I just need a simple yes/no answer (hopefully yes) to confirm I haven't done something stupid here - I'm doing some data analysis and looking at the correlation of 2 variables X and Y over the past 6 years. My correlation over these 6 years comes out in MS Excel as 96% (that is, the usual definition of correlation as detailed here http://office.microsoft.com/en-us/excel-help/correl-HP005209023.aspx): however, my correlations for each of these 6 years are 73%, 84%, 95%, 42%, 84% and 82% supposedly.
Is this possible, that the 6yr correlation is so much higher than any of the individual ones? I was surprised at how much higher the 6-year correlation was than any of the yearly ones. From drawing a picture this seems plausible, but I couldn't find any simple mathematical justification for the fact without things in the formula getting extremely messy, and there are a few hundred data points per year so it's not really feasible to check my data by hand.