I have some data to which I am trying to fit a trendline. I believe the data to follow a power law, and so have plotted the data on log-log axes looking for a straight line. This has resulted in an (almost) straight line and so in Excel I have added a trendline for a power law. Being a stats newb, my question is, what is now the best way for me to go from "well the line looks like it fits pretty well" to "numeric property $x$ proves that this graph is fitted appropriately by a power law"?
In Excel I can get an r-squared value, though given my limited knowledge of statistics, I don't even know whether this is actually appropriate under my specific circumstances. I have included an image below showing the plot of the data I am working with in Excel. I have a little bit of experience with R, so if my analysis is being limited by my tools, I am open to suggestions on how to go about improving it using R.