Hi Byron,
We can break it down in parts:
– R2, R-squared, R^2: This is also called the coefficient of determination. Compared to other statistical methods or economic papers, BN are not using it in a overly complicated manor. My interpretation is this: there is a strong coefficient of determination between oil prices and differential EPS of oil companies. Therefore, it is likely for differential EPS to increase with rises in oil prices, and it is likely for a fall in oil prices to hurt differential EPS. Essentially, war in the Middle East can send the price skyrocketing, and price inflation is the main method for oil companies to profit relative to a benchmark, such as the S&P 500.
– Tying this to OPEC: In my opinion, they are anticipating counter-claims that studying oil in the Middle East is “more complicated” than they present. I imagine a scenario where someone at the end of a presentation says “What about OPEC and its conflict with the interests of [American and British] oil companies?” BN are not denying there is more to research in historical detail, but their evidence shows OPEC exports are not depressing the strength of the relationship between oil prices and profit.