How do you interpret a coefficient in logistic regression?
Each coefficient is the change in log-odds for a one-unit rise in that feature. Exponentiate it to get an odds ratio: a coefficient of 0.693 multiplies the odds by about 2.
Explain it simply
Logistic regression is linear in log-odds, not in probability. Odds are probability divided by the chance of the opposite: probability 0.75 means odds of 0.75 / 0.25 = 3 to 1, like a bookmaker's "3 to 1 on".
A coefficient says how the log-odds move when that feature increases by one unit, holding the others fixed.
Example
Suppose a model predicts "student gets placed" and the coefficient for each extra project is 0.693.
Odds ratio = e^0.693 = 2.0One more project doubles the odds of placement.
Start at a probability of 0.50 (odds 1). Doubling gives odds 2, which is probability 2 / (1 + 2) = 0.667. Start at 0.80 (odds 4): doubling gives odds 8, which is probability 8 / 9 = 0.889. The same odds ratio moves probability by different amounts, because the effect is constant on the odds scale, not on the probability scale.
coefficient 0 -> odds ratio 1 (no effect)
coefficient 1 -> odds ratio 2.72
coefficient -1 -> odds ratio 0.37 (odds fall by about 63%)For fair comparison between features, standardise them first so coefficients share a scale.
What to say in the interview
"A coefficient is the change in log-odds per unit of the feature; e to the power of the coefficient is the odds ratio. Positive coefficients raise the odds, negative lower them. It is not a change in probability, and the probability shift depends on where you start."
Common mistakes
- Saying a coefficient of 0.693 raises probability by 69.3 percentage points.
- Comparing raw coefficients of unscaled features.