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I have data on the daily returns from April 2020 - May 2020 for several tech stocks. I also have data on the daily amount of shares bought and sold from February 2020 - March 2020. I am trying to investigate whether or not the shares bought and sold have any impact on the daily returns.

My approach is to do a simple linear regression of daily returns on net shares bought (i.e., bough - sold). However, I am not really sure and wanted to see if anyone in the community had a smarter or better approach?
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I have no clue what model you should use, but intuitively I would say that a linear approach might be too simple. Curious to what more knowledgeable folks might think though
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There are entire industries devoted to modelling stock returns, so probably sky's the limit on how fancy you could choose to get there, but I'd maybe focus on (a) how would you mathematically state the hypothesis you want to test using your variables, and (b) if that statement looks like a linear regression, are you okay with using linear regression's assumptions? If there are assumptions you aren't comfortable with, then almost certainly there are other modeling steps that can help (for example autoregressive models if you're worried about correlations between one day and the next, possible covariates for periodic trends for day of the week or by subsector, comparison data outside of spring 2020 if you're looking at covid-related effects, etc) but is up to you to decide what features you think are important.
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