Model Data Generator

Overview

The model data generator produces synthetic datasets from a configurable regression model. Unlike the plain random generator, here a directed relationship between inputs and outputs is modeled — ideal for practicing and validating DOE analyses, regression, or optimization methods against a known "true" model.

Factors: The input variables (X1, X2, …) each with a min and max range. The factors are generated within this range according to the chosen sampling method.

Beta coefficients: The model coefficients for intercept, main effects, interactions, and optional quadratic terms. They define the "true" model — the generator model against which later analyses can be compared.

Interactions: Products of two or more factors (X1·X2, X1·X2·X3, …). Supported up to 5th order. Interactions are particularly important for interpreting DOE results.

Sampling method: Controls how factor combinations are generated — Monte Carlo (random), Latin Hypercube Sampling (LHS, more evenly spread), or full factorial (all combinations of a fixed number of levels).

Noise: Additional normally distributed measurement noise is added to the modeled Y value. This simulates realistic scatter and lets you control the signal-to-noise ratio.

Seed: With a fixed seed, every run produces the same dataset — important for reproducible training and comparisons.

Operation

• Add factors — name, min, and max for each input.
• Set the beta coefficients: intercept, main effects, and the interaction terms you want.
• Pick a sampling method: Monte Carlo for fast scatter, LHS for even coverage, full factorial for DOE training.
• Set the sample size n or the number of levels.
• Enter the noise level (e.g. σ = 0.5) — this controls the spread of the response.
• Optionally set a seed, then click "Generate".
• Use "Send to worksheet" to write the dataset as a new table into the worksheet.

Pitfalls

Too many interaction terms: Models with 4th or 5th order interactions are often unrealistic and hard to interpret. In practice main effects and 2nd order interactions dominate — only use higher orders when there is a specific reason.

Scale dependency of beta coefficients: A beta of 5 has very different impact depending on whether X runs from 0–1 or from 0–1000. Keep factor ranges in mind when designing the model, or code factors internally.

Noise vs. effect: If noise is larger than the effects, model parameters can hardly be recovered even with large samples. Pick the effect-to-σ ratio deliberately.

Full factorial explodes with factors: With k factors at l levels, you get l^k design points — 5 factors at 5 levels already gives 3 125. Only use full factorial for small factor counts.

Document the seed: Without a documented seed, a dataset is not reproducible — important for training, comparisons, and validation studies.

Synthetic stays synthetic: A model dataset has no measurement drift, no machine changes, and no operator effects. Real-world scatter often exceeds synthetic by a wide margin — re-validate methods in practice.