R Programming -- real-world data

Real-World Data

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So far, we've been working purely in the abstract. It's time to take a look at some real data, and see if we can make any observations about it.

Some Real World Data7.1

Modern pirates plunder software, not silver. We have a file with the software piracy rate, sorted by country. Here's a sample of its format:

Country,Piracy
Australia,23
Bangladesh,90
Brunei,67
China,77
...

We'll load that into the 

piracy

 data
frame for you:

> piracy <- read.csv("piracy.csv")

We also have another file with GDP per capita for each country (wealth produced, divided by population):

Rank    Country        GDP
1       Liechtenstein  141100
2       Qatar          104300
3       Luxembourg     81100
4       Bermuda        69900
...

4000
That will go into the 

gdp

 frame:

> gdp <- read.table("gdp.txt", sep="  ", header=TRUE)

We'll merge the frames on the country names:

> countries <- merge(x = gdp, y = piracy)

Let's do a plot of GDP versus piracy. Call the 

plot

 function,
using the 

"GDP"

 column
of 

countries

 for
the horizontal axis, and the 

"Piracy"

 column
for the vertical axis:

RedoComplete

> plot(countries$GDP,countries$Piracy)

02000040000600008000020406080countries$GDPcountries$Piracy

It looks like there's a negative correlation between wealth and piracy - generally, the higher a nation's GDP, the lower the percentage of software installed that's pirated. But do we have enough data to support this connection? Is there really a connection
at all?

R can test for correlation between two vectors with the cor.test function. Try calling it on the GDP and Piracy columns of the countries data frame:

RedoComplete

> cor.test(countries$GDP,countries$Piracy)

Pearson's product-moment correlation

data:  countries$GDP and countries$Piracy
t = -14.8371, df = 107, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.8736179 -0.7475690
sample estimates:
cor
-0.8203183

The key result we're interested in is the "p-value". Conventionally, any correlation with a p-value less than 0.05 is considered statistically significant, and this sample data's p-value is definitely below that threshold. In other words, yes, these data do
show a statistically significant negative correlation between GDP and software piracy.

We have more countries represented in our GDP data than we do our piracy rate data. If we know a country's GDP, can we use that to estimate its piracy rate?

We can, if we calculate the linear model that best represents all our data points (with a certain degree of error). The 

lm

 function
takes a model formula, which is represented by a response
variable (piracy rate), a tilde character (

~

),
and a predictor variable (GDP). (Note that the response variable comes first.)

Try calculating the linear model for piracy rate by GDP, and assign it to the 

line

 variable:

RedoComplete

> line <- lm(countries$Piracy ~ countries$GDP)

You can draw the line on the plot by passing it to the abline function. Try it now:

RedoComplete

> abline(line)

Now, if we know a country's GDP, we should be able to make a reasonable prediction of how common piracy is there!

02000040000600008000020406080countries$GDPcountries$Piracy

ggplot27.2

The functionality we've shown you so far is all included with R by default. (And it's pretty powerful, isn't it?) But in case the default installation doesn't include that function you need, there are still more libraries available on the servers of the Comprehensive
R Archive Network, or CRAN. They can add anything from new statistical functions to better graphics capabilities. Better yet, installing any of them is just a command away.

Let's install the popular 

ggplot2

 graphics
package. Call the 

install.packages

 function
with the package name in a string:

RedoComplete

> install.packages("ggplot2")

c381

You can get help for a package by calling the help function and passing the package name in the package argument. Try displaying help for the "ggplot2" package:

RedoComplete

> help(package = "ggplot2")
Information on package 'ggplot2'

Description:

Package:            ggplot2
Type:               Package
Title:              An implementation of the Grammar of Graphics
Version:            0.9.1

...

Here's a quick demo of the power you've just added to R. To use it, let's revisit some data from a previous chapter.

> weights <- c(300, 200, 100, 250, 150)
> prices <- c(9000, 5000, 12000, 7500, 18000)
> chests <- c('gold', 'silver', 'gems', 'gold', 'gems')
> types <- factor(chests)

The qplot function is a commonly-used part of ggplot2. We'll pass the weights and values of our cargo to it, using the chest types vector for the color argument:

RedoComplete

> qplot(weights, prices, color = types)

Not bad! An attractive grid background and colorful legend, without any of the configuration hassle from before!

ggplot2

 is
just the first of many powerful packages awaiting discovery on CRAN. And of course, there's much, much more functionality in the standard R libraries. This course has only scratched the surface!

80001200016000100150200250300..1..2..3gemsgoldsilver

Chapter 7 Completed

Share your plunder:

Captain's Log: The end of chapter 7. Supplies are running low. Luckily, we've spotted another badge!

We've covered how to take some real-world data sets, and test whether they're correlated with `cor.test`. Then we learned how to show that correlation on plots, with a linear model.

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