A medical doctor has a few questions regarding the results of her regression analysis. She wishes to study of the effect of a treatment on the progression of a disease. For each patient, her dataset consists of a quantitative measure of disease progression, a binary predictor that indicates whether or not the patient received the treatment, and a vector of other covariates that include the patient's age, body mass index (BMI), and gender.

1. The doctor posits the effect of the treatment may be different from men and women. How should she adjust the model in (a) to separately estimate the effect of treatment on men and women? Specify the model and related model assumptions (please introduce proper notations).