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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?

Harry Stuart
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    Also see https://stats.stackexchange.com/questions/29781/when-conducting-multiple-regression-when-should-you-center-your-predictor-varia – mkt Sep 24 '19 at 09:09
  • 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. – Glen_b Sep 24 '19 at 09:20
  • It turns out our site has a great many posts discussing collinearity and interaction: see [this search](https://stats.stackexchange.com/search?q=multicol*+interaction). – whuber Sep 24 '19 at 12:17

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