A data scientist has developed a logistic regression model to predict the likelihood of loan default, where the outcome variable is binary (1 for default, 0 for no default). The model uses a logit link function. After training, the coefficient for the continuous predictor variable DebtToIncomeRatio is 0.05.
How should the data scientist interpret this coefficient?
For each one-unit increase in the DebtToIncomeRatio, the odds of the loan defaulting increase by a factor of 1.5.
For each one-unit increase in the DebtToIncomeRatio, the probability of the loan defaulting increases by 5 %.
For each one-unit increase in the DebtToIncomeRatio, the odds of the loan defaulting increase by 0.05.
For each one-unit increase in the DebtToIncomeRatio, the log-odds of the loan defaulting increase by 0.05.
In a logistic regression with a logit link, coefficients represent changes in the log-odds of the outcome. A coefficient of 0.05 means that for every one-unit increase in DebtToIncomeRatio, the log-odds of defaulting rise by 0.05. Converting to odds, the multiplicative change is exp(0.05) ≈ 1.051 (a 5 % increase). Thus:
Log-odds interpretation is correct.
Probability interpretation is wrong because the relationship between predictors and probability is nonlinear.
The distractor stating a 1.5× change in odds is incorrect because it mis-computes exp(0.05).
The distractor giving an additive 0.05 change in odds is wrong because coefficients affect log-odds, not odds directly.
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What are log-odds in logistic regression?
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Why can't you directly interpret logistic regression coefficients as changes in probability?