linear.sql_in File Reference

SQL functions for linear regression. More...

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Functions
aggregate heteroskedasticity_test_result	heteroskedasticity_test_linregr (float8 dependentVariable, float8[] independentVariables, float8[] olsCoefficients)
	Compute studentized Breuch-Pagan heteroskedasticity test for linear regression. More...
aggregate linregr_result	linregr (float8 dependentVariable, float8[] independentVariables)
	Compute linear regression coefficients and diagnostic statistics. More...

Detailed Description

Date

January 2011

See Also

For a brief introduction to linear regression, see the module description Linear Regression.

Definition in file linear.sql_in.

Function Documentation

aggregate heteroskedasticity_test_result heteroskedasticity_test_linregr	(	float8	dependentVariable,
		float8[]	independentVariables,
		float8[]	olsCoefficients
	)

Parameters

dependentVariable	Column containing the dependent variable
independentVariables	Column containing the array of independent variables
olsCoefficients	Column containing the array of the OLS coefficients (as obtained by linregr)

To include an intercept in the model, set one coordinate in the independentVariables array to 1.

Returns

A composite value:

• test_statistic FLOAT8[] - Prob > test_statistc
• p_value FLOAT8[] - Prob > test_statistc

Usage:

 SELECT (heteoskedasticity_test_linregr(dependentVariable,
 independentVariables, coef)).*
 FROM (
   SELECT linregr(dependentVariable, independentVariables).coef
 ) AS ols_coef, sourceName as src;

Definition at line 455 of file linear.sql_in.

aggregate linregr_result linregr	(	float8	dependentVariable,
		float8[]	independentVariables
	)

Parameters

dependentVariable	Column containing the dependent variable
independentVariables	Column containing the array of independent variables

To include an intercept in the model, set one coordinate in the independentVariables array to 1.

Returns

A composite value:

• coef FLOAT8[] - Array of coefficients, \( \boldsymbol c \)
• r2 FLOAT8 - Coefficient of determination, \( R^2 \)
• std_err FLOAT8[] - Array of standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)
• t_stats FLOAT8[] - Array of t-statistics, \( \boldsymbol t \)
• p_values FLOAT8[] - Array of p-values, \( \boldsymbol p \)
• condition_no FLOAT8 - The condition number of matrix \( X^T X \).

Usage:

• Get vector of coefficients \( \boldsymbol c \) and all diagnostic statistics:
  

  SELECT (linregr(dependentVariable,
          independentVariables)).*
  FROM sourceName;

• Get vector of coefficients \( \boldsymbol c \):
  

  SELECT (linregr(dependentVariable,
          independentVariables)).coef
  FROM sourceName;

• Get a subset of the output columns, e.g., only the array of coefficients \( \boldsymbol c \), the coefficient of determination \( R^2 \), and the array of p-values \( \boldsymbol p \):

  SELECT (lr).coef, (lr).r2, (lr).p_values
  FROM (
      SELECT linregr( dependentVariable,
                      independentVariables) AS lr
      FROM sourceName
  ) AS subq;

Definition at line 508 of file linear.sql_in.