CORR_WELFORD

Description

Calculates the Pearson correlation coefficient between two random variables using the Welford algorithm, which effectively reduces calculation errors.

Syntax

CORR_WELFORD(<expr1>, <expr2>)

Parameters

Parameters	Description
<expr1>	Double expression (column)
<expr2>	Double expression (column)

Return Value

Returns a DOUBLE type value, which is the covariance of expr1 and expr2 divided by the product of their standard deviations. Special cases:

• If the standard deviation of expr1 or expr2 is 0, returns 0.
• If expr1 or expr2 contains NULL values, those rows are excluded from the final result.
• If the group has no valid data, returns NULL.

Example

-- setup
create table test_corr(
    id int,
    k1 double,
    k2 double
) distributed by hash (id) buckets 1
properties ("replication_num"="1");

insert into test_corr values 
    (1, 20, 22),
    (1, 10, 20),
    (2, 36, 21),
    (2, 30, 22),
    (2, 25, 20),
    (3, 25, NULL),
    (4, 25, 21),
    (4, 25, 22),
    (4, 25, 20);

select * from test_corr order by id, k1, k2;

+------+------+------+
| id   | k1   | k2   |
+------+------+------+
|    1 |   10 |   20 |
|    1 |   20 |   22 |
|    2 |   25 |   20 |
|    2 |   30 |   22 |
|    2 |   36 |   21 |
|    3 |   25 | NULL |
|    4 |   25 |   20 |
|    4 |   25 |   21 |
|    4 |   25 |   22 |
+------+------+------+

select id, corr_welford(k1, k2) from test_corr group by id order by id;

+------+----------------------+
| id   | corr_welford(k1, k2) |
+------+----------------------+
|    1 |                    1 |
|    2 |   0.4539206495016017 |
|    3 |                 NULL |
|    4 |                    0 |
+------+----------------------+

When the group contains no valid (k1, k2) pairs (here, no rows match id = 999), the aggregate returns NULL.

select corr_welford(k1, k2) from test_corr where id = 999;

+----------------------+
| corr_welford(k1, k2) |
+----------------------+
|                 NULL |
+----------------------+