In the following problem, determine whether a straight line is a good model for the data....

In the following problem, determine whether a straight line is a good model for the data. You may do this either visually, by plotting the data points, or analytically, by finding the correlation coefficient for the least-squares regression line. (See Examples 5 and 6.)

Health The accompanying table shows the number of deaths per 100,000 people from heart disease in selected years.* Let x = 0 correspond to 1960.

Example 6

Education Enrollment projections (in millions) for all U.S. colleges and universities in selected years are shown in the following table*:

(a) Let x = 0 correspond to 2000. Use a graphing calculator or spreadsheet program to find a linear model for the data and determine how well il fits the data points.

Solution The least-squares regression line (with coefficients rounded) is

 

as shown in Figure 1. The correlation coefficient is r ≈ .96, which is very close to 1, so this line fits the data well.

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(b) Assuming the trend continues, predict the enrollment in 2014.

Solution Let x = 14 (corresponding to 2014) in the regression equation:

 

Therefore, the enrollment in 2014 will be approximately 19,959,300 students.

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(c) According to this model, in what year will enrollment reach 21 million?

Solution Let y = 21 and solve the regression equation for x:

 

Since these enrollment figures change once a year, use the nearest integer value for x, namely, 17. So enrollment will reach 21 million in 2017.

FIGURE 1

*As of fall of each year; Statistical Abstracts of the United States: 2008.

*U.S. National Center for Health Statistics.