TD_LINEAR_REGR Output - Teradata Vantage

Database Unbounded Array Framework Time Series Functions

Deployment
VantageCloud
VantageCore
Edition
VMware
Enterprise
IntelliFlex
Product
Teradata Vantage
Release Number
17.20
Published
June 2022
ft:locale
en-US
ft:lastEdition
2025-04-04
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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.