This tutorial is a bit of a grab-bag. The first part shows you how to calculate the remaining summary statistics from the lectures and introduces a few new plotting commands. The second part describes one of the most fundamental parts of R: creating your own functions. Finally, the third part shows you how to import stock return data in R and introduces some related concepts and tools. Rather than appearing at the end, six exercises are scattered throughout the parts of this tutorial.

More Summary Statistics

First we’ll load the survey data from R Tutorial #2.

Like before we’ll only need a subset of the columns available; rather than go to the hassle of deleting these columns afterwards, we can specify which columns to keep simultaneously with reading in the data using the select argument to fread. (There is also a drop argument for the reverse – specifying columns to exclude)

library(data.table)
survey = fread("http://www.ditraglia.com/econ103/old_survey.csv",
               select = c("handedness", "height", "handspan"))

Correlation: cor

This command calculates sample correlation coefficients. If you pass it two vectors of the same length it returns the correlation between them. If you feed it a data.table or matrix it returns a matrix containing all pairwise correlations between the columns (we haven’t covered matrices in R since you’ll only need to interpret them as output for this class – for a primer on handling matrix objects, see here). Unlike the univariate summary statistics, in which we used na.rm = TRUE to ignore missing observations, for cor we use the argument use = "complete.obs". The reason for this difference is that cor can handle a matrix or data.table as its input. In this case there are actually many different ways of handling missing observations. For more details, see ?cor. Setting use = "complete.obs" removes any rows with missing observations before proceeding.

survey[ , cor(handspan, height, use = "complete.obs")]
## [1] 0.6042423

Of course, we could use the approach we saw in R Tutorial #2 as well; whichever feels more natural:

survey[!is.na(handspan) & !is.na(height), cor(handspan, height)]
## [1] 0.6042423

We can also feed the full data.table to cor like so:

cor(survey, use = "complete.obs")
##             handedness    height    handspan
## handedness  1.00000000 0.1125605 -0.01719909
## height      0.11256055 1.0000000  0.60942759
## handspan   -0.01719909 0.6094276  1.00000000
#alternatively, there's the na.omit
#  function, which does just what it says:
cor(na.omit(survey))
##             handedness    height    handspan
## handedness  1.00000000 0.1125605 -0.01719909
## height      0.11256055 1.0000000  0.60942759
## handspan   -0.01719909 0.6094276  1.00000000

We see that there is a large positive correlation between height and handspan and a slight positive correlation between height and handedness. There’s basically no correlation between handedness and handspan. The preceding matrix has ones on its main diagonal since the correlation between any variable and itself is identically one. (A good exercise for extra practice would be to prove this assertion using the formula for correlation from class. It’s not very difficult.)

If you look carefully, you’ll notice that the correlation between height and handspan is slightly different when calculated at the same time as all the other correlations. This is because of the way that use = "complete.obs" drops rows. In this case, it indicates that there is at least one observation in our dataset for which we have height and handspan but not handedness.

For practice, we can find this with judicious use of is.na and logical operators:

survey[is.na(handedness) & !is.na(height) & !is.na(handspan)]
##    handedness height handspan
## 1:         NA     70     19.5

Covariance: cov

This command works just like cor but returns covariances rather than correlations:

survey[ , cov(handspan, height, use = "complete.obs")]
## [1] 5.910786
cov(survey, use = "complete.obs")
##            handedness    height   handspan
## handedness  0.1685042  0.206959 -0.0155499
## height      0.2069590 20.062517  6.0121751
## handspan   -0.0155499  6.012175  4.8510260
cov(na.omit(survey))
##            handedness    height   handspan
## handedness  0.1685042  0.206959 -0.0155499
## height      0.2069590 20.062517  6.0121751
## handspan   -0.0155499  6.012175  4.8510260

Regression: lm and abline

This command stands for “_l_inear _m_odel" and is R’s general-purpose regression command. Its syntax is similar to that of boxplot from R Tutorial #2 in that we use a tilde (~) to indicate a functional relationship. Here the variable to the left of the tilde is the “y” variable, while the variable to the right is the “x” variable.

survey[ , lm(height ~ handspan)]
## 
## Call:
## lm(formula = height ~ handspan)
## 
## Coefficients:
## (Intercept)     handspan  
##      42.251        1.229

Remember: unlike correlation and covariance, regression is not symmetric:

survey[ , lm(handspan ~ height)]
## 
## Call:
## lm(formula = handspan ~ height)
## 
## Coefficients:
## (Intercept)       height  
##      0.5305       0.2970

It turns out that we can use the same syntax with the command plot:

survey[ , plot(handspan ~ height)]

To add the regression line, we follow the plot command with the function abline like so:

survey[ , plot(handspan ~ height)]
survey[ , abline(lm(handspan ~ height))]

Note that abline can only be used after you’ve already made a plot. It adds a line to the existing plot rather than making a plot of its own.

You can also use abline to plot different kinds of lines. For example, we can show that the regression line goes through the means of the data as follows:

survey[ , {
  plot(handspan ~ height)
  abline(lm(handspan ~ height))
  abline(v = mean(height, na.rm = TRUE),
         h = mean(handspan, na.rm = TRUE),
         col = 'red', lty = 2)
}]