I know there exist rules to calculate for the minimum bin size for 2d histograms.

However, I would like to calculate the minimum bin size for a 3d histogram.

I have a lot of data of home-work trips made in the past. (>10000) For every trip I have information about the trip length, the travel-time ratio between car and bicycle, and the chosen travel mode. (car or bicycle) Based on the trip length and the travel time ratio I want to calculate the percentage bicycle use.

I have a table with on the x-axis the travel-time ratio between car and bicycle. On the y-axis I have the distance of a trip from home. In every cell the percentage bicycle use is

My question is know: how to choose the bin size for both travel time ratio and trip length?

An example of the table: (with 4x5=20 bins)

Code:

0.8-1.0 1.0-1.2 1.2-1.4 1.4-1.6 (<-- travel time ratio)
0 - 2 km 55% 54% 45% 35%
2 - 4 km 46% 41% 39% 27%
4 - 6 km 34% 34% 22% 24%
6 - 8 km 35% 21% 19% 19%
>8 km 11% 9% 5% 5%