RunningCOVAR
Updated: 31 Oct 2012
Use the RunningCOVAR function to calculate the covariance through data points in y- and x-values within a resultant table or partition, without the need for a self-join. The covariance is calculated from the first row of the resultant table or partition through to the current row. If the column values are presented to the functions out of order, an error message will be generated.
Syntax
SELECT [Example].[wct].[RunningCOVAR](
<@Y, float,>
,<@X, float,>
,<@RowNum, int,>
,<@Id, tinyint,>)
GO
Arguments
@Y
the y-value passed into the function. @Y is an expression of type float or of a type that can be implicitly converted to float.
@X
the x-value passed into the function. @X is an expression of type float or of a type that can be implicitly converted to float.
@RowNum
the number of the row within the group for which the sum is being calculated. If @RowNum for the current row in a set is less than or equal to the previous @RowNum and @RowNum is not equal to 1, an error message will be generated. @RowNum is an expression of type int or of a type that can be implicitly converted to int.
@Id
a unique identifier for the RunningCOVAR calculation. @Id allows you to specify multiple RunningCOVAR calculations within a resultant table. @Id is an expression of type tinyint or of a type that can be implicitly converted to tinyint.
Remarks
· If @Id is NULL then @Id = 0.
· @RowNum must be in ascending order.
· To calculate the covariance over a window of x- and y-values use the MovingCOVAR function.
· If @RowNum = 1 then RunningCOVAR is NULL.
· To calculate a single covariance value for an entire set of data use the COVAR function.
· There may be cases where the order in which the data are returned to the function and the order in which the results are returned are different, generally due to parallelism. You can use OPTION(MAXDOP 1) or OPTION(MAXDOP 1,FORCE ORDER) to help eliminate this problem.
Example
In this example we will calculate the covariance between square footage and house prices. We will create a temporary table, #se, populate it with some data and then run the SELECT.
SET NOCOUNT ON
--Create the temporary table
CREATE TABLE #se(
rn int,
id_lot int,
amt_sqft int,
amt_price int,
PRIMARY KEY (rn)
)
--Put some date in the table
INSERT INTO #se VALUES (1,21783,1147,393918)
INSERT INTO #se VALUES (2,94729,1313,470479)
INSERT INTO #se VALUES (3,33028,1433,512474)
INSERT INTO #se VALUES (4,59446,1724,610477)
INSERT INTO #se VALUES (5,97646,1162,388196)
INSERT INTO #se VALUES (6,44823,1813,636916)
INSERT INTO #se VALUES (7,88397,1105,374348)
INSERT INTO #se VALUES (8,13588,1555,559149)
INSERT INTO #se VALUES (9,13891,1775,623900)
INSERT INTO #se VALUES (10,90957,1585,563947)
INSERT INTO #se VALUES (11,44167,1510,529806)
INSERT INTO #se VALUES (12,75533,1628,592533)
INSERT INTO #se VALUES (13,56812,1145,408634)
INSERT INTO #se VALUES (14,12897,1632,589522)
INSERT INTO #se VALUES (15,93826,1850,668852)
INSERT INTO #se VALUES (16,74510,1867,633400)
INSERT INTO #se VALUES (17,17262,1587,552178)
INSERT INTO #se VALUES (18,30929,1809,633141)
INSERT INTO #se VALUES (19,49030,1521,555713)
INSERT INTO #se VALUES (20,33431,1195,434542)
--Calculate CORREL
SELECT rn
,id_lot
,amt_sqft
,amt_price
,wct.RunningCORREL(amt_price,amt_sqft,ROW_NUMBER() OVER (ORDER BY rn),NULL) as CORREL
FROM #se
--Clean up
DROP TABLE #se
This produces the following result.
rn id_lot amt_sqft amt_price COVAR
----------- ----------- ----------- ----------- ----------------------
1 21783 1147 393918 0
2 94729 1313 470479 3177281.5
3 33028 1433 512474 5739504.66666667
4 59446 1724 610477 16416758.5
5 97646 1162 388196 17344331.96
6 44823 1813 636916 24728367.1666667
7 88397 1105 374348 26310103.3673469
8 13588 1555 559149 24419454.6875
9 13891 1775 623900 26461392.382716
10 90957 1585 563947 24510824.82
11 44167 1510 529806 22348813.4132231
12 75533 1628 592533 21449604.125
13 56812 1145 408634 22474025.7751479
14 12897 1632 589522 21778746.0255102
15 93826 1850 668852 23925253.9466667
16 74510 1867 633400 24742460.515625
17 17262 1587 552178 23356114.4290657
18 30929 1809 633141 23537179.2222222
19 49030 1521 555713 22287858.2216066
20 33431 1195 434542 22907483.2