Please assist in this homework practical. Please ONLY USE R for this question showing the full code and outputs for extra practice.

Consider the linear model 1'2 = :30 + 5131+ 321?? +56\" where 8,- ~ N([},02) independently, i = 1, 2, . . . , 5. Observations are taken at 3,3 = -3, -1, 0, l, and 3. a) If we write the model in the matrix form: Y = X13 + e where [3 = (.60, 11, 32F, write down the design matrix X for the given model. b) Denote the least squares estirnators by E! = (1%, 31, 32)? Find Var (B) as a function of 0'2. Hence deduce that 31 and 32 are uncorrelated. c) Determine if the observation at :1: = 3 is a high leverage point