When your experimental data shows curvature or a clear peak, a linear model is no longer enough. Use this method to map complex relationships between multiple factors and your results. It helps you visualize where your process performs best, such as finding the exact temperature and pressure for peak yield.
Mapping Complex Process Trends
A quadratic response surface creates a mathematical map of how your inputs, such as temperature, pressure, or time, interact to affect a final output. By fitting a second-order polynomial, this method accounts for both the main effect of each factor and how they influence one another.
This is particularly useful when you need to move beyond simple 'increase x to get more y' logic and into 'find the perfect combination of x and z' territory.
Understanding the Model Output
The analysis yields a detailed coefficient table that clarifies which factors are statistically significant. It separates the influence of individual factors, their squared terms (which represent curvature), and their interactions (where one factor's impact changes based on the level of another).
All calculations are performed using encoded levels to ensure that coefficients are directly comparable, regardless of the different units—such as Celsius or PSI—used for your inputs.
From Data to Decision
Once the model is built, you can use the resulting data to generate visual contour plots or 3D surfaces. These visualizations make it clear where your process achieves the highest performance and where you should focus your operational range.
Because this method is deterministic, the output is clear and based strictly on the experimental runs you provide, ensuring the insights you gain about your process window are reproducible and mathematically grounded.
1 · Intent → method
An LLM picks rsm_fit_quadratic from a fixed catalog.
2 · Method → numbers
Deterministic Python engine runs the math. Same input → same output.
3 · Numbers → plain language
A second LLM translates the result into your domain’s vocabulary.
Why is this better than a simple linear model?
A linear model only assumes straight-line trends. A quadratic response surface adds 'square' and 'interaction' terms, allowing the model to capture curves, peaks, and valleys in your data that simple models would miss.
What happens if my data doesn't fit a quadratic shape?
Lattice provides diagnostic tools to check your model. If the results show a high lack-of-fit or poor statistical indicators, you can review the diagnostics to decide if you need to refine your experimental design or adjust which factors are included.
Tool input schema
Schema for rsm_fit_quadratic not exported yet (run pnpm export:registry).