corrStable

Calculates the Pearson correlation coefficient:

$$\frac{\Sigma{(x - \bar{x})(y - \bar{y})}}{\sqrt{\Sigma{(x - \bar{x})^2} * \Sigma{(y - \bar{y})^2}}}$$

Similar to the corr function, but uses a numerically stable algorithm. As a result, corrStable is slower than corr but produces a more accurate result.

Syntax

corrStable(x, y)

Arguments

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

Returned Value

• The Pearson correlation coefficient. 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 corrStable(x_value, y_value)
FROM series;

Result:

┌─corrStable(x_value, y_value)─┐
│          0.17302657554532558 │
└──────────────────────────────┘