# Question: With x01 x02 x0k and X0

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.

## Relevant Questions

The following data give the diffusion time (hours) of a silicon wafer used in manufacturing integrated circuits and the resulting sheet resistance of transfer: (a) Find the equation of the least squares line fit to these ...Use the coding of Exercise 14.15 to rework both parts of Exercise 14.42. In exercise When the x’s are equally spaced, the calculation of and can be simplified by coding the x’s by assigning them the values . . . ,- ...With reference to Exercise 14.44, test the null hypothesis β = 0.350 against the alternative hypothesis β < 0.350 at the 0.05 level of significance. In exercise Raw material used in the production of a synthetic fiber is ...With reference to Exercise 3.71 on page 100, find an expression for µY|x. With reference to Exercise 14.67, use the formula obtained in Exercise 14.31 to construct a 99% confidence interval for ρ. In exercise FormulaPost your question