Question 3 Consider a full rank linear model y = X3 + e. We wish to derive the formula for a prediction interval for the sum of the responses of two independent future observations with predictors x] and x2 respectively. This uses the unbiased point estimator (x1 + x2) b, where b is the least squares estimator of B. (a) Calculate the variance of the prediction error of this estimator. (b) Show that this estimator is normally distributed. (c) Show that this estimator is independent of SSRes