Say I am interested in how many apples people eat in a year. This varies by many factors. First I look at the country difference (the US vs. Canada). From historical data of the average number of apples consumed every year, the correlation between these two countries is, say 0.7.

Then I want to look more closely, and this time also by age. By age I look at older (>=65) and younger (<65) groups and found the correlation coefficient is 0.8 in the US and 0.9 in Canada.

Now I compare younger group in the US to the older group in Canada. Without running through historical data again is there a way to calculate the correlation between these two sub-groups based on the above correlation coeffiecients?

I need this because there could be other variables I need to factor in, so that a comprehensive correlation coefficient matrix can be very large. And there are not enough data to support certain variables. If I can use a formula to derive the correlation as it goes it'll be much more efficient.

Thank you.