I am trying to test a hypothesis I have about consolidation in the real-world market for a certain machine. (My apologies in advance for obfuscating a bit here, but some of the data is proprietary and may not be redistributed.)
1) The market has two components: new machines sold and existing machines in use. Companies act as agents who sell new machines and service the old machines. Machines can be used for 10-15 years before becoming unfit for use. The pool of machines in use has risen steadily over the years.
2) The data show that over the decades the number of agents has fallen steadily, although over the same period the number of machines in use has risen steadily. If you divide the number of machines by the number of agents to get a "agents per machines in use" value, this has risen steadily over time. In effect, the industry has become more efficient: it sells and services more machines with fewer (but presumably larger) agents.
3) My hypothesis is that the driver of this increased efficiency has been the rise in the ratio of machines in use to new machines sold. My theory is that the increase in machines in use offered an opportunity to some agents in the form of increased service revenues. Those opportunities required a broader set of skills and more organisation than simply selling new machines, so some agents out-competed others. Over time - decades, in fact - the stronger agents drove the weaker ones out of the industry or consolidated them. This led to an increase in overall efficiency.
I want to find out whether there is indeed a relationship between market maturity and market efficiency. My approach to testing this hypothesis has been as follows. (a) Calculate the ratio of machines in use to new machine sales as a proxy for market maturity; the higher the number, the more mature the market. (b) Calculate the ratio of machines to the number of dealers operating in the market as a proxy for market efficiency.
This gave me 45 yearly data points for each of the two data series. I then made a scatter plot in Excel, with the machines per agent in use on the x axis and the ratio of machines in use to new machines sold on the y axis. (I planned to post the chart here but I don't yet have enough reputation to do include images in posts.) The linear trend line equation of the plot is y = 0.7277x + 6.528 with an R2 of 0.7488. This looks like a fairly strong relationship but not suspiciously high. However, I have no formal training in statistics, so I'm concerned that I may be making a gross methodological mistake.
Q. My question is... is this approach valid or irredeemably flawed? I have tried to normalise the data somewhat but I am still comparing a ratio and an absolute figure. Is there something else I should do?
(Another approach I considered was simply comparing the machines in use per dealer to the number of machines in the market, but the scales are different by a couple of orders of magnitude. I got a 45-degree line and an R2 of 0.99.)
I use Stack Overflow (mostly for R) but this is my first time on CrossValidated. I realise this is a question that may have a discussion element to it rather than the preferred "answerable question". Happy to edit the question as required.