Is there a way to calculate correlation in TSQL using OVER Clauses instead of CTE's?

Let's say you have a table with columns, Date, GroupID, X and Y.

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

DECLARE @date DATETIME = getdate()

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

and you want to calculate the correlation of X and Y for each group. Currently I use CTEs which get a little messy:

;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  

It seems like there should be a way to use OVER and PARTITION to do this in one fell swoop without any subqueries. Ideally TSQL would have a function so you could write:

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