Hi there!

(background, skip if wanted)
New member here. Finance student with an exciting area to write a paper about but I have not taken any statistics course, which might seem stupid but I'we taken a non-standard study-route and I'm doing statistics this autumn.

We are interested in studying the connection between borrowing rates for stocks (when you borrow a stock to short it) and the connection to the following stock price movements. Basically figuring out if the people who take size enough to move the borrowing rate is outperforming the market.
We have been thinking about doing a linear regression analysis by just taking the stockprice, cleaning it from market-movements by removing the beta component and then doing a regression analysis on the numbers in excel. We have 2 different stocks with 1 year of daily data each, so all in all its over 500 data points which should be quite sufficient.

The questions:
Is this a suitable method to analyze the data with or would anyone with a good knowledge of statistics suggest another way?
What would be the biggest mistakes to make with this type of analysis? What do we have to make sure we cover?
Since the expected movement in the stock might not come straight away we were thinking of doing a chart with the different r2 values that we would get if we move the data 1-2-3 days back and forth. Would this properly capture if the shorting is following the movements or predict them?

Thanks for reading!