[AllanG]

I have just tested and with an intermittent input voltage of 15,7-13,7 the regulator intermittently outputs 8,8 to 9,2 v.

Given those figures, your regulator is working exactly as expected and within parameters - even a regulated output varies very slightly. The Datasheet for a Fairchild LM7809 specifies a minimum output of 8.6v, typical voltage of 9.0 and a maximum of 9.4v

I do not know whether a difference of ~0.2v can and will affect the accuracy of the Arduino or other components, I'm sure others will comment on that.

(Is your voltmeter properly calibrated and capable of measuring with absolute accuracy??)