The Firebird 5.0 Language Reference | Statistical Aggregate Functions

`CORR()`

Correlation coefficient

Result type

DOUBLE PRECISION

Syntax

CORR ( <expr1>, <expr2> )

Table 1. `CORR` Function Parameters
Parameter	Description
exprN	Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The CORR function return the correlation coefficient for a pair of numerical expressions.

The function CORR(<expr1>, <expr2>) is equivalent to

COVAR_POP(<expr1>, <expr2>) / (STDDEV_POP(<expr2>) * STDDEV_POP(<expr1>))

This is also known as the Pearson correlation coefficient.

In a statistical sense, correlation is the degree to which a pair of variables are linearly related.A linear relation between variables means that the value of one variable can to a certain extent predict the value of the other.The correlation coefficient represents the degree of correlation as a number ranging from -1 (high inverse correlation) to 1 (high correlation).A value of 0 corresponds to no correlation.

If the group or window is empty, or contains only NULL values, the result will be NULL.

`CORR` Examples

select
  corr(alength, aheight) AS c_corr
from measure

`COVAR_POP()`

Population covariance

Result type

DOUBLE PRECISION

Syntax

COVAR_POP ( <expr1>, <expr2> )

Table 1. `COVAR_POP` Function Parameters
Parameter	Description
exprN	Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function COVAR_POP returns the population covariance for a pair of numerical expressions.

The function COVAR_POP(<expr1>, <expr2>) is equivalent to

(SUM(<expr1> * <expr2>) - SUM(<expr1>) * SUM(<expr2>) / COUNT(*)) / COUNT(*)

If the group or window is empty, or contains only NULL values, the result will be NULL.

`COVAR_POP` Examples

select
  covar_pop(alength, aheight) AS c_covar_pop
from measure

`COVAR_SAMP()`

Sample covariance

Result type

DOUBLE PRECISION

Syntax

COVAR_SAMP ( <expr1>, <expr2> )

Table 1. `COVAR_SAMP` Function Parameters
Parameter	Description
exprN	Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function COVAR_SAMP returns the sample covariance for a pair of numerical expressions.

The function COVAR_SAMP(<expr1>, <expr2>) is equivalent to

(SUM(<expr1> * <expr2>) - SUM(<expr1>) * SUM(<expr2>) / COUNT(*)) / (COUNT(*) - 1)

If the group or window is empty, contains only 1 row, or contains only NULL values, the result will be NULL.

`COVAR_SAMP` Examples

select
  covar_samp(alength, aheight) AS c_covar_samp
from measure

`STDDEV_POP()`

Population standard deviation

Result type

DOUBLE PRECISION or NUMERIC depending on the type of expr

Syntax

STDDEV_POP ( <expr> )

Table 1. `STDDEV_POP` Function Parameters
Parameter	Description
expr	Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function STDDEV_POP returns the population standard deviation for a group or window.NULL values are skipped.

The function STDDEV_POP(<expr>) is equivalent to

SQRT(VAR_POP(<expr>))

If the group or window is empty, or contains only NULL values, the result will be NULL.

`STDDEV_POP` Examples

select
  dept_no
  stddev_pop(salary)
from employee
group by dept_no

`STDDEV_SAMP()`

Sample standard deviation

Result type

DOUBLE PRECISION or NUMERIC depending on the type of expr

Syntax

STDDEV_POP ( <expr> )

Table 1. `STDDEV_SAMP` Function Parameters
Parameter	Description
expr	Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function STDDEV_SAMP returns the sample standard deviation for a group or window.NULL values are skipped.

The function STDDEV_SAMP(<expr>) is equivalent to

SQRT(VAR_SAMP(<expr>))

If the group or window is empty, contains only 1 row, or contains only NULL values, the result will be NULL.

`STDDEV_SAMP` Examples

select
  dept_no
  stddev_samp(salary)
from employee
group by dept_no

`VAR_POP()`

Population variance

Result type

DOUBLE PRECISION or NUMERIC depending on the type of expr

Syntax

VAR_POP ( <expr> )

Table 1. `VAR_POP` Function Parameters
Parameter	Description
expr	Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function VAR_POP returns the population variance for a group or window.NULL values are skipped.

The function VAR_POP(<expr>) is equivalent to

(SUM(<expr> * <expr>) - SUM (<expr>) * SUM (<expr>) / COUNT(<expr>))
  / COUNT (<expr>)

If the group or window is empty, or contains only NULL values, the result will be NULL.

