Scatter plots are simple but yetvery powerful presentations oftwo variables and how they are related.Two sets of random variables containthe coordinates of the samplepoints.

R-Code: plot() arguments:

pch=3 tells plot() to use ‘+’ as symbol cex=0.3 scales the size of the symbol

+x2(k)=0.32

x1(k)=0.65

R has built-in random number generators:Samples can be drawn using functionsUniform distribution: runif()Gaussian distribution: rnorm()

Samples drawn from uniform distributions

Scatter plots are simple but yetvery powerful presentations oftwo variables and how they are related.Two sets of random variables containthe coordinates of the samplepoints.

R-Code: plot() arguments:

pch=3 tells plot() to use ‘+’ as symbol cex=0.3 scales the size of the symbol

Samples drawn from Gaussian distributions

Albany monthly mean temperature anomalies and New York Central Parktemperature anomalies 1950-2010

Albany NY Central Park

Whenever two variables are sampled along a ‘physically meaningful’ dimensionsuch as time, repeated controlled experiments, or geographic coordinates, we candefine pairs of data. These pairs form a 2-dimensional coordinate system => Scatter diagram.

Albany monthly mean temperature anomalies and New York Central Parktemperature anomalies 1950-2010

R-Code:x is a vector with Albany temperature anomaliesy is a vector with Central Park temp. anomalies.Elements in the vectors x, y at position k share the same time coordinate and form a data pair.Plotting a point symbol ‘+’ requires 2 coordinates:The x-coordinates comes from vector xThe y-coordiantes comes from vector y

Regression lines are the simplest functionsthat we can try to fit with the data. In this example the relationship between the twotemperature time series is obviously linearand can be well fitted by a linear regressionline. R-Code:x is a vector with Albany temperature anomaliesy is a vector with Central Park temp. anomalies.

The function lm( y ~ x ) {lm short name for ‘linear model’} is used for ‘Ordinary Least Squares Regression Analysis’

Vectors in R:

y<-c(x1,x2,x3,…xn)

R-Code:

Another common notation for vector dot products

Another common notation for vector dot products

Equivalent to the R notation as seen in graph:

abs( mean(x1) – mean(x2) )/ sqrt ( sd(x1) * sd(x2) )

In this example mean(x1) = -1 and mean(x2) = +1; sd(x1) = 1 and sd(x2) = 1 The equation gives a value of 2. That is the difference is 2 times the length ofthe (geometrically averaged) samples standard deviations.

With the function par() we can manipulateThe plot appearance in many ways (see help(par))The function is usually called at the begin of a script, or Right before a plotting function.For example to split the plot window into a 2x2 panel of

subfigures:

par(mfrow=c(2,2))

NOTE: You must call par(mfrow=c(1,1)) again to get the single-figure mode back.