LINEAR REGRESSION¶
Fits a polynomial regression model (order 1–5 or auto-selected) of a dependent scalar variable against an independent scalar variable. Optionally scans the fitted curve over a user-defined range to find the independent value that minimizes or maximizes the dependent response.
When to use¶
Tagged: curve_fit, linear_regression, optimization, polynomial_regression, r2, regression, simulation.
Inputs¶
| Label | ID | Type | Default | Required | Description |
|---|---|---|---|---|---|
| Independent | independent | scalar | — | ✓ | Name or column reference of the independent (predictor) variable; must resolve to a numeric scalar series. |
| Dependent | dependent | scalar | — | ✓ | Name or column reference of the dependent (response) variable to be regressed against the independent variable; must resolve to a numeric scalar series. |
| Optimize | optimize | select | no | Whether to scan the fitted polynomial for an optimum value within [minimum, maximum]; default ‘no’ skips the optimisation step. | |
| Minimum | minimum | scalar | — | ✓ | Lower bound of the independent-variable search range used during optimisation; ignored when ‘optimize’ is ‘no’. |
| Maximum | maximum | scalar | — | ✓ | Upper bound of the independent-variable search range used during optimisation; ignored when ‘optimize’ is ‘no’. |
| Step | step | scalar | 0.0001 | ✓ | Step size for the grid scan over [minimum, maximum] during optimisation; default 0.0001 — reduce only if finer resolution is needed, as smaller values increase compute time. |
| Objective | objective | select | minimize | Direction of optimisation: ‘minimize’ finds the independent value yielding the lowest predicted response, ‘maximize’ finds the highest; default is ‘minimize’. | |
| Order | order | select | 1 | Polynomial degree of the regression fit (1 = linear, 2–5 = higher-order polynomial); select ‘auto’ to let the worker choose the best-fitting degree via cross-validation; default is 1. |
Outputs¶
| Label | ID | Type | Description |
|---|---|---|---|
| R2 of the Fit | r2 | scalar | Coefficient of determination (R²) of the polynomial fit; dimensionless scalar in [0, 1], where values closer to 1 indicate a better fit. |
| Optimum value | optimum_independent | scalar | Independent-variable value within [minimum, maximum] at which the fitted polynomial is minimized or maximized according to the chosen objective; only meaningful when ‘optimize’ is ‘yes’. |
| Independents | independents | keyvalue | Key-value map of the independent variable data points used in the regression, keyed by index or original label. |
| Dependents | dependents | keyvalue | Key-value map of the dependent variable data points used in the regression, keyed by index or original label. |
| Error vs Dependents | idc | vector | Vector of residual errors (predicted minus actual dependent values) plotted against the dependent variable, useful for diagnosing fit quality and heteroscedasticity. |
Disciplines¶
- ai_ml.supervised.regression
- data.curve.transform
- design_exploration.optimization
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