Did Clara influence who the 9th Doctor was?

I believe the Doctor’s are somewhat influenced by their companions when they regenerate. I think there was a scene cut whereby the 10th Doctor explains he for his accent from Rose.

But I do think 12 was Scottish and grumpy because of Amy for example.

In Day of the Doctor, the War Doctor does say how he hopes to one day be half the man that Clara is. And then regenerates. So is he northern because Clara was?