statistics: covariance() Stays Silent on Constant Input (tested)

statistics.covariance(), correlation(), and linear_regression() are closely related -- all three take two equal-length data series and describe how they move together. We measured what each one does when one of the series is constant (zero variance), and the three functions don't agree at all.

1. covariance() returns 0.0 silently; correlation() raises StatisticsError

import statistics as st

x = [1, 1, 1, 1]
y = [1, 2, 3, 4]

print(st.covariance(x, y))

try:
    st.correlation(x, y)
except st.StatisticsError as e:
    print("correlation raised:", e)

0.0
correlation raised: at least one of the inputs is constant

Measured: with x constant, covariance(x, y) returns 0.0 -- mathematically correct, since a constant has zero variance and therefore zero covariance with anything -- but gives no indication that the result is a degenerate edge case rather than "genuinely no relationship." correlation(x, y) on the exact same data raises StatisticsError instead, because computing the correlation coefficient requires dividing by each series' standard deviation, and dividing by zero is undefined.

2. linear_regression() also raises, with a different message

import statistics as st

x = [1, 1, 1, 1]
y = [1, 2, 3, 4]

try:
    st.linear_regression(x, y)
except st.StatisticsError as e:
    print("linear_regression raised:", e)

linear_regression raised: x is constant

Measured: linear_regression(x, y) also raises StatisticsError on the same constant x -- fitting a line needs a slope, and a constant x makes the slope undefined (division by zero variance again) -- but with yet a third distinct message ("x is constant" vs. correlation's "at least one of the inputs is constant"), so code catching one function's exact text won't reliably catch the other's.

3. Swapping which series is constant doesn't change the pattern

import statistics as st

both_constant = (st.covariance([5, 5, 5], [5, 5, 5]))
print(both_constant)

try:
    st.correlation([5, 5, 5], [5, 5, 5])
except st.StatisticsError as e:
    print("correlation raised:", e)

0.0
correlation raised: at least one of the inputs is constant

Measured: even with both series constant, covariance() still returns 0.0 with no error at all, while correlation() still raises. A pipeline that calls covariance() on a batch of sensor readings that occasionally includes a flat (unchanging) channel will get a silent 0.0 for that channel instead of a signal that the input was degenerate -- but the same pipeline calling correlation() on that channel would crash and reveal the problem immediately. Catching StatisticsError around correlation() or linear_regression() won't protect a nearby covariance() call from the same underlying issue, since it never raises.

Written with AI assistance. Measured on 2026-10-04 with Python 3.13.5's built-in statistics module: called covariance(), correlation(), and linear_regression() with the same constant-valued input and compared behavior. PlainHeaders is our extension; Python's statistics module is built in.