Difference between revisions of "R1"
Line 31: | Line 31: | ||
From the above example, we can see that both the '''<-''' and '''=''' operators can be used for assignment. | From the above example, we can see that both the '''<-''' and '''=''' operators can be used for assignment. | ||
+ | Vectors are commonly used data structures in R: | ||
+ | |||
+ | <source> | ||
+ | coords.bris <- c(51.5, 2.6) | ||
+ | </source> | ||
+ | |||
+ | As are matrices: | ||
+ | |||
+ | <source> | ||
+ | > magic <- matrix(data=c(2,7,6,9,5,1,4,3,8),nrow=3,ncol=3) | ||
+ | > magic | ||
+ | [,1] [,2] [,3] | ||
+ | [1,] 2 9 4 | ||
+ | [2,] 7 5 3 | ||
+ | [3,] 6 1 8 | ||
+ | </source> | ||
+ | |||
+ | We can access portions of the array using the syntax shown in the square brackets. For example, we can access the first row using the '''[1,]''' notation, and similarly the second column using '''[,2]'''. Since the square is 3x3 magic, the numbers in both slices should sum to 15: | ||
+ | |||
+ | <source> | ||
+ | > sum(magic[1,]) | ||
+ | [1] 15 | ||
+ | > sum(magic[,2]) | ||
+ | [1] 15 | ||
+ | </source> | ||
+ | |||
+ | Single elements and ranges can also accessed: | ||
+ | |||
+ | <source> | ||
+ | > magic[2,2] | ||
+ | [1] 5 | ||
+ | > magic[2:3,2:3] | ||
+ | [,1] [,2] | ||
+ | [1,] 5 3 | ||
+ | [2,] 1 8 | ||
+ | </source> | ||
=Graphics: A taster= | =Graphics: A taster= |
Revision as of 13:44, 21 June 2013
Open Source Statistics with R
Introduction
R is a mature, open-source (i.e. free!) statistics package, with an intuitive interface, excellent graphics and a vibrant community constantly adding new methods for the statistical investigation of your data to the library of packages available.
The goal of this tutorial is to introduce you to the R package, and not to be an introductory course in statistics.
Some excellent examples of using R can also be found at: http://msenux.redwoods.edu/math/R
Getting Started
The very simplest thing we can do with R is to perform some arithmetic at the command prompt:
> phi <- (1+sqrt(5))/2
> phi
[1] 1.618034
Parentheses are used to modify the usual order of precedence of the operators (/ will typically be evaluated before +). Note the [1] accompanying the returned value. All numbers entered at the console are interpreted as a vector. The '[1]' indicates that the line in question is displaying the vector of values starting at first index. We can use the handy sequence function to create a vector containing more than a single element:
> odds <- seq(from=1, to=67, by=2)
> odds
[1] 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
[26] 51 53 55 57 59 61 63 65 67
From the above example, we can see that both the <- and = operators can be used for assignment.
Vectors are commonly used data structures in R:
coords.bris <- c(51.5, 2.6)
As are matrices:
> magic <- matrix(data=c(2,7,6,9,5,1,4,3,8),nrow=3,ncol=3)
> magic
[,1] [,2] [,3]
[1,] 2 9 4
[2,] 7 5 3
[3,] 6 1 8
We can access portions of the array using the syntax shown in the square brackets. For example, we can access the first row using the [1,] notation, and similarly the second column using [,2]. Since the square is 3x3 magic, the numbers in both slices should sum to 15:
> sum(magic[1,])
[1] 15
> sum(magic[,2])
[1] 15
Single elements and ranges can also accessed:
> magic[2,2]
[1] 5
> magic[2:3,2:3]
[,1] [,2]
[1,] 5 3
[2,] 1 8
Graphics: A taster
R has some very handy built-in data sets. They allow us to, for example, very simply plot the carbon dioxide concentrations as observed from 1959 to 1997 high above Hawaii at the Mauna Loa observatory.
> plot(pressure)
> plot(co2)
> class(co2)
[1] "ts"
https://www.gov.uk/government/.../5942-uk-energy-in-brief-2012.pdf
> uk.electricty.sources.2011 <- c(41,29,18,5,4,2,1)
> names(uk.electricty.sources.2011) <- ("Gas", "Coal", "Nuclear", "Hydro & other", "Wind", "Imports", "Oil")
> pie(uk.electricty.sources.2011, main="UK Electricty Generating Mix, 2011", col=rainbow(7))
http://www.worldweatheronline.com
> bristol.precip <- c(82.9, 56.1, 59.2, 69, 50.8, 50.9, 50.8, 74.8, 74.7, 91.1, 94.5, 93.6)
> names(bristol.precip) <- c("Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec")
> barplot(bristol.precip,
+ main="Average Monthly Precipitation in Bristol",
+ ylab="Mean precipitation (mm)",
+ ylim=c(0,100),
+ col=c("darkblue"))
> boxplot(mpg~cyl,data=mtcars, main="Car Milage Data",
+ xlab="Number of Cylinders", ylab="Miles Per Gallon")
> ?filled.countour
Data Structures
Packages
Examples of Common Tasks
Linear Regression
> plot(cars)
> res=lm(dist ~ speed, data=cars)
> abline(res)
Exercise
- Weighted least squares. The lm function will accept a vector of weights, lm(... weights=...). If given, the function will optimise the line of best fit according a the equation of weighted least squares. Experiment with different linear model fits, given different weighting vectors. Some handy hints for creating a vector of weights:
- w1<-rep(0.1,50) will give you a vector, length 50, where each element has a value of 0.1. W1[1]<-10 will give the first element of the vector a value of 10.
- w2<-seq(from=0.02, to=1.0, by=0.02) provides a vector containing a sequence of values from 0.02 to 1.0 in steps of 0.02 (handily, again 50 in total).
Significance Testing
> boys_2=c(90.2, 91.4, 86.4, 87.6, 86.7, 88.1, 82.2, 83.8, 91, 87.4)
> girls_2=c(83.8, 86.2, 85.1, 88.6, 83, 88.9, 89.7, 81.3, 88.7, 88.4)
> res=var.test(boys_2,girls_2)
> res=t.test(boys_2, girls_2, var.equal=TRUE, paired=FALSE)