Chapter 4.4, Problem 3GP

To determine

Use the equation for line of fit for the table shown below for the sales of CDs in million dollar for a particular year and estimate the CD sales in year 2015.

Year	2000	2001	2002	2003	2004	2005
Sales	13215	12909	12044	11233	11447	10520

Answer to Problem 3GP

The estimated CDs sales in 2015 is 5130.

Explanation of Solution

Given information: The sales of CDs in million dollars for a particular year is shown in the table below.

Year	2000	2001	2002	2003	2004	2005
Sales	13215	12909	12044	11233	11447	10520

Graph: The scatter plot and line of fit graph for the bivariate data is shown as,

  

Calculation: The slope $\left(m\right)$ for the line of fit passing through the points $\left(2000,13215\right)\text{ and }\left(2005,10520\right)$ can be calculated as,

  $\begin{array}{c}m=\frac{10520-13215}{2005-2000}\\ =-539\end{array}$

Now, equation for the line of fit is written as,

  $\begin{array}{c}y-13215=-539\left(x-2000\right)\\ y-13215=-539x+1078000\\ y=-539x+\mathrm{1091215......}\left(1\right)\end{array}$

The number of CDs sales in 2015 can be calculated by plugging $\left(x=2015\right)$ in (1).

  $\begin{array}{c}y=-539\left(2015\right)+\mathrm{1091215......}\left(\text{Using }\left(1\right)\right)\\ =5130\end{array}$