Solve the double inequality

Question

Solve the double inequality -t_{α/2,n-2 α/2,n-2} with t given by the formula of Exercise 25 so that the middle term is y₀ and the two limits can be calculated without knowledge of y₀. Note that although the resulting double inequality may be interpreted like a confidence interval, it is not designed to estimate a parameter; instead, it provides limits of prediction for a future observation of Y that corresponds to the (given or observed) value x₀

Exercise 25

Use the results of Exercises 20 and 21 and the fact that

is a random variable having a normal distribution with zero mean and the variance

Exercises 20

Under the assumptions of normal regression analysis, show that

(a) the least squares estimate of α in Theorem 2 can be written in the form

(b)  has a normal distribution with

Theorem 2

Exercises 21

This question has been intentionally omitted for this edition.