Multiple regression and model checks

Learning objectives

• Build a multiple regression model driven by process theory.
• Detect collinearity and confounding.
• Validate residuals and predictions.

Model discipline

Choose predictors from the process theory, not from a shopping list. Check VIF for collinearity, residual diagnostics for shape and influence, and validate on held-out data when possible.

Coefficient meaning is conditional on the other terms in the model.

Garment-factory example

Explain seam strength using SPI, thread ticket, needle size, fabric weight and selected interactions; validate on a held-out sample of the same fabric family.

Method

1. State the causal/process model.
2. Clean predictors and code categoricals.
3. Fit and inspect diagnostics.
4. Simplify only when theory supports it; validate.

Common mistakes

• Stepwise fishing without theory.
• Interpreting collinear coefficients causally.