Consider the model Y = 0 + 1 x 1 + for the following data: a. Determine the X and y matrices

Consider the model Y =  β₀ + β₁x₁ + ε for the following data:

a. Determine the X and y matrices and express the normal equations in terms of matrices.

b. Determine the β̂ vector, which contains the estimates for the two coefficients in the model.

c. Determine ŷ and e.

d. Calculate SSE (by summing the squared residuals) and then the estimated variance MSE.

e. Use MSE and (X'X)^–1 to construct a 95% confidence interval for β₁.

f. Carry out a t test of H₀: β₁ = 0 against a two-sided alternative.

g. Carry out the F test of H₀: β₁ = 0. How is this related to part (f)?

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