EXAMPLE 5 Interpreting the Slope of a Regression Line

The slope of the line in Example 4 is . This says that as we move to the right along the line, predicted BAC goes up by 0.01796 for each additional beer that a student drinks. So, if a student has 3 additional beers, the BAC would increase by . The slope tells us how quickly changes as we change , which is important for understanding the pattern in the data. The slope is positive () when there is a positive association between the variables, as there is between BAC and beers consumed. It is negative when there is a negative association.

You might think that because the slope is small that , beers consumed, has little influence on , BAC. Unfortunately, the size of a slope is affected by the units in which we measure the two variables. In Table 6.1, BAC is measured in grams of alcohol per deciliter (g/dl) of blood. That is, when the number of beers consumed increases by 1, the alcohol in a deciliter of blood increases by 0.01796 grams. There are 1000 milligrams in a gram. So, if we changed the BAC units to milligrams of alcohol per deciliter (mg/dl) of blood, the slope would be 1000 times as large: . You can’t say how important a relationship is just by looking at how big the slope is.