Please assist in this homework practical. Please also provide screenshots of R outputs and code for a,b,c for extra practice.

For this question, there should be no visible R code and output. Consider the linear model 1'} = :30 + 31331: + 3231-2 + 51': where 5,; N N{0,02) independently, i = 1, 2, . . . , 5. Observations are takBH at m, = 3, 1, 0, 1, and 3. a) If we write the model in the matrix form: Y = X + e where 8 = $0,181, g)T, write down the design matrix X for the given model. b) Denote the least Squares eetirnatore by E! = (5'0, 81,33)? Find Var (E) as a function of 02. Hence deduce that 31 and 32 are uncorrelated. c) Determine if the observation at a: = 3 is a high leverage point