REGR_R2
Purpose
Returns the coefficient of determination for all non‑null data pairs of the dependent and independent variable arguments.
Syntax
where:
|
Syntax element … |
Specifies … |
|
dependent_variable_expression |
the dependent variable for the regression. A dependent variable is something that is measured in response to a treatment. The expression cannot contain any ordered analytical or aggregate functions. |
|
independent_variable_expression |
the independent variable for the regression. An independent variable is a treatment: something that is varied under your control to test the behavior of another variable. The expression cannot contain any ordered analytical or aggregate functions. |
ANSI Compliance
This is ANSI SQL:2011 compliant.
Setting Up Axes for Plotting
If you export the data for plotting, define the y-axis (ordinate) as the dependent variable and the x-axis (abscissa) as the independent variable.
Combination With Other Functions
REGR_R2 can be combined with any of the ordered analytical functions in a SELECT list, QUALIFY clause, or ORDER BY clause. For more information on ordered analytical functions, see Chapter 22: “Ordered Analytical / Window Aggregate Functions.”
REGR_R2 cannot be combined with aggregate functions within the same SELECT list, QUALIFY clause, or ORDER BY clause.
Computation
The coefficient of determination for two variables is the square of their Pearson product-moment correlation.
The equation for computing REGR_R2 is defined as follows:
where:
|
This variable … |
Represents … |
|
x |
independent_variable_expression x is the independent, or predictor, variable expression. |
|
y |
dependent_variable_expression y is the dependent, or response, variable expression. |
When there are fewer than two non-null data point pairs in the data used for the computation, then REGR_R2 returns NULL.
Division by zero results in NULL rather than an error.
Result Type and Attributes
The data type, format, and title for REGR_R2(y, x) are as follows.
Data type: REAL
For information on the default format of data types and an explanation of the formatting characters in the format, see “Data Type Formats and Format Phrases” in SQL Data Types and Literals.
Support for UDTs
By default, Teradata Database performs implicit type conversion on UDT arguments that have implicit casts that cast between the UDTs and any of the following predefined types:
To define an implicit cast for a UDT, use the CREATE CAST statement and specify the AS ASSIGNMENT clause. For more information on CREATE CAST, see SQL Data Definition Language.
Implicit type conversion of UDTs for system operators and functions, including REGR_R2, is a Teradata extension to the ANSI SQL standard. To disable this extension, set the DisableUDTImplCastForSysFuncOp field of the DBS Control Record to TRUE. For details, see Utilities: Volume 1 (A-K).
For more information on implicit type conversion of UDTs, see Chapter 13: “Data Type Conversions.”
REGR_R2 Window Function
For the REGR_R2 window function that performs a group, cumulative, or moving computation, see “Window Aggregate Functions” on page 984.
Example
This example is based the following regrtbl data. Nulls are indicated by the QUESTION MARK character.
c1 height weight
-- ------ ------
1 60 84
2 62 95
3 64 140
4 66 155
5 68 119
6 70 175
7 72 145
8 74 197
9 76 150
10 76 ?
11 ? 150
12 ? ?
The following SELECT statement returns the coefficient of determination for height and weight where neither height nor weight is null.
SELECT CAST(REGR_R2(weight,height) AS DECIMAL(4,2))
FROM regrtbl;
REGR_R2(weight,height)
----------------------
.58