days_to_payMore predictors is not a better model. Below is a live OLS regression predicting how many days a Summit Gear customer takes to pay an invoice. Toggle predictors in and out and watch three things move at once: the fitted coefficients (with confidence bands), R-squared and adjusted R-squared, and a correlation matrix that lights up whenever two predictors move together. The goal is to feel — not just be told — what multicollinearity does to a model you would otherwise trust.
New to reading how two columns move together? Warm up in the Correlation trainer first, then come back here to see what happens when you put predictors that move together into the same model.
Before you build anything, here is the pairwise correlation among every predictor on the table — computed once, always on. Read it like a heat map: a dark-red cell off the diagonal means those two columns move together, and two predictors that move together cannot be told apart by a regression. The size cluster — credit_limit, avg_balance, annual_spend — is the solid red block (pairwise r about 0.96 to 0.99). Keep that block in mind when you start toggling predictors below; putting two of its members into the same model is what destabilizes their coefficients.
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days_to_payTags: clean predictors carry independent signal, collinear ones move together (the size cluster), noise columns carry no real signal — random draws or decoys that do not move days-to-pay.
| predictor | coef | std err | 95% confidence |
|---|---|---|---|
| Select at least one predictor. | |||
Read a coefficient as: holding the others fixed, a one-unit rise in this predictor changes predicted days-to-pay by this many days.
This is the multicollinearity check. It is the same correlation matrix as the one up top, but restricted to the predictors you currently have in the model, so it updates every time you toggle one. A dark-red block off the diagonal is the warning sign: two predictors moving together is exactly what destabilizes their coefficients. Pull in two size-cluster members and their cell turns solid red — that hot cell is your cue to keep one and drop the rest.
| Select at least two predictors. |
Forward selection starts empty and repeatedly adds the single predictor that raises adjusted R-squared the most. Run it and watch where it plateaus: the clean predictors lift the model, then the collinear leftovers and the noise columns stop helping — adjusted R-squared flattens and even ticks down. That flattening is the signal to stop adding.