Measure mapping for the Multiple Regression algorithm
The Multiple Regression algorithm in the ATT engine adds a number of additional outputs that can be selected in the measure mapping. Each of these measures is specific to the Multiple Regression algorithm and the values are not used for other algorithms.
| Field Name | Scope | Description |
|---|---|---|
| Adjusted R-Squared | Static (PCONST) | Includes the adjusted R squared value for
a multiple regression model fit. Adjusted R-squared is an adjustment to the R
Squared calculation that is used to consider the number of independent
variables and the number of observations. Generally, it is recommended that you
use the statistic rather than the R Squared statistic.
However, errors can occur if you select too many parameters. When you add too many 'useless' variables to a model, the adjusted r-squared option is used to decrease the number of errors. However, adding more 'useful' variables to the model increases the errors. The Adjusted R-squared value is always less than or equal to R-squared. |
| Cross-Validation | Static (PCONST) | Includes the cross-validation value for a multiple regression model fit. This is a statistic to help in model selection. This is also known as the LOOCV (Leave One Out Cross Validation) and is an alternative to the AICc and the BIC. For this statistic, the model with the lowest value is considered the best. |
| Intercept | Static (PCONST) | Includes the intercept weightings for a multiple regression model fit. This represents the levels of the model, that is, when the values of all the independent variables are zero. |
| F Statistic | Static (PCONST) | Includes the overall F statistic for a multiple regression fit. This is a test statistic that relates to all the independent variables when considered together (excluding the intercept). The statistic is the ratio of the explained variance for each degree of freedom with the unexplained variance for each degree of freedom. |
| F Statistic P-Value | Static (PCONST) | Includes the overall F statistic P-value
for a multiple regression model fit. It is the probability of generating a
larger value if all the true coefficients are zero, when the P value < 0.05
implies significance, that is, at least some of the variables are significant.
The P-value is typically lesser than the lowest P value for the individual t statistics, excluding the intercept. Therefore, if at least one independent variable includes a significant P value, the F statistic P value is not relevant. This value is mainly relevant when the independent variables are only marginally significant and there may be reasons to consider the group as significant. |
| R-Squared | Static (PCONST) | Includes the R squared (Regression standard deviation) value for a multiple regression model fit. This deviation represents the square of the correlation coefficient and measures the strength of the regression when compared to a model that only uses the intercept. This only increases the value when adding additional regressors and can therefore be misleading, because although the number of new regressors increases, value is not added to the forecasting performance of the model. |
| t Statistic Intercept | Static (PCONST) | Includes 't statistic' as an intercept for a multiple regression model fit. This represents the intercept divided by the standard error; that is, when the value of the independent variables are zero, the intercept represents the next lower level of the model. |
| t Statistic P-Value Intercept | Static (PCONST) | Includes the 't statistic' P-values for a multiple regression model fit. The t statistic P-Value represents the observed Significance level for the 't statistic'. |