in 2007...\\~\\ What's odd about this record? \\~\\ \pause Let's look at our records from Kelly...\\~\\ \end{frame} %%%%%% \begin{frame}[fragile]{Data visualization} <<eval=false>>= Kelly @ \scriptsize <<echo=false>>= Kelly @ \normalsize \vspace{0.2in} \pause 2007 was cold and rainy, could that have been the reason?\\~\\ Let's look at 2007 for all sites... \end{frame} %%%%%% \begin{frame}[fragile]{Data visualization} <<eval=false>>= subset(dat,dat$Year=='2007') @ \pause \scriptsize <<echo=false>>= subset(dat,dat$Year=='2007') @ \normalsize \vspace{0.2in} \pause IGH and Carlton don't have high abundances at their reference sites during 2007 even though the weather was the same \\~\\ What else could have caused this outlier?\\~\\ \pause <<eval=false>>= summary(dat$ObserverNames) @ \pause \scriptsize <<echo=false>>= summary(dat$ObserverNames) @ \end{frame} %%%%%% \begin{frame}[fragile]{Data visualization} <<eval=false>>= summary(dat$ObserverNames) @ \scriptsize <<echo=false>>= summary(dat$ObserverNames) @ \normalsize \vspace{0.2in} This is probably Jeremy and/or Lucy's fault, most likely switched the restoration and reference records \\~\\ \pause What to change? \pause <<eval=false>>= dat[out.row,'Restoration']<-18 dat[out.row,'Reference']<-2 @ Or... <<eval=true>>= dat<-dat[-out.row,] #do this one @ Or... fire Jeremy and Lucy. \end{frame} \section{Data analysis and hypothesis testing} %%%%%% \begin{frame}{Data analysis and hypothesis testing} Now we need to evaluate the statistical certainty of our data, i.e., are our results due to random chance and how can we quantify this?\\~\\ \begin{columns} \begin{column}{0.5\textwidth} \begin{center} \includegraphics[width=\textwidth,trim=0in 0in 0.3in 0.3in]{R_for_data_analysis-box2.pdf} \end{center} \end{column} \begin{column}{0.5\textwidth} \pause We want to determine if the abundance of birds or variation among sites is actual or random\\~\\ \end{column} \end{columns} \pause \centerline{What is an appropriate hypothesis?} \end{frame} <<hyp1,fig=T,include=false,eval=true,width=3.5,height=4.5,echo=false>>= boxplot(dat$Reference,col='lightblue',main='Boxplot of abundance\nat reference sites',ylab='Bird abundance',ylim=c(-1,8)) abline(h=0,lty=2,lwd=2) @ %%%%%% \begin{frame}{Data analysis and hypothesis testing} \centerline{What is an appropriate hypothesis? Let's start simple...} \vspace{0.2in} \pause \begin{columns} \begin{column}{0.5\textwidth} \begin{block}{Null hypothesis} The mean abundance of breeding birds at our reference site is zero. \end{block} \pause \vspace{0.2in} \begin{block}{Alternative hypothesis} The mean abundance of breeding birds at our reference site is not zero. \end{block} \end{column} \begin{column}{0.5\textwidth} \pause \centerline{\includegraphics[width=0.85\textwidth,trim=0in 0.8in 0in 0in]{R_for_data_analysis-hyp1.pdf}} \end{column} \end{columns} \end{frame} %%%%%% \begin{frame}[t,fragile]{Data analysis and hypothesis testing} The t.test function lets us test this hypothesis, very simple...\\~\\ <<eval=false>>= t.test(dat$Reference) @ \pause \small <<echo=false>>= t.test(dat$Reference) @ \normalsize \vspace{0.2in} \pause What does this mean? \pause What are default arguments?\\~\\ \end{frame} %%%%%% \begin{frame}[t]{Data analysis and hypothesis testing} Perhaps a one-tailed alternative hypothesis is better, we have prior assumptions about the data...\\~\\ \pause \begin{columns} \begin{column}{0.5\textwidth} \begin{block}{Null hypothesis} The mean abundance of breeding birds at our reference site is zero. \end{block} \pause \vspace{0.2in} \begin{block}{Alternative hypothesis} The mean abundance of breeding birds at our reference site is greater than zero. \end{block} \end{column} \begin{column}{0.5\textwidth} \pause \centerline{\includegraphics[width=0.85\textwidth,trim=0in 0.8in 0in 0in]{R_for_data_analysis-hyp1.pdf}} \end{column} \end{columns} \end{frame} %%%%%% \begin{frame}[fragile]{Data analysis and hypothesis testing} Slight modification of alternative argument for one-tailed test, default is two-tailed\\~\\ <<eval=false>>= t.test(dat$Reference, alternative='greater') @ \pause \small <<echo=false>>= t.test(dat$Reference, alternative='greater') @ \normalsize \pause What does this