covarPop

Calculates the population covariance:

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

Note

This function uses a numerically unstable algorithm. If you need numerical stability in calculations, use the covarPopStable function. It works slower but provides a lower computational error.

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 covarPop(x_value, y_value)
FROM series;

Result:

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

covarPop

Introduced in: v1.1

Calculates the population covariance:

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

Note

This function uses a numerically unstable algorithm. If you need numerical stability in calculations, use the covarPopStable function. It works slower but provides a lower computational error.

Syntax

covarPop(x, y)

Aliases: COVAR_POP

Arguments

x — First variable. (U)Int* or Float* or Decimal
y — Second variable. (U)Int* or Float* or Decimal

Returned value

Returns the population covariance between x and y. Float64

Examples

Basic population covariance calculation

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 covarPop(x_value, y_value)
FROM series

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

covarPop​

covarPop