This function outputs a result set that contains the estimated coefficients with accompanying per-coefficient statistical ratings. This result set is retrieved by issuing a SELECT against the ART.
The function can output a secondary (ARTFITMETADATA) result set with goodness-of-fit metadata, a tertiary (ARTFITRESIDUALS) result set with residuals from the fitting operation, a quaternary (ARTMODEL) result set with validation model context, and a quinary (ARTVALDATA) result set with the validation series. These result sets are retrieved directly using the TD_EXTRACT_RESULTS function. Additionally, the residuals can be indirectly referenced by passing the ART name into a UAF function that requires the residual series as an input.
RETURNS TABLE Schema for Primary Result Set
| Name | Data Type | Description |
|---|---|---|
| derived-series-identifier | Varies | The resultant series identifying the field list. |
| ROW_I | BIGINT | The indices, starting with 0, are associated with coefficients in accordance to order in which they appeared in the formula. The last index is the constant coefficient, if constant was requested. |
| COEFF_NAME | VARCHAR (128) | Name of the coefficient. |
| COEFF_VALUE | FLOAT | The calculated value of the coefficient determined by the regression process. |
| STD_ERROR | FLOAT | The standard error associated with the calculated value for that coefficient. Only returned if COEFF_STATS(1). |
| ZSTAT_VALUE | FLOAT | Column is included only if MLE/CSS_MLE/CSS algorithms are used. The z-statistic associated with the calculated value for that coefficient. Purpose is to determine how significant a given coefficient is, relative to a statistical value of 0. Only returned if COEFF_STATS(1). |
| ZSTAT_PROB | FLOAT | Column is included only if MLE/CSS_MLE/CSS algorithms are used. The probability associated with the z-statistic. It is the probability of obtaining an absolute value of z as large as the one that was calculated for the data, if the coefficient is 0. Only returned if COEFF_STATS(1). |
| TSTAT_VALUE | FLOAT | Column is included only if OLE algorithm is used. For OLE algorithm, the t-statistic associated with the calculated value for that coefficient. Purpose is to determine how significant a given coefficient is relative to a statistical value of 0. Only returned if COEFF_STATS(1). For coefficient A : t-statisticA = value of A / STD_ERROR(A) For coefficient B : t-statisticB = value of B / STD_ERROR(B) and so on. |
| TSTAT_PROB | FLOAT | Column is included only if OLE algorithm is used. The probability associated with the t-statistic. It is the probability of obtaining an absolute value of t as large as the one calculated for the data, if the coefficient is equal to 0. Only returned if COEFF_STATS(1). |
RETURNS TABLE Schema for Secondary Result Set (ARTFITMETADATA)
| Name | Data Type | Description |
|---|---|---|
| derived-series-identifier | Varies | The resultant series identifying the field list. |
| ROW_I | BIGINT | Index associated with the result series in this layer. |
| NUM_SAMPLES | INTEGER | The number of sample points used to fit the model. |
| VAR_COUNT | INTEGER | Number of explanatory variables, including the constant, in the original regression. |
| R_SQUARE | FLOAT | The calculated R-squared value from the original and calculated values. |
| R_ADJ_SQUARE | FLOAT | The calculated adjusted R-squared value from the original and calculated values. |
| STD_ERROR | FLOAT | The standard error or deviation associated with the model. |
| STD_ERROR_DF | INTEGER | The degrees of freedom associated with the standard error calculation. |
| ME | FLOAT | The Mean Error. |
| MAE | FLOAT | The Mean Absolute Error. |
| MSE | FLOAT | The Mean Squared Error. |
| MPE | FLOAT | The Mean Percent Error. |
| MAPE | FLOAT | The Mean Absolute Percent Error. |
| F_STAT_CALC | FLOAT | The calculated F-statistic value for the ordinary least squares (OLS) regression. |
| P_VALUE | FLOAT | The p-value corresponding to the calculated test statistic. |
| NUM_DF | INTEGER | The degrees of freedom in the numerator associated with the unexplained portion of the F-statistic. |
| DENOM_DF | INTEGER | The degrees of freedom in the denominator associated with the explained portion of the F-statistic. |
| SIGNIFICANCE_LAYER | FLOAT | Level of significance for the test. |
| F_CRITICAL | FLOAT | The chi-squared critical value extracted from the chi-squared statistic tables. |
| F_CRITCAL_P | FLOAT | The p-value corresponding to the calculated critical value. |
| NULL_HYPOTH | VARCHAR(25) | The result of the test.
|
RETURNS TABLE Schema for Tertiary Result Set (ARTFITRESIDUALS)
| Name | Data Type | Description |
|---|---|---|
| derived-series-identifier | Varies | The resultant series identifying the field list. |
| ROW_I | Varies | Indexing column for the multivariate output array containing the residuals. Its associated data type is dependent on the OUTPUT_FMT (INDEX_STYLE) input. If NUMERICAL_SEQUENCE is used, then the data type is BIGINT and it is incremented by 1 for each row, starting from 0. If FLOW_THROUGH is used, then the value could be another data type based on the data type of the passed in ROW_AXIS. |
| ACTUAL_VALUE | FLOAT | The actual value of the response variable. |
| CALC_VALUE | FLOAT | The calculated value of the response variable using the model. |
| RESIDUAL | FLOAT | The difference between the calculated response value and the actual response value. |
RETURNS TABLE Schema for Quaternary Result Set (ARTMODEL)
| Name | Data Type | Description |
|---|---|---|
| derived-series-identifier | Varies | The resultant series identifying the field list. |
| ROW_I | BIGINT | The model row number. Used to support model sizes larger than 32000 bytes. |
| MODEL_DATA | VARBYTE (32000) | Model context in binary form. |
RETURNS TABLE Schema for Quinary Result Set (ARTVALDATA)
| Name | Data Type | Description |
|---|---|---|
| derived-series-identifier | Varies | The resultant series identifying the field list. |
| ROW_I | Varies | Indexing column for the multivariate output array containing the residuals. Its associated data type is dependent upon the OUTPUT_FMT(INDEX_STYLE). If NUMERICAL_SEQUENCE is used, then the data type is BIGINT and it is incremented by 1 for each row, starting from 0. If FLOW_THROUGH is used, then the value is another data type based on the data type of the passed in ROW_AXIS. |
| VAL_ACTUAL_VALUE | FLOAT | The unused sample data actual value. This is the portion of the series reserved for validation. |
| VAL_CALC_VALUE | FLOAT | The unused sample data fitted value. This is the portion of the series reserved for validation. |
| VAL_RESIDUAL | FLOAT | The unused sample data residuals. This is the portion of the series reserved for validation. |