How do you interpret a coefficient in a multiple linear regression?
easyAnswer
- The coefficient is the expected change in y per one-unit increase in while holding all other features fixed — the partial or ceteris-paribus effect.
- Sign gives the direction; magnitude depends on the scale of .
- If features are standardized, | comparable across features (standardized beta / beta weight).
- Careful: 'holding others fixed' only makes sense if features are not perfectly collinear.
Check yourself — multiple choice
- The coefficient equals the correlation with y
- It's the expected change in y per unit increase in , holding other features fixed
- It's the contribution of that feature
- It's independent of other features
Coefficients are conditional (partial) effects — 'holding other features fixed'.
#linear-regression#interpretability
Practise Supervised Learning
215 interview questions in this topic.
Related questions
- Why does OLS have a closed-form solution but logistic regression doesn't?
- What are the classical assumptions of linear regression?
- What is VIF and when do you worry about multicollinearity?
- How do you handle strong multicollinearity in a linear model?
- How do you detect and fix heteroscedasticity?
- Adding a feature raised R^2. Does that mean the model improved?