EXAMPLE 4 Predicting Blood Alcohol Content (BAC)

The scatterplot in Figure 6.2 shows a straight-line relationship between how many beers a student drinks and his or her BAC 30 minutes later. Figure 6.6 repeats this scatterplot and adds a regression line that summarizes the pattern of the data. We can use this line to predict BAC for a student based on the number of beers consumed.

Figure 6.6 shows the prediction in graphical form for a student who drinks 6 beers. Start at , go up to the line, and then head left to the y-axis. We hit the y-axis at . This is the BAC that corresponds to 6 beers, according to the regression line. (Recall that the legal limit for driving is 0.08.) The line represents only the overall pattern of the data, so the BAC of a randomly chosen student after 6 beers will probably not be exactly 0.095. But because the points for the 16 students in the Ohio State study are not far from the line, we expect the prediction to be reasonably accurate.

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However, for a more precise prediction, it is easier to use the equation of the line than to estimate the prediction from the graph. With the application of formulas that will be given in Section 6.4, the equation of the line in Figure 6.6 is

For a student who drinks 6 beers, we have

Because two points determine a unique line, you could plot a line by using its equation to determine any two particular points that lie on that line, plot those points, and then draw the line through them. For example, from the equation

we just determined that one point is (6, 0.095). By plugging in , we could obtain another point. Drawing the line through those two points yields the line in Figure 6.6.