Please provide detailed explanation.

In a multiple linear regression model Y = Bo + Bit1 + B2x2 + e with e ~ N(0, 02), the design matrix X, response vector Y and (X X)-1 are given below. 0 1 0 N 1 0 3 1 04 0.65 -0.20 -0.15 1 0 5 X = Y = -0.20 0.40 0.00 1 1 1 ( X X) -1 = -0.15 0.00 0.05 1 2 (a) (2 points) Please calculate the ordinary least squares estimates of B = (Bo, B1, B2) T. (b) (2 points) Please calculate the fitted values from this model and further provide an unbiased estimate of the error variance o2 (c) (2 points) Please construct 95% confidence intervals for B1 and B2. (d) (2 points) Please test the hypotheses Ho : B2 = 1 vs Ha : B2 # 1. (Hint: One needs to clearly state each step of a complete hypothesis testing process.) (e) (2 points) Please give a point estimate and a 95% confidence interval for the quantity / = Bo + B1 + 3B2. (f) (2 points) Please predict the response value for a new observation with x1 = 0 and $2 = 5 and give a 95% prediction interval