This is the situation. I am running trials with a population simulator, which produces various outputs, with the variance of these outputs being dependent on the number of clones (recursions) the simulator has gone through.
Generally speaking, the higher the cloning; the lower the variance. My task is to prove this relationship. So my variables are x = # of clones (let's say 0 to 10), and y = total population. So far I've done several tests pertaining to things like %change between each x, and distance from the mean of each x, etc. to show the relationship, and now I would like to do the ln differences.
MY QUESTION IS: On Excel, would plotting the ln of y against x, then adding the "Logarithmic Trendline" option make sense? The log trendline seems to fit my data the best (for obvious reasons), and I was planning to take the distance from each (x,y) to the trendline equation to have %values to show the relationship I am trying to prove. But I'm wondering if this makes mathematical sense. I know that plotting the ln of y with x with a linear trendline makes sense, similar in the way that plotting non-logged y with x with a logarithmic trendline makes sense, but I'm kind of stumped as to justifying why fitting a logarithmic trendline on already-logged values of y makes sense (even though it makes for the best graph).
Should I continue with my idea or should I be content with simply plotting plotting ln y with x with a linear trendline to show the relationship?
***EDIT
#1. This is what I have and what makes mathematical sense to me
#2. This is what I want to use (but not sure if it makes sense)
***essentially, I am wondering if option #2 would result in mathematically-useful value for analysis, or would I just be analyzing mathematical nonsense?
Nothing of what you are doing makes sense. You are trying to fit "noise" and any model you will try will be as bad/useless as any other.
The best model: $$y=17.4$$