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Suppose that I have $X_1$ and $X_2$ to forecast $Y$. If I run a regression on them separately, the coefficients are both positive. But if I a regression $Y = \beta_1X_1 + \beta_2X_2$ then wlog, $\beta_1$ is positive and $\beta_2$ is negative. What does this tell you about $X_1$ and $X_2$?

My thoughts are that this means $X_1$ and $X_2$ are highly correlated which throws off the betas but is there a more concrete explanation?

user371506
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    It seems this might be a self-study question? See https://stats.meta.stackexchange.com/questions/12/how-should-we-deal-with-obvious-homework-questions – Bryan Krause Oct 29 '22 at 00:42
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    I agree with @BryanKrause that this has the look of a homework question. Please add the self-study tag & read its wiki. Then explain what progress you've made so far and where you are stuck. You can also simulate some data for illustration. – dipetkov Oct 29 '22 at 13:18
  • The duplicate is one of many threads answering this question. For more, see https://stats.stackexchange.com/search?q=regression+coefficient+change+sign. – whuber Oct 29 '22 at 14:24

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