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. (a)[5 pts] The doctor wishes to estimate the effect of the treatment adjusted for a patient's BMI, age, and gender. What is the linear model she should fit? Specify the model and related model assumptions (please introduce proper notations).