COVAR
Updated 2023-10-21 19:34:31.497000
Syntax
SELECT [westclintech].[wct].[COVAR] (
,<@Known_y, float,>
,<@Known_x, float,>)
Description
Use the aggregate function COVAR to calculate the average of the products of the deviations for each data point pair. The equation for covariance is
COV(X,Y)=\frac{\sum(x-\bar{x})(y-\bar{y})}{n}
Arguments
@Known_x
the x-values to be used in the COVAR calculation. @Known_x is an expression of type float or of a type that can be implicitly converted to float.
@Known_y
the y-values to be used in the COVAR calculation. @Known_y is an expression of type float or of a type that can be implicitly converted to float.
Return Type
float
Remarks
COVAR is an AGGREGATE function and follows the same conventions as all other AGGREGATE functions in SQL Server.
Examples
In this example, we calculate the covariance for a single set of x- and y-values
SELECT wct.COVAR(y, x) as COVAR
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
{"columns":[{"field":"COVAR","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"COVAR":"4"}]}
In this example, we will populate some temporary table with some historical financial information and then calculate the covariance. 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 covariance of the revenue (REV) against the year (YE) for each company (SYM)
SELECT #c.SYM,
wct.COVAR(REV, YE) as COVAR
FROM #c
GROUP BY SYM;
This produces the following result.
SYM COVAR
----- ----------------------
GOOG 9242.926
MSFT 8743.8
ORCL 6027.2
SAP 1301.6
YHOO -789.576
In this example, we will calculate the correlation of the operating income (OPINC) against the revenue (REV)
SELECT #c.SYM,
wct.COVAR(OPINC, REV) as COVAR
FROM #c
GROUP BY SYM;
This produces the following result.
SYM COVAR
----- ----------------------
GOOG 12281522.966476
MSFT 19038574.4
ORCL 6855059.76
SAP 117904.8
YHOO 676127.183864
Let’s say we wanted to perform the same analysis as above, but we only want to return the results where the covariance is negative.
SELECT #c.SYM,
wct.COVAR(REV, YE) as COVAR
FROM #c
GROUP BY SYM
HAVING wct.COVAR(REV, YE) < 0;
This produces the following result.
SYM COVAR
----- ----------------------
YHOO -789.576