R graphics  R has several graphics packages  The plotting functions are quick and easy to use  We will cover:  Bar charts – frequency, proportion  Pie charts  Histograms  Box plots  Scatter plots  Explore further on your own - R help, demo(graphics)

Bar charts  A bar chart draws a bar with a height proportional to the count in the table  The height could be given by the frequency, or the proportion, where the graph will look the same, but the scales may be different  Use scan() to read in the data from a file or by typing  Try ?scan for more information  Usage is simple: type in the data. It stops adding data when you enter a blank row

Bar charts Example:  Suppose, a group of 25 animals are surveyed for their feeding preference. The categories are (1) grass, (2) shrubs, (3) trees and (4) fruit. The raw data is  Let's make a barplot of both frequencies and proportions…

Bar chart - frequency 1: : Example: Feeding preference > feed = scan() Read 25 items > barplot(table(feed)) Frequency Note: barplot(feed) is not correct. Use table command to create summarized data, and the result of this is sent to barplot creating the barplot of frequencies

Bar chart - proportion > barplot(table(feed)/length(feed)) # divide by n for proportion Example cont… > table(feed)/length(feed) feed

Pie charts  The same data can be studied with pie charts, using the pie function  Following are some simple examples illustrating usage - similar to barplot(), but with some added features  We use names to specify names to the categories  We add colour to the pie chart by setting the pie chart attribute col  The help command (?pie) gives some examples for automatically getting different colours

Pie charts > feed.counts = table(feed)# store the table result > pie(feed.counts) # first pie -- kind of dull Boring pie Named pie Coloured pie > names(feed.counts) = c(“grass",“shrubs", “trees",“fruit") # give names > pie(feed.counts) # prints out names > pie(feed.counts,col=c("purple","green2","cyan","white")) # with colour

Histograms  Histograms are similar to the bar chart, but the bars are touching  The height can be the frequencies, or the proportions  In the latter case, the areas sum to 1 -- a property you should be familiar with, since you’ve already studied probability distributions  In either case the area is proportional to probability

Histograms  To draw a histogram, the hist() function is used  A nice addition to the histogram is to plot the points using the rug command  As you will see in the next example, it is used to give the tick marks just above the x-axis. If the data is discrete and has ties, then the rug(jitter(x)) command will give a little jitter to the x values to eliminate ties

Histograms Example: Suppose a lecturer recorded the number of hours that 15 students spent studying for their exams during one week Example: Suppose a lecturer recorded the number of hours that 15 students spent studying for their exams during one week Enter the data: > a=scan() 1: : Read 15 items

Histograms Draw a histogram: > hist(a) # frequencies > hist(a,probability=TRUE) # proportions (or probabilities) > rug(jitter(a)) # add tick marks NULL histogram of frequencies (default) preferred histogram of proportions (total area = 1) Note different y-axis

Histograms  The basic histogram has a predefined set of break points for the bins  You can, however, specify the number of breaks or break points Use: hist(a,breaks=3) or hist(a,3) Try it….

Boxplots  The boxplot is used to summarize data succinctly, quickly displaying whether the data is symmetric or has suspected outliers  Typical boxplot: Lower hinge/quartile Upper hinge/quartile Whiskers Median Upper extreme Lower extreme

Boxplots  To showcase possible outliers, a convention is adopted to shorten the whiskers to a length of 1.5 times the box length - any points beyond that, are plotted with points MinMaxOutliers  Thus, the boxplots allows us to check quickly for symmetry (the shape looks unbalanced) and outliers (lots of data points beyond the whiskers)  In the example we see a skewed distribution with a long tail

Boxplots  To draw boxplots, the boxplot function is used  As sample data, let’s get R to produces random numbers with a normal distribution: > z = rnorm(100)# generate random numbers > z# list numbers in z > z = rnorm(100)# generate random numbers > z# list numbers in z  Because the generated numbers are produced at random, each time you execute this command, different numbers will be produced

Boxplots  Now you draw a boxplot of the dataset (z, in this case)….  Use the boxplot command, in conjunction with various arguments  You must indicate the dataset name, but then you can also label the plot and orientate the plot  A notch function is useful to put a notch on the boxplot, at the median > boxplot(z,main="Horizonal z boxplot",horizontal=TRUE) > boxplot(z,main="Vertical z boxplot",vertical=TRUE) > boxplot(z,notch=T) > boxplot(z,main="Horizonal z boxplot",horizontal=TRUE) > boxplot(z,main="Vertical z boxplot",vertical=TRUE) > boxplot(z,notch=T)  What do you get, when you try it?

Boxplots A side-by-side boxplot to compare two treatments Data: experimental: control: > x = c(5, 5, 5, 13, 7, 11, 11, 9, 8, 9) > y = c(11, 8, 4, 5, 9, 5, 10, 5, 4, 10) > boxplot(x,y) Data: experimental: control: > x = c(5, 5, 5, 13, 7, 11, 11, 9, 8, 9) > y = c(11, 8, 4, 5, 9, 5, 10, 5, 4, 10) > boxplot(x,y)

Plotting  The functions plot(), points(), lines(), text(), mtext(), axis(), identify(), legend() etc. form a suite that plots points, lines, and text, gives fine control over axis ticks and labels, and adds a legend as specified  Change the default parameter settings -permanently using the par() function -only for the duration of the function call e.g., > plot(x, y, pch="+") # produces scatterplot using a + sign  Time restriction - but you should be aware of the power of R, and explore these options further

Scatter plots  The plot function will draw a scatter plot  Additional descriptions of the plot can be included  Using the data from the previous example, draw some scatter plots…. > plot(x) > plot(x,y) > plot(y,x) # change axis > plot(x,pch=c(2,4)) # print character > plot(x,col=c(2,4)) # adds colour > plot(x) > plot(x,y) > plot(y,x) # change axis > plot(x,pch=c(2,4)) # print character > plot(x,col=c(2,4)) # adds colour

Linear regression  Linear regression is the name of a procedure that fits a straight line to the data  Remember the equation of the line:y = b 0 + b 1 x  The abline(lm(y ~ x)) function will plot the points, find the values of b 0, b 1, and add a line to the graph  The lm function is that for a linear model  The funny syntax y ~ x tells R to model the y variable as a linear function of x