Learning objectives
What you will be able to do
By the end of this lesson, you will be able to configure Minitab to search a controlled set of linear, interaction, and polynomial terms—and distinguish a model that merely fits the current data from one that is likely to predict new production data.
Construct
Build a candidate model with main effects, squares, and defensible interactions without creating an uncontrolled term explosion.
Configure
Use centering, hierarchical forward selection, and cross-validation correctly in Minitab.
Compare
Challenge polynomial regression with MARS and automated machine-learning models while preserving interpretability.
Diagnose
Review residual patterns, VIF, leverage, Cook’s distance, time order, and extrapolation risk.
Select
Choose the simplest model whose validation performance is practically equivalent to the strongest competitor.
Defend
Document the model search, validation design, limitations, and engineering rationale for technical review.
The real problem
You are not searching for the equation with the largest R²
A model can fit historical data extremely well and still fail on the next heat, coil, batch, customer, or production campaign. The objective is to find a model that balances predictive accuracy, stability, interpretability, and process credibility.
Track 1 — Interpretable polynomial regression
Search a controlled pool of main effects, square terms, and two-way interactions. This produces a conventional equation, coefficient table, VIF values, residual plots, and familiar engineering interpretations.
Track 2 — Interpretable nonlinear regression
Use MARS when the process contains thresholds, slope changes, or operating regions that a single quadratic curve cannot represent well.
Step 1
Build a large enough—but still defensible—candidate pool
Start with process physics and measurement logic. Give Minitab plausible terms to consider; do not ask it to manufacture meaning from every mathematical combination.
Candidate-term builder
See how quickly model complexity grows as you add squares, interactions, and individual cubic terms.
14 terms
candidate terms, excluding the intercept
Recommended first-pass candidate model
This is exactly what Minitab’s Terms through order: 2 option creates for selected continuous predictors: powers through order 2 and interactions through order 2. If categorical predictors are selected, Minitab also creates the applicable interactions with those predictors.
Use individual cubic terms only when justified
Add Xᵢ³ selectively when process knowledge or residual curvature suggests asymmetric behavior that a quadratic cannot represent. For more complicated nonlinear structure, MARS is usually a better challenger than a high-order global polynomial.
Hierarchy challenge
Select every lower-order term required to support the chosen higher-order term.
Step 2
Design validation before model selection
Validation is part of the model-building design—not a final decorative statistic. Decide what constitutes an independent future prediction before opening the regression dialog.
Prevent group leakage
If multiple rows come from the same heat, coil, pipe, batch, customer, production campaign, or test specimen, keep that entire group in one fold. Otherwise, the validation set contains near-duplicates of information already seen during training.
Random rows vs grouped folds
Toggle the split method and observe whether the same production group appears in both training and validation folds.
CV_Fold containing fold labels 1–5 or 1–10. Assign every row from the same heat or coil to the same fold label. Do not use a raw identifier with hundreds of unique values unless those values are intentionally the folds you want Minitab to use.Recommended worksheet structure
| Column | Example | Role |
|---|---|---|
| Response | Yield Strength | Continuous outcome to predict |
| Continuous predictors | Temperature, CE, Gauge | Numeric inputs |
| Categorical predictors | Grade, Mill, Shift | Factor levels coded by Minitab |
| Group ID | Heat_ID | Defines the unit that must stay together |
| CV fold | 1, 2, 3, 4, 5 | Used by Minitab’s “Assign rows of each fold by ID column” option |
| Time order | Production timestamp | Used to detect drift, cycles, and serial dependence |
Step 3
Exact Minitab workflow: polynomial regression with validated selection
The sequence below is designed for a continuous response and a mix of continuous and categorical predictors.
1Define the model purpose and data boundaryPrediction target, operating range, grouping unit, and holdout logic⌄
State what the model will predict, for which population, and within what process range. Decide whether the validation target is a new row, a new heat, a new coil, a future campaign, or a later time period.
- Exclude post-outcome variables and data created after the prediction decision.
- Flag impossible values, missingness, duplicate records, and data-quality rules before fitting.
- Reserve a true future or external test set when the decision is high consequence.
2Open Fit Regression ModelAssign the response and predictor types correctly⌄
- Enter the continuous outcome in Response.
- Enter numeric process inputs in Continuous predictors.
- Enter grade, mill, product family, shift, operator, or other factors in Categorical predictors.
- Verify the categorical reference level under Coding so coefficients compare against a meaningful baseline.
3Create the candidate term poolMain effects, squares, and two-way interactions⌄
- Select the continuous predictors you want to expand.
- Choose Terms through order.
- Enter 2.
- Click Add.
- Review the term list and remove combinations that are physically impossible, redundant, or unsupported.
Terms through order 2 adds individual squares for continuous predictors and all interactions through order 2 among the selected predictors.
4Center continuous predictorsReduce nonessential collinearity from powers and interactions⌄
Centering changes each predictor from X to X − X̄. This reduces the artificial correlation between X, X², and interaction terms and makes lower-order coefficients meaningful near the center of the observed operating region.
Do not confuse centering with dividing by the standard deviation. Scaling can be useful for coefficient comparison, but it changes the unit interpretation.
