Textbook Problem

Modeling Data Personal consumption expenditures (in billions of dollars) for several types of recreation from 2008 through 2013 are shown in the table, where a is the expenditures on amusement parks and campgrounds, y is the expenditures on live entertainment (excluding sports), and z is the expenditures on spectator sports.

Year	2008	2009	2010	2011	2012	2013
X	38.3	37.2	38.8	41.3	44.4	46.5
y	24.3	25.2	26.3	28.3	28.4	28.7
z	19.4	18.8	19.2	20.4	21.2	22.3

Spreadsheet at LarsonAppliedCalculus.com

A model for the data in the table is given by

$-0.391x+0.069x+z=6.$

(Source: U.S. Bureau of Economic Analysis)

(a) Add a fifth row to the table using the model to approximate z for the given values of x and y. Compare the approximations with the actual values of z.

(b) According to this model, increases in expenditures of recreation types y and z would correspond to what kind of change in expenditures of recreation type x?