Machine Learning problem.

A logistic model can be used to evaluate the effect of a (binary) factor combined with other variables on the observed consequences. Consider the example as follows. In a five year follow-up study on N disease-free human subjects, researchers aim to assess the effect of the environmental exposure to a heavy metal (E=1, exposed or 0 not exposed) on the development (or not) of a certain disease. The continuous variables of interests are age (AGE) and obesity status (OBS), the environmental factor E of each subject was determined at the start of the study. Devise the logit form of a logistic regression model that assesses the interaction effects of AGE with E and OBS with E, and explain how the model can be learned from the data (where each data point represents a human subject with the known disease status (0/1), AGE, OBS and E). (Hint: the interaction effects of AGE and E can be modeled by a created variable AGEE=AGE * E; similar for OBSE=OBE * E. You also need to consider the effects of the independent variables AGE, OBS and E, respectively).