We are often interested in predicting octane performance in cars as a function of Research and Motor octane numbers. Prediction equation parameters can be developed by regressing data taken directly from Coordinating Research Council reports on annual car octane requirement surveys. However, there is a major problem with these data. They are pooled in such a way that data points for different fuel series do not correspond to the same cars in each case. This paper presents a better method that makes use of Individual car data and also fuel data.