Statistics · medium
Asked in Data Analyst interviews, in the Statistics round.
A one-unit increase in the feature is associated with a coefficient-sized change in the outcome, holding the other features fixed. Wrong when features cannot move independently, when the relationship is nonlinear, when the outcome is logged or logistic, or when you read it as causal.
The textbook sentence: a one-unit increase in x is associated with a b-unit change in y, holding the other predictors constant. Every clause in it can fail.
"Holding others constant" fails when the features move together. Age and years of experience cannot be varied independently, so the coefficient on one is answering a question nobody can act on.
"One-unit increase" depends on scale. A coefficient of 0.002 on income in dollars and 2 on income in thousands describe the same effect. Standardize or state the units.
Transformed outcomes change the reading. With log(y), a coefficient b means roughly a 100 times b percent change in y for small b. In logistic regression the coefficient is a change in log odds, and exp(b) is the odds ratio, which is not a probability change.
Nonlinearity means there is no single slope. If the true relationship curves, the coefficient is the average slope over the range of the data and can be zero for a strong U-shaped effect.
And none of it is causal without design. A regression on observational data with controls is a description of the data, not an intervention.