# Log scale on two axis vs 1 vs none

I would appreciate some advice on the most appropriate way of displaying the behaviour between two variables: # of subscribers in the first month and # activity (combination of actions)

I'm not sure what is the best of way doing so. Should I log scale the y axis or x axis? Should I log scale both or none. The benefit of scaling with log is that we can discount the skewness towards large values which will group all small values close the axis line

An additional data point is the correlation between both variable is 0.26. I would assume this is a slighlt moderate strength which means there is a positive relationship but not strong enough

I personally prefer log scaling both axis but never really seen this before. How would you interpret this relationship?

Here are some images

Edit: Adding new image to restrict

• How many different types of actions do you summarize in #activity? Commented Aug 31, 2022 at 17:37
• I summarize 3 actions Commented Aug 31, 2022 at 19:00
• With just 3 actions it will be possible and perhaps very informative to make the log-log plot for each action separately. Commented Aug 31, 2022 at 19:00

Your log-log plot communicates the patterns in the data most clearly to me. There is far too much overlap in a tiny region of the plot in the other versions. Regions of high point density can be addressed by using hexbin plots instead of scatter plots, but you lose information and it's best avoided if good alternatives exist.

Other points:

1. I'd recommend making the points slightly transparent even for the log-log plot, because some of them still overlap.
2. Your fitted line in the log-log plot is a very poor description of the data. There was probably an error in drawing that, associated somehow with the axis transformation.
3. "...the correlation between both variable is 0.26. I would assume this is a slight moderate strength which means there is a positive relationship but not strong enough". The relationship is not linear and is fairly complex. I would use a spline/GAM instead of a correlation coefficient here and be very careful about drawing simple statistical conclusions.
4. "How would you interpret this relationship?". Sorry, that's not really answerable. This is your dataset and we don't understand what the values represent or how the data was collected.
• 1. makes sense 2. that was the automated trend line from google sheets 3. Could pearson R still be used (see point 4 below) 4. for more context, we're looking into identifying an optimal time to send a marketing email based on the # of subscribers to generate more activity. In theory we wouldn't want to wait anything over 30 because the email would be sent in months. Ill edit with a restriction on the dataset with that number Commented Aug 31, 2022 at 14:55
• the new image isn't on log scale . Commented Aug 31, 2022 at 14:58
• @RogerSteinberg Rather than editing this question with new images, I suggest you ask a new one with that context and ask about how to take the decision. This question is already a bit too broad.
– mkt
Commented Aug 31, 2022 at 15:30
• @RogerSteinberg No, Pearson r is not a good descriptor of such a complex pattern and more importantly, it doesn't really help you achieve your goal. The best approach can be addressed in a new question, if you can provide more context.
– mkt
Commented Aug 31, 2022 at 15:33