A regression model includes both years of work experience and age as separate independent variables, two measures that are naturally highly correlated with each other in most datasets, and the resulting coefficients on both variables come back unstable — sensitive to which specific observations are included, and prone to changing meaningfully, sometimes even flipping sign, with small changes to the model or dataset. This is multicollinearity: a statistical condition where two or more independent variables share so much overlapping information that the regression struggles to cleanly attribute the outcome's variation between them.
Why highly correlated predictors create this specific problem
A regression coefficient represents the estimated effect of one variable holding the others constant — but when two independent variables are themselves highly correlated, there's very little independent variation in one that isn't also present in the other, making it statistically difficult for the model to determine how much of the outcome's variation to attribute to each variable individually, even though the two variables together may predict the outcome quite well as a combined pair.
Why this specifically produces unstable, unreliable individual coefficients
With limited independent variation to work from, small changes in the specific data sample, or minor changes to which other variables are included in the model, can shift how the overlapping predictive power gets divided between the two correlated variables in the estimation process, producing coefficients that swing considerably in size and sometimes direction between what should be minor changes to the model — a direct, diagnosable symptom of the underlying multicollinearity rather than evidence that either individual variable's true relationship with the outcome is genuinely unstable in the real world.
The often-missed nuance about what multicollinearity does and doesn't affect
Multicollinearity primarily damages the interpretability and reliability of individual coefficients — it doesn't necessarily damage the overall model's ability to predict the outcome accurately using the full combination of correlated variables together, which is a distinction worth being precise about: a model with severe multicollinearity between two predictors can still make quite accurate overall predictions, while being nearly useless for answering the specific question of how much each individual predictor independently contributes.
What actually diagnoses and addresses this
The variance inflation factor, a standard diagnostic statistic calculated for each independent variable in a regression, directly quantifies how much a given variable's correlation with the other independent variables is inflating its coefficient's estimated variance — a high variance inflation factor is the standard, direct flag for problematic multicollinearity affecting that specific variable. Combining highly correlated variables into a single composite measure, or removing one of the redundant variables entirely when the research question doesn't specifically require distinguishing between their individual effects, are the most common practical remedies once multicollinearity is identified as a real problem for the specific analysis at hand.
What this means for building and interpreting a regression model with multiple predictors
- Check variance inflation factors routinely when including multiple, plausibly correlated independent variables in a model
- Treat an individual coefficient's instability across minor model changes as a specific signal to check for multicollinearity, rather than assuming the underlying relationship is genuinely volatile
- Consider combining or removing highly correlated predictors when the research question doesn't specifically require isolating each one's individual, independent effect
- Remember that overall model predictive accuracy can remain strong even when multicollinearity has made individual coefficients unreliable — the two are separate properties
Multicollinearity doesn't mean a model is wrong or useless — it means a specific question, how much each of several highly correlated variables individually contributes, often can't be answered reliably from that particular data, regardless of how sophisticated the regression technique applied to it happens to be.