Updated: 31 Oct 2012

Use the RunningRSQ function to calculate the square of the Pearson product moment correlation coefficient through data points in y- and x-values within a resultant table or partition, without the need for a self-join. The correlation coefficient 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.

SELECT [Example].[wct].[RunningRSQ](

<@Y, float,>

,<@X, float,>

,<@RowNum, int,>

,<@Id, tinyint,>)

GO

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**.

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**.

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**.

a unique identifier for the RunningRSQ calculation. *@Id* allows you to specify multiple RunningRSQ calculations within a resultant table. *@Id* is an expression of type **tinyint** or of a type that can be implicitly converted to **tinyint**.

· If *@Id* is NULL then *@Id* = 0.

· *@RowNum* must be in ascending order.

· To calculate the square of the correlation coefficient over a window of x- and y-values use the MovingRSQ function.

· If *@RowNum* = 1 then RunningRSQ is NULL.

· To calculated a single square of the correlation coefficient value for a set of x- and y-values, use the RSQ 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.

In this example we will calculate the square of the correlation coefficient in the relationship 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 RSQ

SELECT rn

,id_lot

,amt_sqft

,amt_price

,wct.RunningRSQ(amt_price,amt_sqft,ROW_NUMBER() OVER (ORDER BY rn),NULL) as RSQ

FROM #se

--Clean up

DROP TABLE #se

This produces the following result.

rn id_lot amt_sqft amt_price RSQ

----------- ----------- ----------- ----------- ----------------------

1 21783 1147 393918 NULL

2 94729 1313 470479 1

3 33028 1433 512474 0.994508459443581

4 59446 1724 610477 0.993395382191858

5 97646 1162 388196 0.988456339599465

6 44823 1813 636916 0.991135178527575

7 88397 1105 374348 0.992548648834574

8 13588 1555 559149 0.991549672349918

9 13891 1775 623900 0.992331371968798

10 90957 1585 563947 0.992357626842498

11 44167 1510 529806 0.992343210114028

12 75533 1628 592533 0.990249419721381

13 56812 1145 408634 0.98989235167382

14 12897 1632 589522 0.989566123744144

15 93826 1850 668852 0.990925385225506

16 74510 1867 633400 0.984082874500432

17 17262 1587 552178 0.98361449791164

18 30929 1809 633141 0.984148573328568

19 49030 1521 555713 0.981801120674846

20 33431 1195 434542 0.981670150999315