有没有办法使用OVER子句而不是CTE来计算TSQL中的相关性？

假设您有一个包含列,Date,GroupID,X和Y的表.

CREATE TABLE #sample
  (
     [Date]  DATETIME,GroupID INT,X       FLOAT,Y       FLOAT
  )

DECLARE @date DATETIME = getdate()

INSERT INTO #sample VALUES(@date,1,3)
INSERT INTO #sample VALUES(DATEADD(d,@date),1)
INSERT INTO #sample VALUES(DATEADD(d,2,4,2)
INSERT INTO #sample VALUES(DATEADD(d,3,6,4)
INSERT INTO #sample VALUES(DATEADD(d,5,7,5)
INSERT INTO #sample VALUES(DATEADD(d,6)

并且您想要计算每个组的X和Y的相关性.目前我使用的CTE有点乱：

;WITH DataAvgStd
     AS (SELECT GroupID,AVG(X)   AS XAvg,AVG(Y)   AS YAvg,STDEV(X) AS XStdev,STDEV(Y) AS YSTDev,COUNT(*) AS SampleSize
         FROM   #sample
         GROUP  BY GroupID),ExpectedVal
     AS (SELECT s.GroupID,SUM(( X - XAvg ) * ( Y - YAvg )) AS ExpectedValue
         FROM   #sample s
                JOIN DataAvgStd das
                  ON s.GroupID = das.GroupID
         GROUP  BY s.GroupID)
SELECT das.GroupID,ev.ExpectedValue / ( das.SampleSize - 1 ) / ( das.XStdev * das.YSTDev )
       AS
       Correlation
FROM   DataAvgStd das
       JOIN ExpectedVal ev
         ON das.GroupID = ev.GroupID

DROP TABLE #sample

似乎应该有一种方法可以使用OVER和PARTITION一次性执行此操作而不需要任何子查询.理想情况下,TSQL会有一个函数,所以你可以写：

SELECT GroupID,CORR(X,Y) OVER(PARTITION BY GroupID)
FROM #sample
GROUP BY GroupID

解决方法

你的代码看起来就像那样

;WITH DataAvgStd
     AS (SELECT GroupID,STDEV(X) over(partition by GroupID) AS XStdev,STDEV(Y) over(partition by GroupID) AS YSTDev,COUNT(*) over(partition by GroupID) AS SampleSize,( X - AVG(X) over(partition by GroupID)) * ( Y - AVG(Y) over(partition by GroupID)) AS ExpectedValue
         FROM   #sample s)         
SELECT distinct GroupID,SUM(ExpectedValue) over(partition by GroupID) / (SampleSize - 1 ) / ( XStdev * YSTDev ) AS Correlation
FROM DataAvgStd

另一种方法是使用等效公式进行相关,如Wikipedia所述.

这可以写成

SELECT GroupID,Correlation=(COUNT(*) * SUM(X * Y) - SUM(X) * SUM(Y)) / 
                   (SQRT(COUNT(*) * SUM(X * X) - SUM(X) * SUM(x))
                    * SQRT(COUNT(*) * SUM(Y* Y) - SUM(Y) * SUM(Y)))
FROM #sample s
GROUP BY GroupID;

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