REGR_INTERCEPT
Purpose
Returns the intercept of the univariate linear regression line through 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. The expression cannot contain any ordered analytical or aggregate functions. |
|
independent_variable_expression |
the independent variable for the regression. The expression cannot contain any ordered analytical or aggregate functions. |
ANSI Compliance
This is ANSI SQL:2011 compliant.
Definition
The intercept is the point at which the regression line through the non-null data pairs in the sample intersects the ordinate, or y-axis, of the graph.
The plot of the linear regression on the variables is used to predict the behavior of the dependent variable from the change in the independent variable.
Note that this computation assumes a linear relationship between the variables.
There can be a strong nonlinear relationship between independent and dependent variables, and the computation of the simple linear regression between such variable pairs does not reflect such a relationship.
Independent and Dependent Variables
An independent variable is a treatment: something that is varied under your control to test the behavior of another variable.
A dependent variable is something that is measured in response to a treatment.
For example, you might want to test the ability of various promotions to enhance sales of a particular item.
In this case, the promotion is the independent variable and the sales of the item made as a result of the individual promotion is the dependent variable.
The value of the linear regression intercept tells you the predicted value for sales when there is no promotion for the item selected for analysis.
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_INTERCEPT 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_INTERCEPT cannot be combined with aggregate functions within the same SELECT list, QUALIFY clause, or ORDER BY clause.
Computation
The equation for computing REGR_INTERCEPT is defined as follows:
where:
|
This variable … |
Represents … |
|
x |
independent_variable_expression |
|
y |
dependent_variable_expression |
When there are fewer than two non-null data point pairs in the data used for the computation, then REGR_INTERCEPT returns NULL.
Division by zero results in NULL rather than an error.
Result Type and Attributes
The data type, format, and title for REGR_INTERCEPT(y, x) are as follows.
|
Data Type |
Format |
Title |
|
REAL |
Default format of the REAL data type |
REGR_INTERCEPT(y,x) |
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_INTERCEPT, 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 details on implicit type conversion of UDTs, see Chapter 13: “Data Type Conversions.”
REGR_INTERCEPT Window Function
For the REGR_INTERCEPT window function that performs a group, cumulative, or moving computation, see “Window Aggregate Functions” on page 984.
Example
This example uses the data from the HomeSales table.
|
SalesPrice |
NbrSold |
Area |
|
160000 |
126 |
358711030 |
|
180000 |
103 |
358711030 |
|
200000 |
82 |
358711030 |
|
220000 |
75 |
358711030 |
|
240000 |
82 |
358711030 |
|
260000 |
40 |
358711030 |
|
280000 |
20 |
358711030 |
The following query returns the intercept of the regression line for NbrSold and SalesPrice in the range of 160000 to 280000 in the 358711030 area.
SELECT CAST (REGR_INTERCEPT(NbrSold,SalesPrice) AS DECIMAL (5,1))
FROM HomeSales
WHERE area = 358711030
AND SalesPrice BETWEEN 160000 AND 280000;
Here is the result:
REGR_INTERCEPT(NbrSold,SalesPrice)
----------------------------------
249.9