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XLeratorDB/statistics Documentation

SQL Server PEARSON function


PEARSON

Updated: 30 September 2010

Note: This documentation is for the SQL2008 (and later) version of this XLeratorDB function, it is not compatible with SQL Server 2005.
Click here for the SQL2005 version of the PEARSON function


Use the multi-input aggregate PEARSON function to calculate the correlation coefficient between two datasets. The equation for the correlation coefficient is
 
PEARSON function for SQL Server 
Syntax
SELECT [wctStatistics].[wct].[PEARSON] (
 ,<@Known_y, float,>
 ,<@Known_x, float,>)
Arguments
 
@Known_y
the y-values to be used in the PEARSON calculation. @Known_y is an expression of type float or of a type that can be implicitly converted to float.
@Known_x
the x-values to be used in the PEARSON calculation. @Known_x is an expression of type float or of a type that can be implicitly converted to float.
Return Types
float
Remarks
·         PEARSON is an AGGREGATE function and follows the same conventions as all other AGGREGATE functions in SQL Server.
Examples
In this example, we calculate the Pearson coefficient as correlation for a single set of x- and y-values
SELECT wct.PEARSON(y, x) as PEARSON
FROM (
      SELECT 0.75, 1 UNION ALL
      SELECT 2.5, 2 UNION ALL
      SELECT 6.75, 3 UNION ALL
      SELECT 10, 4
      ) n(x,y)
 
This produces the following result
PEARSON
----------------------
0.988719187867937
 
(1 row(s) affected)
In this example, we will populate some temporary table with some historical financial information and then calculate the Pearson coefficient of correlation. First, create the table and put some data in it:
CREATE TABLE #c(
      SYM         NVARCHAR(5),
      YE          BIGINT,
      REV         FLOAT,
      GPROF       FLOAT,
      OPINC       FLOAT,
      NETINC      FLOAT
      )
     
INSERT INTO #c VALUES('YHOO',2009,6460.32,3588.57,386.69,597.99)
INSERT INTO #c VALUES('YHOO',20,72.5,4185.14,12.96,418.92)
INSERT INTO #c VALUES('YHOO',2007,6969.27,4130.52,695.41,639.16)
INSERT INTO #c VALUES('YHOO',2006,6425.68,3749.96,940.97,751.39)
INSERT INTO #c VALUES('YHOO',2005,5257.67,3161.47,1107.73,1896.23)
INSERT INTO #c VALUES('GOOG',2009,23650.56,14806.45,8312.19,6520.45)
INSERT INTO #c VALUES('GOOG',20,21795.55,13174.04,5537.21,4226.86)
INSERT INTO #c VALUES('GOOG',2007,16593.99,9944.9,54.44,4203.72)
INSERT INTO #c VALUES('GOOG',2006,10604.92,6379.89,3550,3077.45)
INSERT INTO #c VALUES('GOOG',2005,6138.56,3561.47,2017.28,1465.4)
INSERT INTO #c VALUES('MSFT',2010,62484,509,24167,18760)
INSERT INTO #c VALUES('MSFT',2009,58437,46282,21225,14569)
INSERT INTO #c VALUES('MSFT',20,60420,48822,22271,17681)
INSERT INTO #c VALUES('MSFT',2007,51122,40429,18438,14065)
INSERT INTO #c VALUES('MSFT',2006,44282,36632,16064,12599)
INSERT INTO #c VALUES('ORCL',2010,26820,21056,9062,6135)
INSERT INTO #c VALUES('ORCL',2009,23252,18458,8321,5593)
INSERT INTO #c VALUES('ORCL',20,22430,17449,7844,5521)
INSERT INTO #c VALUES('ORCL',2007,17996,13805,5974,4274)
INSERT INTO #c VALUES('ORCL',2006,14380,11145,4736,3381)
INSERT INTO #c VALUES('SAP',2009,10672,6980,2588,1748)
INSERT INTO #c VALUES('SAP',20,11575,7370,2701,1847)
INSERT INTO #c VALUES('SAP',2007,10256,6631,2698,1906)
INSERT INTO #c VALUES('SAP',2006,9393,6064,2578,1871)
INSERT INTO #c VALUES('SAP',2005,8509,5460,2337,1496)
Now, calculate the correlation of the revenue (REV) againt the year (YE) for each company (SYM)
SELECT #c.SYM
,wct.PEARSON(REV,YE) as PEARSON
FROM #c
GROUP BY SYM
This produces the following result.
SYM   PEARSON
----- ----------------------
GOOG 0.988604792733014
MSFT 0.91861026921264
ORCL 0.983795721235544
SAP   0.873067973316442
YHOO 0.669694544702289
 
(5 row(s) affected)
In this example, we will calculate the Pearson coefficient of correlation of the operating income (OPINC) against the revenue (REV)
SELECT #c.SYM
,wct.PEARSON(OPINC,REV) as PEARSON
FROM #c
GROUP BY SYM
 
This produces the following result.
SYM   PEARSON
----- ----------------------
GOOG 0.941767754970464
MSFT 0.987612258172035
ORCL 0.9924157389967
SAP   0.844595495520328
YHOO -0.767769278048799
 
(5 row(s) affected)
Let’s say we wanted to perform the same analysis as above, but we only want to return the results where the Pearson coefficient of correlation is positive.
SELECT #c.SYM
,wct.PEARSON(OPINC,REV) as PEARSON
FROM #c
GROUP BY SYM
HAVING wct.PEARSON(OPINC,REV) > 0
 
This produces the following result.
SYM   PEARSON
----- ----------------------
GOOG 0.941767754970464
MSFT 0.987612258172035
ORCL 0.9924157389967
SAP  0.844595495520328
 

(4 row(s) affected)



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