If I have the predictors $X$, $Y$, and $XY$ to fit a linear regression model. Won't I be increasing the standard error of the regression coefficients? This is because $XY$ is collinear with $X$ and $Y$ correct?
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1$\begingroup$ Also see stats.stackexchange.com/questions/29781/… $\endgroup$– mktSep 24, 2019 at 9:09
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$\begingroup$ XY is not necessarily highly related to any linear combination of X and Y; it depends on the circumstances. Standard errors might well go down. $\endgroup$– Glen_bSep 24, 2019 at 9:20
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$\begingroup$ It turns out our site has a great many posts discussing collinearity and interaction: see this search. $\endgroup$– whuber ♦Sep 24, 2019 at 12:17
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