`VAR_POP` Examples

select
  dept_no
  var_pop(salary)
from employee
group by dept_no

`VAR_SAMP()`

Sample variance

Result type

DOUBLE PRECISION or NUMERIC depending on the type of expr

Syntax

VAR_SAMP ( <expr> )

Table 1. `VAR_SAMP` Function Parameters
Parameter	Description
expr	Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function VAR_POP returns the sample variance for a group or window.NULL values are skipped.

The function VAR_SAMP(<expr>) is equivalent to

(SUM(<expr> * <expr>) - SUM(<expr>) * SUM (<expr>) / COUNT (<expr>))
  / (COUNT(<expr>) - 1)

If the group or window is empty, contains only 1 row, or contains only NULL values, the result will be NULL.

`VAR_SAMP` Examples

select
  dept_no
  var_samp(salary)
from employee
group by dept_no

Linear Regression Aggregate Functions

Linear regression functions are useful for trend line continuation.The trend or regression line is usually a pattern followed by a set of values.Linear regression is useful to predict future values.To continue the regression line, you need to know the slope and the point of intersection with the y-axis.As set of linear functions can be used for calculating these values.

In the function syntax, y is interpreted as an x-dependent variable.

The linear regression aggregate functions take a pair of arguments, the dependent variable expression (y) and the independent variable expression (x), which are both numeric value expressions.Any row in which either argument evaluates to NULL is removed from the rows that qualify.If there are no rows that qualify, then the result of REGR_COUNT is 0 (zero), and the other linear regression aggregate functions result in NULL.

`REGR_AVGX()`

Average of the independent variable of the regression line

Result type

DOUBLE PRECISION

Syntax

REGR_AVGX ( <y>, <x> )

Table 1. `REGR_AVGX` Function Parameters
Parameter	Description
y	Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.
x	Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_AVGX calculates the average of the independent variable (x) of the regression line.

The function REGR_AVGX(<y>, <x>) is equivalent to

SUM(<exprX>) / REGR_COUNT(<y>, <x>)

<exprX> :==
  CASE WHEN <x> IS NOT NULL AND <y> IS NOT NULL THEN <x> END

`REGR_AVGY()`

Average of the dependent variable of the regression line

Result type

DOUBLE PRECISION

Syntax

REGR_AVGY ( <y>, <x> )

Table 1. `REGR_AVGY` Function Parameters
Parameter	Description
y	Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.
x	Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_AVGY calculates the average of the dependent variable (y) of the regression line.

The function REGR_AVGY(<y>, <x>) is equivalent to

SUM(<exprY>) / REGR_COUNT(<y>, <x>)

<exprY> :==
  CASE WHEN <x> IS NOT NULL AND <y> IS NOT NULL THEN <y> END

`REGR_COUNT()`

Number of non-empty pairs of the regression line

Result type

DOUBLE PRECISION

Syntax

REGR_COUNT ( <y>, <x> )

Table 1. `REGR_COUNT` Function Parameters
Parameter	Description
y	Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.
x	Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_COUNT counts the number of non-empty pairs of the regression line.

The function REGR_COUNT(<y>, <x>) is equivalent to

COUNT(*) FILTER (WHERE <x> IS NOT NULL AND <y> IS NOT NULL)

See also

[fblangref50-aggfuncs-count]

`REGR_INTERCEPT()`

Point of intersection of the regression line with the y-axis

Result type

DOUBLE PRECISION

Syntax

REGR_INTERCEPT ( <y>, <x> )

Table 1. `REGR_INTERCEPT` Function Parameters
Parameter	Description
y	Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.
x	Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_INTERCEPT calculates the point of intersection of the regression line with the y-axis.

The function REGR_INTERCEPT(<y>, <x>) is equivalent to

REGR_AVGY(<y>, <x>) - REGR_SLOPE(<y>, <x>) * REGR_AVGX(<y>, <x>)

`REGR_INTERCEPT` Examples

Forecasting sales volume

with recursive years (byyear) as (
  select 1991
  from rdb$database
  union all
  select byyear + 1
  from years
  where byyear < 2020
),
s as (
  select
    extract(year from order_date) as byyear,
    sum(total_value) as total_value
  from sales
  group by 1
),
regr as (
  select
    regr_intercept(total_value, byyear) as intercept,
    regr_slope(total_value, byyear) as slope
  from s
)
select
  years.byyear as byyear,
  intercept + (slope * years.byyear) as total_value
from years
cross join regr

BYYEAR TOTAL_VALUE
------ ------------
  1991    118377.35
  1992    414557.62
  1993    710737.89
  1994   1006918.16
  1995   1303098.43
  1996   1599278.69
  1997   1895458.96
  1998   2191639.23
  1999   2487819.50
  2000   2783999.77
...

