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XLeratorDB/statistics Documentation

RSQ


RSQ

Updated: 15 January 2011


Use the aggregate RSQ function to return the Pearson product moment correlation coefficient through data points in known-y’s and known-x’s. The r-squared value can be interpreted as the proportion of the variance in y attributable to the variance in x. The equation for the Pearson product moment correlation coefficient is:

RSQ function for SQL Server
 
 
RSQ returns r2, which is the square of this correlation coefficient
Syntax
SELECT [wctStatistics].[wct].[RSQ] (
   <@fmtRSQ, nvarchar(4000),>)
 
The syntax has changed as of release 1.07 and the function has changed from a scalar to an aggregate. Please make the appropriate changes when you upgrade to 1.07.
Arguments
 
@fmtRSQ
An nvarchar string formatted by the fmtRSQ function containing the known-y and known-x values to be used by the RSQ calculation.
Return Types
float
Remarks
·         RSQ is an AGGREGATE function and follows the same conventions as all other AGGREGATE functions in SQL Server.
·         RSQ is a one-pass solution. For a two-pass solution use the scalar RSQ_q function.
Examples
In this example, we calculate the RSQ coefficient as correlation for a single set of x- and y-values
SELECT wct.RSQ(wct.fmtRSQ(y, x)) as RSQ
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
                   RSQ
----------------------
     0.977565632458234
 
(1 row(s) affected)

In this example, we will populate some temporary table with some historical financial information and then calculate the RSQ value. 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',2008,72.5,4185.14,12.96,418.92)
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',2008,21795.55,13174.04,5537.21,4226.86)
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',2008,60420,48822,22271,17681)
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',2008,22430,17449,7844,5521)
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',2008,11575,7370,2701,1847)
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.RSQ(wct.fmtRSQ(REV,YE)) as RSQ
FROM #c
GROUP BY SYM
This produces the following result.
SYM                      RSQ
----- ----------------------
GOOG       0.977339436214685
MSFT        0.84384482670292
ORCL       0.967854021121364
SAP        0.762247686030879
YHOO      0.0481295961999752
 
(5 row(s) affected)

In this example, we will calculate the RSQ of the operating income (OPINC) against the revenue (REV)
SELECT #c.SYM
,wct.RSQ(wct.fmtRSQ(OPINC,REV)) as RSQ
FROM #c
GROUP BY SYM
 
This produces the following result.
SYM                      RSQ
----- ----------------------
GOOG       0.424982363587281
MSFT       0.975377972491666
ORCL       0.984888999008367
SAP        0.713341551053228
YHOO       0.458857018017385
 
(5 row(s) affected)


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