I think people are to harsh on OP.
Although there may not be a definitive correlation between hashing power/difficulty, it surely does say something about the interest/commitment to BTC.
I for one would like to see a chart like this. Ideally it should be corrected for advances in computing power/cost.
With minimal value people would still mine, but when a lot of people invest in fairly expensive dedicated hardware etc. just to mine, it shows a dedication and confidence in BTC value.
Fun thing is, people love to rely in these things in trading, but Nash them Art other times.
Statistics are merely tools to depict certain constructs in mathematical language.
There are some ideas I have had to analyse this. Psychologists use the constructs I am thinking of with quite success, although in this regard we will never reach the accuracy of physics.
What I want, actually, is to find connections between variables and their impact on price. I would try to get enough significant data points and then create a model that shows data points that do not conform to the model. Finding more and more points with actual probable causes, I would then try to run a tractor analysis, considering the data is sufficient.
This way, I would gain some understanding in short, mid any long term variance of how it has played out so far. This goes only so far in prediction value, but it could give me some insights into how the whole trading community thinks on a systems models.
I would then write a paper about it and try to get to t published in a journal on behavioural economics.
Whether or not it will have predictive value is up in the stars. It could use news indicators and weight them like other trading systems, but it could be pure voodoo as well.
