Forgive me for my ignorance, but I've been asked a question that I need some stats help on (I'm not a statistician, and have only a rudimentary knowledge!).
I've been supplied a data set which compares a daily average rank against a success KPI. The daily average rank varies from 1-10 (continuous) while the KPI varies from 0 to 1 (also continuous).
From this data, I have fitted a decay curve, of the form
y ~ rank^-x , and simplistically run a grid search over values of x between 0.01 to 9.99 to maximise the adjusted r2. This may or may not be a good method (!) but the shape looks sensible and it's a better fit than a simple linear model.
The question I have been asked is: how much better is this at fitting the data than if I just take an average of the KPI at discrete ranks (i.e. rank=1, rank=2, ... rank=10 - given that the real world data [non-averaged] exists only at these positions) ?
I'm a bit stumped on how to actually quantify this! Can I calculate an "adjusted r2" for the combination of 10 discrete data points?
Thanks for any help!