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Statistically speaking you should not include the factor that aren't significant. Economically speaking you should take all the factors because intuitively they explain the returns of the assets, and if you don't do it will incur in specification bias by omit the factors and will cause the the estimates aren't efficient, unbiased and consistent


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The R function you have to use is the lm() function. On QuickR you can find a simple and clear tutorial on how to estimate a linear (multiple) regression model generally using the lm(). As further reference, I suggest you to read the Introducing R tutorial about linear model by G. Rodriguez. I did not read the paper you cited, but, anyway, you should ...


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Portfolio behaving like a small cap portfolio is not necessarily a small cap portfolio. Your regression shows the appearance, not the fundamentals.



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