Question: Consider a logistic regression model with a linear predictor that includes an interaction term, say (mathbf{x}^{prime} boldsymbol{beta}=beta_{0}+beta_{1} x_{1}+beta_{2} x_{2}+beta_{12} x_{1} x_{2}). Derive an expression for

Consider a logistic regression model with a linear predictor that includes an interaction term, say $\mathbf{x}^{\prime} \boldsymbol{\beta}=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{12} x_{1} x_{2}$. Derive an expression for the odds ratio for the regressor $x_{1}$. Does this have the same interpretation as in the case where the linear predictor does not have the interaction term?

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