If you have two or more data samples with an equal number of
elements, you can estimate how similar these data samples are. The
most common measures of similarity of two data samples are the covariance
and the correlation. MuPAD^{®} provides the following functions for
computing the covariance and the correlation of two data samples:

The

`stats::covariance`

function calculates the covariance. Here is the arithmetic average of the data sample

*x*_{1},*x*_{2},*...*,*x*_{n}, and is the arithmetic average of the data sample*y*_{1},*y*_{2},*...*,*y*_{n}.The

`stats::correlation`

function calculates the linear (Bravais-Pearson) correlation coefficient. Here is the arithmetic average of the data sample

*x*_{1},*x*_{2},*...*,*x*_{n}, and is the arithmetic average of the data sample*y*_{1},*y*_{2},*...*,*y*_{n}.

Create the lists `x`

and `y`

:

x := [1, 1, 0.1]: y := [1, 2, 0.1]:

To estimate the similarity of these lists, compute their covariance.
For completely uncorrelated (nonsimilar) data, the covariance is a
small value. A positive covariance indicates that the data change
in the same direction (increases or decreases together). A negative
covariance indicates the data change in opposite directions. There
are two common definitions of the covariance. By default, the `stats::covariance`

function
uses the definition with the divisor `n - 1`

. To
switch to the alternative definition, use the `Population`

option:

stats::covariance(x, y), stats::covariance(x, y, Population)

The covariance of a data sample with itself is the variance of that data sample:

stats::covariance(x, x) = stats::variance(x)

The correlation of data samples indicates the degree of similarity
of these data samples. For completely uncorrelated data, the value
of the correlation (as well as the covariance) tends to 0. For correlated
data that change in the same direction, the correlation tends to 1.
For correlated data that change in the opposite directions, the correlation
tends to -1. Compute the correlation of `x`

and `y`

:

stats::correlation(x, y), stats::correlation(x, x), stats::correlation(x, -x)

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