TD_LINEAR_REGR Output - Teradata Vantage

Database Unbounded Array Framework Time Series Functions

Deployment
VantageCloud
VantageCore
Edition
Enterprise
IntelliFlex
VMware
Product
Teradata Vantage
Release Number
17.20
Published
June 2022
Language
English (United States)
Last Update
2024-10-04
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This function returns a primary layer and several auxiliary layers. The function can output a secondary (ARTFITMETADATA) result set with goodness-of-fit metadata, and a tertiary (ARTFITRESIDUALS) result set with residuals from the fitting operation.

The function returns a primary RETURNS TABLE, which has an ordered list of solved coefficients. If you specified MODEL_STATS (1), then a secondary layer has the model statistics. If you specified RESIDUALS (1), then a tertiary layer has residual statistics.

You display the primary layer with a SELECT statement. You display the secondary (ARTFITMETADATA) and tertiary (ARTFITRESIDUALS) layers with the TD_EXTRACT_RESULTS function.

Key to Variables in Formulas in RETURNS TABLE Schema Description Columns

Variable Description
Yactual[i] Actual coefficient with index (position) i in formula.
Ycalc[i] Calculated coefficient with index (position) i in formula.
n Number of sample points in input time series.
R[i] Variance between actual and calculated coefficients with index (position) i in formula.
k Number of explanatory variables in formula.

Primary RETURNS TABLE Schema

Name Data Type Description
derived-series-identifier Varies The resultant series identifier inherited from the SERIES_ID.
ROW_I INTEGER Index (position) of coefficient in formula.
COEFF_NAME VARCHAR(120) Coefficient name.
COEFF_VALUE FLOAT Calculated value of coefficient.
STD_ERROR FLOAT [Appears only with COEFF_STATS (1).] Standard error associated with calculated value of coefficient.
TSTAT_VALUE FLOAT [Appears only with COEFF_STATS (1).] The significance of coefficient relative to 0.t-statistic calculated for coefficient:

coefficient_value / STD_ERROR (coefficient_value)

TSTAT_PROB FLOAT [Appears only with COEFF_STATS (1).] Probability associated with t-statistic calculated for input time series if coefficient is 0. (More specifically, probability of getting |t| value as large as that calculated for input time series if coefficient is 0.)
SIGNIF_RATING VARCHAR(20) [Appears only with COEFF_STATS (1).] The rating or confidence level range associated with the coefficient.
CONF_INT_LOW FLOAT Lowest value of coefficient, given confidence level specified in brackets, such as '[0.95]'. Only valid with COEFF_STATS (1).
CONF_INT_HIGH FLOAT Highest value of coefficient, given confidence level specified in brackets, such as '[0.95]'. Only valid with COEFF_STATS(1).

Secondary RETURNS TABLE Schema

Name Data Type Description
derived-series-identifier VARCHAR The resultant series identifier inherited from the SERIES_ID.
ROW_I Integer Index of coefficient in formula.
STD_ERROR2 FLOAT Standard error (standard deviation) associated with formula:

1 / (n - 2) * SUM (Yactual[i] - Ycalc[i])2

STD_ERROR_DF FLOAT Degrees of freedom associated with standard error calculation.
MULTIPLE_R_SQUARED FLOAT Fraction of variance.
ADJUSTED_R_SQUARED FLOAT MULTIPLE_R_SQUARED value adjusted to lessen higher number of explanatory variables.
FSTATISTIC FLOAT The F-statistic associated with a ratio of the two variances (explained / unexplained) .
EXPLAINED_DF FLOAT Degrees of freedom associated with explained part of the F-statistic.
UNEXPLAINED_DF FLOAT Degrees of freedom associated with unexplained part of the F-statistic.
PROB_VALUE FLOAT Probability associated with the F-statistic.

Tertiary RETURNS TABLE Schema

Name Data Type Description
derived-series-identifier VARCHAR The resultant series identifier inherited from the SERIES_ID.
ROW_I Integer Index of coefficient in formula.
X1 FLOAT First explanatory variable in formula, second FIELD in PAYLOAD.
ACTUAL_VALUE FLOAT Actual value of response variable.
CALC_VALUE FLOAT Value of response variable calculated using formula.
RESIDUAL FLOAT Difference between calculated and actual response variable values.