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Regressing price on volume

What are the basic pitfalls of regressing stock price on volume of shares traded? This is a time series dataset.

The model I’m using is:

As you can see I include a time trend $t$.

The R2 and p-value appears to come out good, but I’m more accustomed to cross-sectional analysis so don’t really know what I’m doing. I’d appreciate it if someone with more time series knowledge could let me know if this is totally naive.

Thanks

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