def cov(xdata, ydata):
"""Return the sample covariance between (x, y) data.
>>> cov([(0.1, 2.3), (0.5, 2.7), (1.2, 3.1), (1.7, 2.9)])
... #doctest: +ELLIPSIS
0.201666666666...
>>> cov([0.75, 1.5, 2.5, 2.75, 2.75], [0.25, 1.1, 2.8, 2.95, 3.25])
... #doctest: +ELLIPSIS
1.1675
>>> cov([(0.1, 2.3), (0.5, 2.7), (1.2, 3.1), (1.7, 2.9)])
... #doctest: +ELLIPSIS
0.201666666666...
Covariance reduces down to standard variance when applied to the same
data as both the x and y values:
>>> data = [1.2, 0.75, 1.5, 2.45, 1.75]
>>> cov(data, data) #doctest: +ELLIPSIS
0.40325000000...
>>> stats.variance(data) #doctest: +ELLIPSIS
0.40325000000...
"""
n, s = _sum_prod_deviations(zip(xdata, ydata), None, None)
if n > 1:
return s/(n-1)
else:
raise StatsError('sample covariance requires at least two points')
def pcov(xdata, ydata=None):
"""Return the population covariance between (x, y) data.
>>> pcov([0.75, 1.5, 2.5, 2.75, 2.75], [0.25, 1.1, 2.8, 2.95, 3.25])
... #doctest: +ELLIPSIS
0.93399999999...
>>> pcov([(0.1, 2.3), (0.5, 2.7), (1.2, 3.1), (1.7, 2.9)])
0.15125
"""
n, s = _sum_prod_deviations(zip(xdata, ydata), None, None)
if n > 0:
return s/n
else:
raise StatsError('population covariance requires at least one point')