Reference no: EM131137235
Use the results obtained for the data of Example 9 and the result of part (b) of Exercise 40 to construct 99% limits of prediction for the sales price of a three-bedroom house with two baths in the given housing development.
Exercise 40
With x01, x02, ... , x0k and X0 as defined in Exercise 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 25.
(b) Derive a formula for (1 - α)100% limits of prediction for a future observation of Y0.
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.
Example 9
The following data show the number of bedrooms, the number of baths, and the prices at which a random sample of eight one-family houses sold in a certain large housing development:
Use the method of least squares to fit a linear equation that will enable us to predict the average sales price of a one-family house in the given housing development in terms of the number of bedrooms and the number of baths.
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Use the results obtained for the data
: Use the results obtained for the data of Example 9 and the result of part (b) of Exercise 40 to construct 99% limits of prediction for the sales price of a three-bedroom house with two baths in the given housing development.
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