It sounds like the hose that you are talking about is from the Secondary Air Injection Pump. I had the same issue with my '03...the hose seems to loose it's ability to lock to the airbox (or pump) as it ages. With mine, the hose had come off at both the pump and the air box. When I started the car, it not only idled rough, but sounded like a dustbuster because of the air pump making such a racket.
Regards;
Peter
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