9.4. 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.

9.4.1. `REGR_AVGX()`

Average of the independent variable of the regression line

Result typeDOUBLE PRECISION

Syntax

  |REGR_AVGX ( <y>, <x> )

Table 9.14. 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

9.4.2. `REGR_AVGY()`

Average of the dependent variable of the regression line

Result typeDOUBLE PRECISION

Syntax

  |REGR_AVGY ( <y>, <x> )

Table 9.15. 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

9.4.3. `REGR_COUNT()`

Number of non-empty pairs of the regression line

Result typeDOUBLE PRECISION

Syntax

  |REGR_COUNT ( <y>, <x> )

Table 9.16. 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)

9.4.4. `REGR_INTERCEPT()`

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

Result typeDOUBLE PRECISION

Syntax

  |REGR_INTERCEPT ( <y>, <x> )

Table 9.17. 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>)

9.4.4.1. `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
   |...

9.4.5. `REGR_R2()`

Coefficient of determination of the regression line

Result typeDOUBLE PRECISION

Syntax

  |REGR_R2 ( <y>, <x> )

Table 9.18. 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)

9.4.6. `REGR_SLOPE()`

Slope of the regression line

Result typeDOUBLE PRECISION

Syntax

  |REGR_SLOPE ( <y>, <x> )

Table 9.19. 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

9.4.7. `REGR_SXX()`

Sum of squares of the independent variable

Result typeDOUBLE PRECISION

Syntax

  |REGR_SXX ( <y>, <x> )

Table 9.20. 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

9.4.8. `REGR_SXY()`

Sum of products of the independent variable and the dependent variable

Result typeDOUBLE PRECISION

Syntax

  |REGR_SXY ( <y>, <x> )

Table 9.21. 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>)

9.4.9. `REGR_SYY()`

Sum of squares of the dependent variable

Result typeDOUBLE PRECISION

Syntax

  |REGR_SYY ( <y>, <x> )

Table 9.22. 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

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