Regression Coefficient Plot VIP Exclusive
📐 What is this?
The VIP plot tells you "which variables are important", the S-Plot tells you "which variables are trustworthy", but neither directly answers the most basic question:
"If this variable changes a little, how much does the result change?"
The regression coefficient plot gives exactly this answer——it lays out the model's regression coefficients by variable, showing the size and direction of each feature.
🧐 How to read?
Bar direction: decides "which way to adjust"
| Direction | Meaning |
|---|---|
| Positive (upward) | The variable increases → the predicted result increases (positive correlation) |
| Negative (downward) | The variable increases → the predicted result decreases (negative correlation) |
💡 The most valuable thing about this chart is the direction. VIP only tells you "important"; the coefficient plot tells you "which direction to adjust"——which is exactly what process optimization really needs.
Bar length: decides "how much to adjust"
- The larger the absolute value of the coefficient → the stronger the variable's influence on the result
- A bar close to 0 → the variable hardly affects the result
⚠️ Coefficient magnitudes cannot be compared directly across variables——unless all variables have been standardized. If a variable naturally has a large scale (e.g. temperature 300 vs pH 7), its coefficient will naturally be smaller, which does not mean it is unimportant.
🛠️ How to use?
Configuration items
| Configuration item | Description |
|---|---|
| Number of components | Choose the latent variable / principal component to view (1 ~ optimal number of components) |
Click Draw to generate. Switching components lets you observe how the coefficients change with the number of components.
Typical uses
| Purpose | Method |
|---|---|
| Determine the adjustment direction | Find variables with a positive coefficient for target Y → increasing them is expected to raise Y |
| Identify inhibiting factors | Variables with a negative coefficient and a large absolute value → they are the "resistance" when raising Y |
| Cross-validate VIP | Only variables with a large coefficient and VIP > 1 are truly reliable levers |
| Check business plausibility | If a variable's coefficient direction contradicts process common sense → watch out for data leakage or collinearity problems |
🎯 Division of labor with the VIP plot
| Chart | Question it answers | Does it give direction |
|---|---|---|
| VIP Plot | Who is important? | ❌ Only magnitude |
| Regression Coefficient Plot | Which way to adjust? By how much? | ✅ Has direction |
| SHAP Plot | How does it contribute on each sample? | ✅ Has direction, and per sample |
💡 Recommended combination: VIP screens the candidates → coefficients set the direction → SHAP shows individual differences. Only by using the three together can you move from "which variables are important" to "specifically how to adjust them".
⚠️ Notes
- Only supervised models are supported (PLS / PLS-DA / OPLS / OPLS-DA)
- OPLS model coefficients are "equivalent coefficients": the platform has projected the corrected coefficients back into the original variable space, so they can be interpreted directly in terms of the original process variables
- Collinearity distorts coefficients: for two highly correlated variables, the coefficients may be one large positive and one large negative (canceling each other out); in this case judge with business knowledge or consider removing one of them
- Coefficients are not causation: a large coefficient only means "statistically strongly associated"; to confirm causation use Causal Inference (DML)