# Question

With x01, x02, . . . , x0k and X0 as defined in Exercise 14.39 and Y0 being a random variable that has a normal distribution with the mean β0 + β1x01 + · · · + βkx0k and the variance σ2, 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 – α) 100% limits of prediction for a future observation of Y0.

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 – α) 100% limits of prediction for a future observation of Y0.

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