`REGR_R2()`

Coefficient of determination of the regression line

Result type

DOUBLE PRECISION

Syntax

REGR_R2 ( <y>, <x> )

Table 1. `REGR_R2` Function Parameters
Parameter	Description
y	Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.
x	Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The REGR_R2 function calculates the coefficient of determination, or R-squared, of the regression line.

The function REGR_R2(<y>, <x>) is equivalent to

POWER(CORR(<y>, <x>), 2)

See also

[fblangref50-aggfuncs-corr], POWER

`REGR_SLOPE()`

Slope of the regression line

Result type

DOUBLE PRECISION

Syntax

REGR_SLOPE ( <y>, <x> )

Table 1. `REGR_SLOPE` Function Parameters
Parameter	Description
y	Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.
x	Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_SLOPE calculates the slope of the regression line.

The function REGR_SLOPE(<y>, <x>) is equivalent to

COVAR_POP(<y>, <x>) / VAR_POP(<exprX>)

<exprX> :==
  CASE WHEN <x> IS NOT NULL AND <y> IS NOT NULL THEN <x> END

`REGR_SXX()`

Sum of squares of the independent variable

Result type

DOUBLE PRECISION

Syntax

REGR_SXX ( <y>, <x> )

Table 1. `REGR_SXX` Function Parameters
Parameter	Description
y	Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.
x	Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_SXX calculates the sum of squares of the independent expression variable (x).

The function REGR_SXX(<y>, <x>) is equivalent to

REGR_COUNT(<y>, <x>) * VAR_POP(<exprX>)

<exprX> :==
  CASE WHEN <x> IS NOT NULL AND <y> IS NOT NULL THEN <x> END

`REGR_SXY()`

Sum of products of the independent variable and the dependent variable

Result type

DOUBLE PRECISION

Syntax

REGR_SXY ( <y>, <x> )

Table 1. `REGR_SXY` Function Parameters
Parameter	Description
y	Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.
x	Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_SXY calculates the sum of products of independent variable expression (x) times dependent variable expression (y).

The function REGR_SXY(<y>, <x>) is equivalent to

REGR_COUNT(<y>, <x>) * COVAR_POP(<y>, <x>)

`REGR_SYY()`

Sum of squares of the dependent variable

Result type

DOUBLE PRECISION

Syntax

REGR_SYY ( <y>, <x> )

Table 1. `REGR_SYY` Function Parameters
Parameter	Description
y	Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.
x	Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_SYY calculates the sum of squares of the dependent variable (y).

The function REGR_SYY(<y>, <x>) is equivalent to

REGR_COUNT(<y>, <x>) * VAR_POP(<exprY>)

<exprY> :==
  CASE WHEN <x> IS NOT NULL AND <y> IS NOT NULL THEN <y> END

CORR()

CORR()

CORR Examples

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COVAR_POP()

COVAR_POP Examples

COVAR_SAMP()

COVAR_SAMP Examples

STDDEV_POP()

STDDEV_POP Examples

STDDEV_SAMP()

STDDEV_SAMP Examples

VAR_POP()

VAR_POP Examples

VAR_SAMP()

VAR_SAMP Examples

Linear Regression Aggregate Functions

REGR_AVGX()

REGR_AVGY()

REGR_COUNT()

REGR_INTERCEPT()

REGR_INTERCEPT Examples

REGR_R2()

REGR_SLOPE()

REGR_SXX()

REGR_SXY()

REGR_SYY()

`CORR()`

`CORR` Examples

`COVAR_POP()`

`COVAR_POP` Examples

`COVAR_SAMP()`

`COVAR_SAMP` Examples

`STDDEV_POP()`

`STDDEV_POP` Examples

`STDDEV_SAMP()`

`STDDEV_SAMP` Examples

`VAR_POP()`

`VAR_POP` Examples

`VAR_SAMP()`

`VAR_SAMP` Examples

`REGR_AVGX()`

`REGR_AVGY()`

`REGR_COUNT()`

`REGR_INTERCEPT()`

`REGR_INTERCEPT` Examples

`REGR_R2()`

`REGR_SLOPE()`

`REGR_SXX()`

`REGR_SXY()`

`REGR_SYY()`