Underlying model for prediction using different prediction variables
Have had the same problem before.  Used Weka tool (http://www.cs.waikato.ac.nz/ml/weka/).  

The approach:
• convert time of day into a nominal (non-numeric), eg bins numbered 0-47
• convert day of week into a nominal (non-numeric)
• use M5Tree to construct a model

The rules in the tree will pop out things like "if 0 &lt; bin &lt; 5:30am_bin" then ... which discriminates start of day

It is better with more than 1 month of data.  There will only be 4 samples for certain days of the week, for example.  So more months would be better. And in such case again converting month to a nominal value (non-numeric) lets the rules pick up seasonal and monthly changes.