*By: **Bart Baesens, Seppe vanden Broucke*

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**You asked: **How can you interpret the coefficients of a logistic regression model?

**Our answer: **

Logistic regression estimates the following model:

,

where Y corresponds to fraud, default, churn, response, etc. and X_{1}, …X_{N} are the predictors (e.g. age, income, etc.). This can be reformulated in terms of the odds as follows:

The log(odds) or logit then becomes:

To interpret a logistic regression model, one can calculate the odds ratio. Suppose variable X_{i} (e.g. age, income, etc.) increases with one unit with all other variables being kept constant (ceteris paribus), then the new logit becomes the old logit with β_{i} added. Likewise, the new odds become the old odds multiplied by e^{βi}_{. }The latter represents the odds ratio, i.e. the multiplicative increase in the odds when X_{i} increases by 1 (ceteris paribus). Hence,

- β
_{i }> 0 implies e^{βi}> 1 and the odds and probability increase with X_{i} - β
_{i }< 0 implies e^{βi}< 1 and the odds and probability decrease with X_{i}

Another way of interpreting a logistic regression model is by calculating the doubling amount. This represents the amount of change required for doubling the primary outcome odds. It can be easily seen that for a particular variable X_{i}, the doubling amount equals log(2)/β_{i}.