I've had this discussion before on this forum but the difference between the r squares when using price and when using returns are so different that I thought it necessary to bring it up again. The attached charts are a scatter plot of the AMEX Oil Index and NYMEX prompt Crude contract. I get a very strong R squared when plotting price against against the Index. The r square is very weak when the retruns are plotted against each other. Intutively, price against price makes sense; why: because oil stocks should increase in value if the price of oil increases and the index should exhibit a strong correlation to the price of oil. However, in finance, we uses returns to determine correlations. And so the question: what do we use?The question i'm trying to answer is: What is the impact of a $1 or 1% change in the price of Crude on the Index? Any suggestions?Thanks.

The reason could be that magnitudes of the change are not linearly correlated. i.e. a 5% increase in oil price does not correspond to a 5% increas in the price index. The increase in index may only be 1%.When you are plotting the actual prices, you are basically plotting the directional movement. An increase in oil price increases the oil index and hence the linear correlation.

re: I've had this discussion before on this forum but the difference between the r squares when using price and when using returns are so different that I thought it necessary to bring it up again. i think this is more a statistical problem - not one concerning these two specific time series. If the residuals of your first regression (on the levels) exhibits auto correlation pattterns, if they are heteroscedastic or if they are not normally distributed (use Jarque Bera Test, White Test and Durbin Watson Test for diagnostic checking) you may run into problems and the high R^2 may mislead you. You should not use levels but returns for your linear regression model then. thats a common feature in time series modeling, and regressions. In general you can assume the following:If you use integrated time series (levels) for regression you will end up with misleading results - difference the time series in order to get a stationary process. If you dont find high R^2 in the regression of the differences then try some simple lead/lag models and check for lagged correlations of the two time series. Maybe you will be able to explain more. As rks said correctly, maybe the dependency is not linear - try models that capture convex/concave relations! hope it helps.f.