BIOMEDICAL: Tainted Meat After falling for many years, tire incidence of E. coli sickness...

BIOMEDICAL: Tainted Meat After falling for many years, tire incidence of E. coli sickness in the United States from consuming tainted meat began to increase in 2005, as shown in the following table.

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. Assuming that this trend continues, use the regression function to predict the number of cases per million people in the year 2010.

Source: Centers for Disease Control and Prevention

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.