The Firebird 5.0 Language Reference | Linear Regression Aggregate Functions

`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

REGR_INTERCEPT()

REGR_INTERCEPT()

REGR_INTERCEPT Examples

REGR_R2()

REGR_SLOPE()

REGR_SXX()

REGR_SXY()

REGR_SYY()

`REGR_INTERCEPT()`

`REGR_INTERCEPT` Examples

`REGR_R2()`

`REGR_SLOPE()`

`REGR_SXX()`

`REGR_SXY()`

`REGR_SYY()`