With the goal of estimating the relationship between BAC and VSR, a number of regression relationships were estimated. As the relationship between BAC and volume flattens out (see Figure 2), models that might estimate VSR from BAC would produce a curve that could not reproduce the vertical line for the relationship at higher BAC levels. Therefore, BAC (y-axis) was instead estimated from VSR (x-axis) and the relationship inverted. After examining the bivariate relationship, (more easily seen in the aggregate-level relationship in Figure 2) between BAC and VSR, several potential regression models (including linear, quadratic, cubic) were considered. Curvature in the bivariate relationship was followed by a flattening out of the average BAC levels at higher volume levels that quadratic models could not possibly capture. Although cubic regression models were estimated, it was decided to choose fractional polynomial regression models over cubic models as they allow for a more flexible estimation of the curve while incurring only slightly more complexity in the estimated functional form. The fractional polynomial model was of the form y = α + β1xa + β2xb +
