Chapter 11.10, Problem 70E

1. a Calculate SSE and S² for Exercise 11.4. Use the matrix approach.
2. b Fit the model suggested in Exercise 11.4 for the relationship between audited values and book values by using matrices. We can simplify the computations by defining

$x_i^{*}=x_i-\bar{x}$

and fitting the model $Y={\beta }_0^{*}+{\beta }_1^{*}{x}^{*}+\epsilon$. Fit this latter model and calculate SSE. Compare your answer with the SSE calculation in part (a).

11.4 Auditors are often required to compare the audited (or current) value of an inventory item with the book (or listed) value. If a company is keeping its inventory and books up to date, there should be a strong linear relationship between the audited and book values. A company sampled ten inventory items and obtained the audited and book values given in the accompanying table. Fit the model $Y={\beta }_0+{\beta }_{1}x+\epsilon$ to these data.

1. a What is your estimate for the expected change in audited value for a one-unit change in book value?
2. b If the book value is x = 100, what would you use to estimate the audited value?