Here is some context. I am interested in determining how two environmental variables (temperature, nutrient levels) impact the mean value of a response variable over a 11 year period. Within each year, there is data from over 100k locations.
The goal is to determine whether, over the 11 year period, the mean value of the response variables has responded to changes in environmental variables (e.g. warmer temperature + more nutrients would = greater response).
Unfortunately, since the response is the mean value (without looking at the mean, just regular inter-annual variation will swamp the signal), the regression will be 11 data points (1 mean value per year), with 2 explanatory variables. To me even a linear positive regression will be hard to consider as meaningful given that the dataset is so small (does not even meet the nominal 40 points/variable unless the relationship is super strong).
Am I right to make this assumption? Can anyone offer any other thoughts/perspectives that I may be missing?
PS: Some caveats: There is no way to get more data without waiting additional years. So the data that is available is what we really have to work with.