COVAR_POP

Syntax

covar_pop::=
Description of covar_pop.gif follows

Description of the illustration covar_pop.gif

See Also:

"Analytic Functions " for information on syntax, semantics, and restrictions

Purpose

COVAR_POP returns the population covariance of a set of number pairs. You can use it as an aggregate or analytic function.

This function takes as arguments any numeric datatype or any nonnumeric datatype that can be implicitly converted to a numeric datatype. Oracle determines the argument with the highest numeric precedence, implicitly converts the remaining arguments to that datatype, and returns that datatype.

See Also:

Table 2-11, "Implicit Type Conversion Matrix" for more information on implicit conversion and "Numeric Precedence " for information on numeric precedence

Oracle Database applies the function to the set of (expr1, expr2) pairs after eliminating all pairs for which either expr1 or expr2 is null. Then Oracle makes the following computation:

(SUM(expr1 * expr2) - SUM(expr2) * SUM(expr1) / n) / n

where n is the number of (expr1, expr2) pairs where neither expr1 nor expr2 is null.

The function returns a value of type NUMBER. If the function is applied to an empty set, then it returns null.

See Also:

"About SQL Expressions " for information on valid forms of expr and "Aggregate Functions "

Aggregate Example

The following example calculates the population covariance for the sales revenue amount and the units sold for each year from the sample table sh.sales:

SELECT t.calendar_month_number,
   COVAR_POP(s.amount_sold, s.quantity_sold) AS covar_pop,
   COVAR_SAMP(s.amount_sold, s.quantity_sold) AS covar_samp
   FROM sales s, times t
   WHERE s.time_id = t.time_id
   AND t.calendar_year = 1998
   GROUP BY t.calendar_month_number;

CALENDAR_MONTH_NUMBER  COVAR_POP COVAR_SAMP
--------------------- ---------- ----------
                    1 5437.68586 5437.88704
                    2 5923.72544 5923.99139
                    3 6040.11777 6040.38623
                    4 5946.67897 5946.92754
                    5 5986.22483  5986.4463
                    6 5726.79371 5727.05703
                    7 5491.65269  5491.9239
                    8 5672.40362 5672.66882
                    9 5741.53626 5741.80025
                   10  5050.5683 5050.78195
                   11 5256.50553 5256.69145
                   12  5411.2053 5411.37709

Analytic Example

The following example calculates cumulative sample covariance of the list price and minimum price of the products in the sample schema oe:

SELECT product_id, supplier_id,
   COVAR_POP(list_price, min_price) 
      OVER (ORDER BY product_id, supplier_id)
         AS CUM_COVP,
   COVAR_SAMP(list_price, min_price)
      OVER (ORDER BY product_id, supplier_id)
        AS CUM_COVS 
   FROM product_information p
   WHERE category_id = 29
   ORDER BY product_id, supplier_id;

PRODUCT_ID SUPPLIER_ID   CUM_COVP   CUM_COVS
---------- ----------- ---------- ----------
      1774      103088          0
      1775      103087    1473.25     2946.5
      1794      103096 1702.77778 2554.16667
      1825      103093    1926.25 2568.33333
      2004      103086     1591.4    1989.25
      2005      103086     1512.5       1815
      2416      103088 1475.97959 1721.97619
. . .