Squire training results

I noticed sometimes the training results are increased. I would like to know if there is a pattern to this, whether the amount depends on the squire or total level maybe?

For example: When training Eirlys' INT, the training "preview" shows a 25->31 increase. However, once the training is completed, the results are actually 25->36.

Training has a chance to increase a greater amount when it's the squire's specialty (Logan is Dex, Dai is Str, Kaour is Int), but sometimes you just randomly get an increase. Someone would need to track it - the day, happiness level, etc. to see if there's a pattern, since your squire can also just randomly receive bonus training when training is completed, even if not the squire's specialty.

Going out also has a chance to increase. You can get +12 max? i know that ive had increased due to going out and specialty bonus stack.