BUSINESS: Quest Revenues Operating revenues of Quest Communication International for recen...

BUSINESS: Quest Revenues Operating revenues of Quest Communication International for recent years are given in the following graph.

a. Number the data columns with x-values 1–6 (so that x stands for years since 2000) and use quadratic regression to fit a parabola to the data. State the regression function. [Hint: See Example 10.]

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b. Use the regression function to predict Southwest's operating revenues in the year 2012.

Source: Standard & Poor’s Industry Surveys

Example 10 QUADRATIC REGRESSION USING A GRAPHING CALCULATOR

The following graph gives the total annual sales of Macintosh computers from 2001 through 2007.

Source: systemshootouts.com

a. Use quadratic regression to fit a parabola to the data and state the regression function.

b. Use the regression function to predict Macintosh sales in 2012.

Solution

a. We number the years with x-values 0–7, so x stands for years after 2000. 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 QuadReg) we graph the regression along with the data points.

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

y = 0.20x2 – 0.88x + 3.9 Rounded

b. To predict sales in 2012, we evaluate Y1 at 12 (since x = 12 corresponds to 2012). From the screen on the left, if the current trend continues, Macintosh sales in 2012 will be approximately 22.8 million units.