Question: With x01, x02, . . . , x0k and X0 as defined in Exercise 14.39 and Y0 being a random variable that has a normal

With x01, x02, . . . , x0k and X0 as defined in Exercise 14.39 and Y0 being a random variable that has a normal with the mean Î²0 + Î²1x01 + · · · + Î²kx0k and the variance Ïƒ2, it can be shown that

Is a value of a random variable having the t distribution with n €“ k €“ 1 degrees of freedom.
(a) Show that for k = 1 this statistic is equivalent to the one of Exercise 14.25.
(b) Derive a formula for (1 €“ Î±) 100% limits of prediction for a future observation of Y0.

n-k-1

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