The covariance of two variables x and y in a data set measures how the two are linearly related. A positive covariance would indicate a positive linear relationship between the variables, and a negative covariance would indicate the opposite.
The sample covariance is defined in terms of the sample means as:
Similarly, the population covariance is defined in terms of the population mean μx, μy as:
Find the covariance of eruption duration and waiting time in the data set faithful. Observe if there is any linear relationship between the two variables.
We apply the cov function to compute the covariance of eruptions and waiting.
> waiting = faithful$waiting # the waiting period
> cov(duration, waiting) # apply the cov function
The covariance of eruption duration and waiting time is about 14. It indicates a positive linear relationship between the two variables.