Suppose we have a binary covariate m1 6 {0, 1}; and a continuous covariate 322 E R which is standardized to have sample mean 0 and variance 1. We also have a response variable :9 that follows the linear model 3} = 50 + 51331 + 5232 + 53271232 + 6: with the usual assumptions on e. 0 Suppose we t a linear model with for y on 331 and 332 without including the interaction term $132. What will be bias of the least squares estimators [31 and g? 0 Now, if we t a linear model including the interaction term so that 2*} = 30 + 31331 + 32332 + 33mm. In the setting of the tted mode, we want to test the hypothesis that El?! I 1171 = 1,$2=a) =E(y I $1 =012 =0)- Devise a test for this hypothesis and derive an expression for the power of rejecting this null hypothesis as a function of a (and any other quantities needed). Recall that the power is the probability of rejecting the null hypothesis under an alternative