mean? \end{frame} <<hyp2,fig=T,include=false,eval=true,width=3.5,height=4.5,echo=false>>= boxplot(dat$Reference,col='lightblue',main='Boxplot of abundance\nat reference sites',ylab='Bird abundance',ylim=c(-1,8)) abline(h=4,lty=2,lwd=2) @ %%%%%% \begin{frame}[t]{Data analysis and hypothesis testing} Let's explore more flexibility of the t.test function by changing our basis of comparison for the alternative hypothesis\\~\\ \pause \begin{columns} \begin{column}{0.5\textwidth} \begin{block}{Null hypothesis} The mean abundance of breeding birds at our reference site is four. \end{block} \pause \vspace{0.2in} \begin{block}{Alternative hypothesis} The mean abundance of breeding birds at our reference site is greater than four. \end{block} \end{column} \begin{column}{0.5\textwidth} \pause \centerline{\includegraphics[width=0.85\textwidth,trim=0in 0.8in 0in 0in]{R_for_data_analysis-hyp2.pdf}} \end{column} \end{columns} \end{frame} %%%%%% \begin{frame}[fragile,t]{Data analysis and hypothesis testing} Test a different alternative hypothesis by changing the mu argument\\~\\ <<eval=false>>= t.test(dat$Reference, mu=4, alternative='greater') @ \pause \small <<echo=false>>= t.test(dat$Reference, mu=4, alternative='greater') @ \pause \normalsize What does this mean? \end{frame} %%%%%% \begin{frame}{Data analysis and hypothesis testing} Now the real question, let's compare our sites to one another...\\~\\ What are our hypotheses?\\~\\ \pause \begin{columns} \begin{column}{0.5\textwidth} \begin{block}{Null hypothesis} Differences in the mean abundance between restoration and reference sites is zero. \end{block} \pause \vspace{0.2in} \begin{block}{Alternative hypothesis} Differences in the mean abundance between restoration and reference sites will be greater than zero. \end{block} \end{column} \begin{column}{0.5\textwidth} \pause \centerline{\includegraphics[width=0.85\textwidth,trim=0in 1in 0.5in 0.5in]{R_for_data_analysis-box2.pdf}} \end{column} \end{columns} \end{frame} %%%%%% \begin{frame}[fragile]{Data analysis and hypothesis testing} Use the t.test function again as a two-sample test, order matters as do arguments\\~\\ <<eval=false>>= t.test(dat$Restoration,dat$Reference,     alternative='greater',var.equal=T) @ \pause \small <<echo=false>>= t.test(dat$Restoration,dat$Reference,     alternative='greater',var.equal=T) @ \normalsize \pause What does this mean? \end{frame} %%%%%% \begin{frame}[fragile]{Data analysis and hypothesis testing} Order of arguments matters...\\~\\ <<eval=false>>= t.test(dat$Reference,dat$Restoration,     alternative='greater',var.equal=T) @ \pause \small <<echo=false>>= t.test(dat$Reference,dat$Restoration,     alternative='greater',var.equal=T) @ \normalsize \pause What does this mean? \pause What happens if we change the alternative argument? \end{frame} %%%%% \begin{frame}{Data analysis and hypothesis testing} Our results suggest that the abundance of breeding birds at the restoration site is significantly greater than at the reference site \pause \vspace{0.5in} \begin{columns} \begin{column}{0.5\textwidth} \centerline{\includegraphics[width=0.85\textwidth,trim=0in 1in 0.5in 0.5in]{R_for_data_analysis-box2.pdf}} \end{column} \begin{column}{0.5\textwidth} Our p-value is 4.006e-06, what does this mean?\\~\\ \pause There is a 0.0004006\% chance that our results were observed due to randomness (within the constraints of our test). \end{column} \end{columns} \end{frame} %%%%%% \begin{frame}[t]{Data analysis and hypothesis testing} Other common tests:\\~\\ \begin{itemize} \itemsep20pt \item $\chi^2$ test of independence - chisq.test \item analysis of variance - anova or aov \item correlations - cor.test or cor \item regression - lm or glm \item Much, much more.... \end{itemize} \end{frame} %%%%% \begin{frame}{Data analysis and hypothesis testing} One last example... we've used common tests to compare our data to a standard or reference (e.g., mean is zero, differences in means is greater than zero)\\~\\ What about a more interesting analysis, such as comparison of data over time or relationships between variables?