Consider fitting the model Y = 0 + 1 x 1 + b 2 x 2 + to the following data: a.

Consider fitting the model Y = β₀ + β₁x₁ + b₂x₂ + ε to the following data:

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

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

c. Determine ŷ and e. Then calculate SSE, and use this to get the estimated variance MSE.

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

e. Carry out a t test for the hypothesis H₀: β₁ = 0 against a two-tailed alternative, and interpret the result.
f. Form the analysis of variance table, and carry out the F test for the hypothesis H₀: β₁ = β₂ = 0. Find R² and interpret.

X1 -1 1 1 X2 -1 1 1 y 1 1 04