There are as many different opinions for interpretation of dreams as there are people that do it. It depends on who you ask.
The mechanism of why we dream is not fully understood - by anyone. That it is a function of the sub-conscious is fairly well agreed upon but there are many theories as to why and how we dream.
People have different solutions with the conscious mind when presented with the same data, it is far more difficult to explain the functioning of the unconscious one.
It is, however, a practical certainty that there is no pre-cognition involved.
A different response:
This dream might be a play on words, related to the expression "being dogged by a problem." There is some issue in real life that just won't go away - it keeps "dogging" you, following on your heels like a hound that won't give up. In the dream, stop running, turn around and face the dog. In real life, the solution is to figure out what the issue is, then stop avoiding or running away from it.
The dog in your dream represents a persistant, chronic problem that you would like to avoid or escape. There is an expression about being "dogged" by something or someone, that means that the person or thing never goes away and constantly causes troubles. One might be "dogged" by false rumors or a chronic illness or bill collectors. The dream presents a literal illustration of some problem that you cannot seem to avoid.
Supposing one is not dreaming about a specific undisciplined dog, the dream suggests that something in one's life is reversed. Basset hounds, and hounds in general, are bred to chase game when hunting, not to be chased themselves. Another possibility is that the dog represents someone or something in real life that has similar qualities to a basset hound: cute, faithful and persistent, who seems to be avoiding you.
The coyotes in this dream represent an unpredictable danger. The dream does not foretell any specific future event, but expresses the dreamer's fear and anxiety about that possibility. Coyote is a trickster, so the dream includes the possibility of betrayal or of someone who should not be trusted. Chase dreams almost always indicate that the dreamer is trying to avoid some problem instead of facing and resolving the issue.
...um i think it just means you had a dream about being chased by dogs... sometimes though, dreams are because of events that happened that day.
You're feeling vulnerable, guilty or hurt.
It means " Fat Basset Hound " ( a basset hound is a type of dog ) and the word Davidson comes from France, therefore the basset it from France.
Dwarf
This might be your subconscious mind's humorous comment on your dog's smelly habits. Alternatively, it might relate to recent terrorist bombings and the need to "sniff out" information like a hound.
When anything is chasing you in a dream it usually means that you are under some stress in work, school, or relationships.
chasing your dreams means pursuing a dream, doing what it takes to acheive it, being determined and really wanting to achieve it. :)
it means you should buy a hippo
From the phrasing of the question, this sounds like a one-way affection. The dream illustrates the uselessness of chasing after someone who does not feel the same attraction.
Your "Princess and the Frog". Love, Oliver
it means hamsters hate you
It means you need to run faster.
Maybe you need to lay off the unhealthy foods...
A dream animal of any sort doesn't really exist, so if you're chasing one, you're off on a fruitless quest. In America, we say "off on a wild goose chase."