BUSINESS: DVD Sales Total sales of prerecorded video DVDs in recent years are given in the...

BUSINESS: DVD Sales Total sales of prerecorded video DVDs in recent years are given in the following table.

a. Number the data columns with x-values 1–5 (so that x stands for years since 2001), use power regression to fit a power curve to the data, and state the regression formula. [Hint: See Example 7.]

---

b. Use the regression formula to predict DVD sales in the year 2012.

Source: Standard & Poor’s Industry Surveys

Example 7 POWER REGRESSION USING A GRAPHING CALCULATOR

The following graph gives the total annual U.S. sales of digital mobile telephones from 2003 through 2007.

Source: Euromonitor International

a. Use power regression to fit a power curve to the data and state the regression formula.

---

b. Use the regression formula to predict digital mobile telephone sales in 2012.

Solution

a. We number the years with x-values 1–5, so x stands for years since 2002 (we could choose other x-values instead, but with power regression the x-values must all be positive). We enter the data into lists, as shown in the first screen below (as explained in Graphing Calculator Basics—Entering Data on page xxiii) and use ZoomStat to graph the data points.

Then (using STAT, CALC, and PwrReg), we graph the regression curve along with the data points.

The regression curve, which fits the points reasonably well, is

y = 328x0.143 Rounded

---

b. To predict sales in 2012, we evaluate Y1 at 10 (since x = 10 corresponds to 2012). From the screen on the left, if the current trend continues, digital mobile telephone sales in 2012 will be approximately 456 million units.