EXAMPLE 1 Beer and Blood Alcohol
How well does the number of beers a student drinks predict his or her blood alcohol content (BAC)? In a study at The Ohio State University, 16 student volunteers drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC in grams of alcohol per deciliter of blood. Throughout the United States, the legal BAC limit is 0.08. Here are the data:
| Student | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Beers | 5 | 2 | 9 | 8 | 3 | 7 | 3 | 5 |
| BAC | 0.10 | 0.03 | 0.19 | 0.12 | 0.04 | 0.095 | 0.07 | 0.06 |
| Student | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| Beers | 3 | 5 | 4 | 6 | 5 | 7 | 1 | 4 |
| BAC | 0.02 | 0.05 | 0.07 | 0.10 | 0.085 | 0.09 | 0.01 | 0.05 |
The students were equally divided between men and women and differed in weight and usual drinking habits. Because of this variation, many students don’t believe that the number of drinks ingested predicts BAC well. What do the data say?
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Figure 6.2 is a scatterplot of these data. Because we think that the number of beers helps explain BAC, “number of beers” is the explanatory variable and hence is put on the horizontal axis. This is also indicated by the wording used in the Figure 6.2 caption—it is common usage for the word “against” to follow the response variable and precede the explanatory variable. in terms of plotting the data values, one student (Student 2) drank 2 beers and had a BAC of 0.03. This student’s point on the scatterplot is (2, 0.03), above and to the right of . We have marked this point in Figure 6.2.
