Response-surface modeling
Set up, run, and review this analysis in Lifescio.
Supported analysis
Enter coded numeric factors and a response. The app fits a full quadratic model with main effects, squares and two-factor interactions, then searches within the observed range of each factor for the predicted maximum or minimum.
Supported scope: The data must support all quadratic terms with enough independent runs and a full-rank design. Convert physical settings to coded factors consistently. This is local quadratic optimization, not a guarantee of the best manufacturing process outside the studied region.
Prepare data and configure the analysis
Enter numeric coded factor columns followed by Response as the final column. The engine supports one to five factors and fits every linear, squared, and pairwise interaction term. Choose maximize or minimize and the significance level.
For two factors there are six coefficients, so more than six distinct-information observations are needed; the form also requires at least eight rows. The design must have full rank. Coding and decoding factors is your responsibility; the tool does not know their physical units or joint feasibility constraints.
Input reference (3 fields)
Enter your data and prespecified choices. Ranges include both limits. For table fields, use cell editing, Paste data, or Import CSV / TSV. Review whether the first imported row contains headings and map the source columns before applying the import. Empty numeric cells are not treated as zero. Open file is for an exported Lifescio analysis JSON file, not a spreadsheet.
| Input | Format | Allowed range | Guidance |
|---|---|---|---|
| Coded factors and response | Table | — | Columns in order: Factor 1; Factor 2; Response. |
| Optimization goal | Selection | — | Choices: maximize, minimize. |
| Significance level | Number | 0.001–0.2 | — |
Run and review
- Give the analysis a descriptive name and review every example value. Record units, data preparation, and planning assumptions in Reproducibility & notes. For simulations, record the seed and replication or sampling settings.
- Choose Run analysis. Resolve input errors before interpreting output. In the connected app, a run uses a saved input revision; local preview runs need the page to stay open.
- Review Diagnostics for method limitations, warnings, and available numerical checks. A completed run means computation finished; it does not establish that the assumptions fit your study.
- Use the Result table selector to inspect each output. Editing inputs does not recalculate existing results: an earlier-input notice means you need to run again to obtain matching results.
Understand the outputs
Quadratic coefficients lists the fitted terms and intervals. Predicted optimum reports coded coordinates and the fitted response within the observed minimum/maximum box. It is not an experimentally verified optimum.
Fit diagnostics contains residual degrees of freedom, residual standard deviation, and R squared. Inspect Residuals versus fitted before using the optimized setting. The output does not provide a confidence region for the optimum or impose additional process constraints beyond the rectangular bounds.
Troubleshooting and common mistakes
A rank-deficiency error means the supplied settings cannot distinguish the quadratic terms. Adding repeated copies of the same settings may not solve it; collect a design with appropriate factor levels and combinations.
If the optimum is at a boundary or an untested combination, verify feasibility and plan confirmation runs. A residual pattern or poor fit warrants model/design review. Reversing the optimization goal changes the question and should not be used to make an inconvenient result look better.
After correcting inputs, run again and check that the results belong to the new input snapshot. Increasing simulation draws improves numerical precision only; it does not repair invalid data or an unsuitable model.
Save, compare, and export
In the connected app, Save analysis retains the inputs in your account. Run history lets you inspect earlier runs, each with the input revision it used. In local preview, Save analysis downloads an input file instead; download results before leaving the page.
Use Result + inputs for a JSON archive containing the completed result and its inputs, Download CSV for the selected result table, PDF report for a report, and a chart's SVG button for its figure. Table displays round to three decimals; CSV and JSON exports retain calculation precision. Use those values when assessing a result near a decision boundary.
To reopen an archive, select the matching analysis method and choose Open file. Imported inputs start a new draft; a result archive can also display its retained result. It does not attach itself to an existing account analysis or recompute the result. Save or run the imported draft when you want a new account record.