The functions in this section take two arguments, which must be vectors of equal size. The vectors are each flattened in the same way as by the single-variable statistical functions. Given a numeric prefix argument of 1, these functions instead take one object from the stack, which must be an Nx2 matrix of data values. Once again, variable names can be used in place of actual vectors and matrices.
The u
C (calc-vector-covariance) [vcov]
command computes the sample covariance of two vectors. The
covariance of vectors x and y is the sum of
the products of the differences between the elements of
x and the mean of x times the differences
between the corresponding elements of y and the mean
of y, all divided by ‘N-1’. Note that the variance of a
vector is just the covariance of the vector with itself. Once
again, if the inputs are error forms the errors are used as
weight factors. If both x and y are
composed of error forms, the error for a given data point is
taken as the square root of the sum of the squares of the two
input errors.
The I u C
(calc-vector-pop-covariance) [vpcov]
command computes the population covariance, which is the same as
the sample covariance computed by u C except dividing
by ‘N’ instead
of ‘N-1’.
The H u C
(calc-vector-correlation) [vcorr]
command computes the linear correlation coefficient of two
vectors. This is defined by the covariance of the vectors divided
by the product of their standard deviations. (There is no
difference between sample or population statistics here.)