Statistics and Data Analysis for Microarrays Using R and Bioconductor, 2nd Edition

Elements of statist ics 227

−3 −2 −1 0 1 2 3

−30 −20 −10 0 10 20 30

x

y

−3 −2 −1 0 1 2 3

−30 −20 −10 0 10 20 30

x

z

FIGURE 8.8: The correlation does not provide any information about the

slope of the linear dependency (if such a linear dependency exists). In the left

panel, y = 0.01 · x. In the right pa nel, z = 10 · x. The correlation between

the variables x and y (left panel) is the same as the correlation between the

variables x and z (right panel) cor(x, y) = cor(x, z) = 1.

coefficient, they may or may not be independent. In other words, a high cor-

relation coefficient is not a necessary condition for variable dependency.

Another observation is that the