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Can percentage values be independant variables? Can I use then as it is, or do I need to take log. And also if I have to consider interaction effects when independent variables are percentages, how can I do it?

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Yes, 0.01 actually equals to 1% and so on.

However you need to make sure that all your data and features are on the same scale so your model won`t be biased towards the features with higher values in Error calculations.

you can read more about this here

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