I have 50 thickness data points off 50 wafers from machine A1 and machine A2. Let's assume 25/machine.
I have 50 sheet resistance data points off the same 50 wafers used above but on machine B1 and B2. Let's assume for the time being that wafers measure on A1 were measured on B1 and A2 on B2, for simplicity.
What is the best way to analyze this data for correlation between thickness and sheet resistance? Simple y by x/any other method that takes into account the sensitivity of these 2 different tool sets (A/B) so that I have more precise resolution?
I think the answer very much depends on exactly what you are trying to accomplish (what any results would be used for), and the details of how the data is collected.
Looking at your 'simple' case (machines A1 and B1 only), I assume that you are able to identify which wafer is which. You mention that you have 50 measurements of thickness and 50 measurements of resistivity for each wafer. Important considerations are whether or not both measurements are made at the same physical location on the wafer (the same site), and whether or not you can identify and record which site is which. If so, then I would simply start with a scatterplot of resistivity against thickness, and use colours, markers and a local data filter to look for patterns of variation within and between wafers. What you see will help you to determine what kind of formal analysis may be required.