. Suppose you have conducted a randomized controlled trial of an intervention [TRT = 1] vs. placebo [TRT = 0], where n1 and no patients received the intervention and placebo, respectively. For each patient, you have measured a continuous outcome Y with the goal of comparing E[Y|TRT= 1] to E[Y|TRT=0]. I ask that you t the following linear regression model: Y,- : BO + 31X, + 55,2, iid N(0,02),X,- : 1 if TRT : 1,0 if TRT : O a. Write out the model above using matrix notation and then using matrix calculations solve for the least squares estimates of BB and Bl and Var(1). HINT: You will show that the model above is the same as conducting a two- sample t-test, assuming the same variance in the intervention and placebo groups. The estimate of the intercept should be the sample mean in the placebo arm, the estimate of the slope should be the difference in the sample means comparing the intervention and control groups and the Var(1) : 02/110 + 02/311