ClickHouse/docs/en/sql-reference/aggregate-functions/reference/covarpopstable.md

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covarPopStable

Calculates the value of the population covariance:

\frac{\Sigma{(x - \bar{x})(y - \bar{y})}}{n}

It is similar to the covarPop function, but uses a numerically stable algorithm. As a result, covarPopStable is slower than covarPop but produces a more accurate result.

Syntax

covarPop(x, y)

Arguments

• x — first variable. (U)Int*, Float*, Decimal.
• y — second variable. (U)Int*, Float*, Decimal.

Returned Value

• The population covariance between x and y. Float64.

Example

Query:

DROP TABLE IF EXISTS series;
CREATE TABLE series(i UInt32, x_value Float64, y_value Float64) ENGINE = Memory;
INSERT INTO series(i, x_value, y_value) VALUES (1, 5.6,-4.4),(2, -9.6,3),(3, -1.3,-4),(4, 5.3,9.7),(5, 4.4,0.037),(6, -8.6,-7.8),(7, 5.1,9.3),(8, 7.9,-3.6),(9, -8.2,0.62),(10, -3,7.3);

SELECT covarPopStable(x_value, y_value)
FROM
(
    SELECT
        x_value,
        y_value
    FROM series
);

Result:

┌─covarPopStable(x_value, y_value)─┐
│                         6.485648 │
└──────────────────────────────────┘