I'm working on an ongoing data analysis project about a series of live educational seminars. Each of my data points represents one such event, and for each one I have a multitude of categorical variables, as well as a couple quantitative ones that are my desired response variables (total revenue and number of attendees).
One trend I'm interested in looking at is how the frequency of these events affects my two response variables. Over the years, we have increased the frequency of the events and I'd like to determine whether or not it makes sense to continue doing so. I've created a couple of variables to help track this frequency:
NEAREST.SEM - the number of days between this event and the nearest one to it chronologically in either direction
LAST.SEM - the number of days between this event and the nearest one to it chronologically before it
WEEKLY.SEMS - the total number of events held during the 7-day period starting on Monday within which this event falls
Depending on how I do the analysis, these three variables seem to have varying significance, but the one that seems to consistently come out on top is
NEAREST.SEM, which I have found to be significant at the 0.01 level in one test and the 0.001 level in another. The other two variables are significant in predicting revenue but not number of attendees, which is not ideal since we are more interested in number of attendees. (The data for revenue is not representative of the total revenue for each event due to certain special offers for repeat customers that aren't taken into account there.)
Increasing the frequency of events seems to decrease each event's individual performance, but has so far increased overall performance. I'd like to determine the "turning point" at which overall performance will either dip or level off. Unfortunately, this is going to be tough to predict because my best-fitted variable,
NEAREST.SEM, isn't as good a representation of increased frequency. Note, for example, that it would look exactly the same whether 4 or 5 events were held per week--it would always have the value of 1 in such situations. In fact, any time that events are grouped in clusters of consecutive days, we'll always get 1 for them on this variable...
One option would be to just use
WEEKLY.SEMS as a predictor of revenue, which it is well correlated with, but as I said, we'd much rather do this analysis based on number of attendees, a better measure of an event's success.
So I really have two questions here:
Any suggestions on my dilemma of which variable to use and how to deal with the problems I laid out above?
Once I decide on a predictor factor, how can I go about estimating the average decrease in revenue increasing to various frequencies will have? Should I run a multiple regression using all my variables and use the coefficient on the predictor factor? Or should I run a regression with just the one factor and my response and use that coefficient? Or is there a better test than regression to use?
(By the way, I'm using R for my analysis and I'd appreciate any advice specifically tailored for that language.)
UPDATE: I have tried creating two new measures, one that's the average distance in days of the nearest event on either side, and one that's the number of events within 3 days in both directions...neither of them had any significant correlation. I'm running out of ideas here...