The Firebird 5.0 Language Reference | Linear Regression Aggregate Functions

`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_R2()

REGR_R2()

REGR_SLOPE()

docnext count = 3

REGR_SXX()

REGR_SXY()

REGR_SYY()

`REGR_R2()`

`REGR_SLOPE()`

`REGR_SXX()`

`REGR_SXY()`

`REGR_SYY()`