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Regression Analysis of News Data

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Hi All. I conducting research on news data. In my research the dependent variable is stock price and independent variable is no of news stories on specific firm in a given day. Although the stock price is consistent but the independent variable is inconsistent. There are outliers, scattered values, some companies have no news for several days and some of them have daily data. How can I run regression with this data when it do not meet the normality assumptions? What if we want to use fixed effect panel data analysis? Please advise

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