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Dear Stack community,

My question is the following;

If my dependent variable is twelve month returns.

And as independent variables I have fiscal year variables like ROA and log variables like the log of the market value.

Where ROA = Net income / total assets

Should I scale ROA either as a fraction (e.g 0.05), a log (e.g -1.30) or a % (e.g 5%).

And similarly how should I scale returns?

I guess the anwser depends on what change I want to analyze.

However if I want to fit both slopes in a graph over time and interpret their coefficients for a cross section of stocks, would it make most sense to use a fraction, % or log for ROA?

Any clear intuition for this...?

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    $\begingroup$ Hi Julien :) There's no right answer. It very much depends. You can use ROA, ROA*100 or log(ROA). A few notes: log(ROA) only works if ROA is positive (which it is not necessarily). Scalign ROA by 100 only scales the estimated regression slope. So nothing is gained or lossed. It's up to you to choose a unit that makes your results easy to interpret. I'd probably regress (excess) returns on ROA. Keep things simple. Sometimes, log transformations are important for skewed variables like book/market. For example, you may regress (excess) returns on log(B/M). $\endgroup$
    – Kevin
    Dec 10, 2023 at 17:45

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To graph them I can either keep both the dependent and independent variables as fractions with the log variable as a log. Or both the independent and dependent variables as a % and divide the beta of the log by 100 to get a 1% change interpretation.

Either way will give me a similar graph, and similar interpretations. It's just that when reporting the figures, % returns and % ratio's may be more intuitive.

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