Consider a simple linear regression model with systematic component u Bo + Bx. Suppose we wish to design an experiment with n = 5 observations, when o2 is known to be 1. Suppose three designs for the experiment are considered. In Design A, the values of the explanatory variable are x = 1, 1, -1, -1 and 0. In Design B, the values are a = 1, 1, 1, 1 and -1. In Design C, the values are x = 1, 0.5, 0, -0.5 and -1. (a) Write the model matrix X for each design (b) Compute Var[] for each design. (c) Plot Var[] for g between 1 and 1. When would Design A be preferred, and why? When would Design B be preferred, and why? When would Design C be preferred, and why?