\\~\\ We'll close by illustrating use of linear regression with our data\\~\\ This is an evaluation of the mean response of a variable conditional on another, i.e., a predictor \end{frame} <<reg1,fig=true,include=false,eval=true,echo=false,width=4,height=4>>= par(mar=c(4,4,0.5,0.5)) plot(Restoration~Year,data=dat) @ %%%%%% \begin{frame}[fragile]{Data analysis and hypothesis testing} Perhaps we expect the abundance of breeding birds to increase at our restoration site over time, let's plot it:\\~\\ <<eval=false>>= plot(Restoration~Year,data=dat) @ \vspace{-0.13in} \pause \begin{columns} \begin{column}{0.5\textwidth} The first argument is entered as a `formula' specifying the variables\\~\\ The data argument specifies location of the variables in the workspace \end{column} \begin{column}{0.5\textwidth} \begin{center} \includegraphics[width=0.9\textwidth]{R_for_data_analysis-reg1.pdf} \end{center} \end{column} \end{columns} \end{frame} <<reg2,fig=true,include=false,eval=true,echo=false,width=4,height=4>>= par(mar=c(4,4,0.5,0.5)) plot(dat$Year,dat$Restoration) @ %%%%%% \begin{frame}[fragile]{Data analysis and hypothesis testing} We can also call the variables directly in the plot function, x variable first, y second:\\~\\ <<eval=false>>= plot(dat$Year,dat$Restoration) @ \vspace{-0.13in} \begin{columns} \begin{column}{0.5\textwidth} \onslide<2-> Note the change of the x and y labels, we can modify these using the xlab and ylab arguments in the plot function\\~\\ \onslide<3-> Notice the clear trend... \end{column} \begin{column}{0.5\textwidth} \onslide<2-> \begin{center} \includegraphics[width=0.9\textwidth]{R_for_data_analysis-reg2.pdf} \end{center} \end{column} \end{columns} \end{frame} %%%%%% \begin{frame}[fragile]{Data analysis and hypothesis testing} How do we quantify this trend across time? Use the lm function for regression...\\~\\ <<eval=false>>= lm(Restoration~Year,data=dat) @ \pause <<echo=false>>= lm(Restoration~Year,data=dat) @ \vspace{0.2in} \pause The abundance increases, on average, by \Sexpr{round(lm(Restoration~Year,data=dat)$coefficients[2],3)} birds per year. \end{frame} %%%%%% \begin{frame}[fragile]{Data analysis and hypothesis testing} We can get more information using the summary command \vspace{0.1in} <<eval=false>>= mod<-lm(Restoration~Year,data=dat) summary(mod) @ \pause \scriptsize <<echo=false>>= mod<-lm(Restoration~Year,data=dat) summary(mod) @ \end{frame} %%%%%% \begin{frame}[fragile]{Data analysis and hypothesis testing} What does this mean? \vspace{0.1in} \scriptsize <<echo=false>>= mod<-lm(Restoration~Year,data=dat) summary(mod) @ \end{frame} <<reg3,fig=true,include=false,eval=true,echo=false,width=4,height=4>>= par(mar=c(4,4,0.5,0.5)) plot(Restoration~Year, data=dat) abline(reg=mod) @ %%%%%% \begin{frame}[fragile]{Data analysis and hypothesis testing} How do we plot the model?\\~\\ <<eval=false>>= plot(Restoration~Year, data=dat) abline(reg=mod) @ \vspace{-0.3in} \begin{columns} \begin{column}{0.5\textwidth} We tell the abline function to plot our model, named `mod' \end{column} \begin{column}{0.5\textwidth} \pause \begin{center} \includegraphics[width=0.9\textwidth]{R_for_data_analysis-reg3.pdf} \end{center} \end{column} \end{columns} \end{frame} %%%%% \begin{frame}[fragile]{Data analysis and hypothesis testing} Can we use our model for prediction?\\~\\ What are the predicted data for our observation years?\\~\\ <<eval=false>>= predict(mod) @ \scriptsize \pause <<echo=false>>= predict(mod) @ \vspace{0.2in} \normalsize \pause What about other years not in our dataset? \end{frame} %%%%% \begin{frame}[fragile]{Data analysis and hypothesis testing} Can we use our model for prediction?\\~\\ What about predicted abundance for 2011?\\~\\ <<eval=false>>= predict(mod,newdata=data.frame(Year=2011)) @ \pause <<echo=false>>= predict(mod,newdata=data.frame(Year=2011)) @ \vspace{0.2in} We can expect, on average, \Sexpr{round(predict(mod,newdata=data.frame(Year=2011)),2)} birds at our restoration sites in 2011 (within the constraints of our model) \end{frame} \section{Conclusion} %%%%% \begin{frame}{Conclusion} What we've learned:\\~\\ \begin{itemize} \itemsep20pt \item Data organization - read.csv, read.table \item Data exploration - head, dim, nrow, ncol, summary, [,], \$, names, subset, mean, range, unique \item Data visualization - hist, boxplot, plot, abline \item Data analysis and hypothesis testing - t.test, lm, predict\\~\\ \end{itemize} \LARGE \centerline{\emph{Questions?}} \end{frame} \end{document}