5Configure forward selection with validationLet validation choose the model size⌄
- Method: Forward selection with validation
- Validation: K-fold cross-validation for smaller data; test-set validation for larger data
- Folds: 5 or 10 are practical starting points; Minitab’s regression default is 10
- Group-aware folds: Assign rows by a prepared fold-ID column
- Display: Include model-selection details
- Graph: Display R² versus model-selection step
6Enforce hierarchyKeep higher-order terms statistically coherent⌄
- Hierarchical model: Require a hierarchical model at each step
- Require hierarchy for: All terms
- Terms entering: Extra terms can enter to maintain hierarchy
For X₁X₂, retain X₁ and X₂. For X₁³, retain X₁ and X₁². For X₁²X₂, retain the applicable lower-order components required by the hierarchy rule.
7Request diagnostics and stored statisticsDo not stop at the selected equation⌄
- Display the four-in-one residual plots.
- Display VIF values and unusual observations.
- Store fits, residuals, standardized residuals, leverage, Cook’s distance, and DFITS when deeper investigation is needed.
- Plot residuals against production order or timestamp when the process is time-dependent.
8Interpret the validation curve—not only the peakPrefer a stable plateau over a fragile maximum⌄
If the highest validation R² occurs at step 12 but steps 7–10 are nearly identical, prefer the simpler model unless the additional terms provide a material, repeatable improvement.
- Compare training R² with validation R².
- Look for a widening training–validation gap.
- Check whether selected terms are stable under alternate fold assignments.
- Confirm coefficient directions and interactions make engineering sense.
Step 4
Challenge the polynomial with MARS regression
MARS—Multivariate Adaptive Regression Splines—fits connected piecewise functions. It is especially useful when the process has thresholds, breakpoints, or different slopes in different operating regions.
A “knot” at c allows the slope to change. This can be more interpretable than forcing one cubic curve across the full process range.
526.3 MPa
fictional predicted response
Minitab path and starting settings
Validation
Use K-fold cross-validation or a separate test set. Use a fold-ID column when groups must stay together.
Interactions
Start with an additive model or allow interactions up to order 2. Higher orders rapidly reduce interpretability.
Selection criterion
Compare maximum validation R² with minimum validation MAD. MAD is less influenced by the worst-fitting observations.
Step 5
Use Discover Best Model as a challenger—not an automatic final decision
With Minitab’s Predictive Analytics Module, Discover Best Model for a continuous response compares five model families: multiple regression, MARS, CART, TreeNet, and Random Forests.
Model-selection decision lab
Select a model, then apply the “simplest model within practical equivalence” rule.
| Model | Validation R² | Validation RMSE | MAD | Interpretability | Complexity |
|---|---|---|---|---|---|
| Polynomial regression | 84.6% | 11.2 | 8.2 | High | 8 terms |
| MARS | 88.9% | 9.4 | 6.8 | Good | 11 basis functions |
| CART | 82.1% | 12.1 | 8.9 | Medium | 14 terminal nodes |
| TreeNet | 89.3% | 9.1 | 6.6 | Limited | 300 trees |
| Random Forests | 88.5% | 9.6 | 6.9 | Limited | 500 trees |
Step 6
The selected model is only a candidate until it passes diagnostics
Validation performance answers “how accurately did this workflow predict held-out observations?” Diagnostics answer “is the model structurally credible, stable, and safe to use?”
Residuals versus fits
Look for random scatter around zero. Curvature suggests missing terms; fanning suggests nonconstant variance.
Residuals versus order
Trends, cycles, or shifts indicate dependence, process drift, omitted time effects, or a changing measurement system.
Normal probability plot
Strong curvature or distant points can make p-values and confidence intervals unreliable, even when point predictions remain useful.
Leverage and Cook’s distance
Investigate observations with unusual predictor combinations or disproportionate influence. Never delete a valid point only because it weakens the model.
Required final review
Prediction
Validation R², RMSE, MAD, and the gap between training and validation performance.
Complexity
Number of retained terms or basis functions; stability across alternate folds.
Collinearity
VIF values, coefficient instability, and redundant predictors.
Residual adequacy
Linearity, constant variance, normality when inference matters, and independence.
Influence
Leverage, Cook’s distance, DFITS, data quality, and sensitivity analyses.
Engineering validity
Logical signs, plausible thresholds, operating-range coverage, and no unsafe extrapolation.
Step 7
A defensible model-selection rule
Do not allow a single metric to decide. Use sequential gates so that a model cannot “win” on accuracy while failing interpretability, stability, or process logic.
When to reject the automated winner
- The improvement is smaller than normal measurement or process variation.
- The model relies on unavailable, delayed, expensive, or unreliable predictors.
- The validation split leaked information across the same production units.
- The model extrapolates beyond the observed operating region.
- The predictor effects contradict known physics without a plausible explanation.
- The model is unstable when folds, time windows, or influential points change.
Knowledge check
Can you run the workflow defensibly?
8-question applied quiz
Choose the strongest answer. Feedback is shown after submission.
Field checklist
Your model-selection standard work
Use this checklist each time you search for a predictive regression model in Minitab.
Verified sources
Official Minitab documentation
- Specify model terms for Fit Regression Model
- Specify coding and standardization
- Perform stepwise regression
- Specify the validation method
- Using stepwise and best subsets regression
- Interpret residual plots
- Overview of MARS Regression
- MARS validation methods
- Discover Best Model for a continuous response