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In simple linear regression analysis, is it possible that "two variables are correlated but regression (main effect) is not significant"?

What does the result mean?

NOTE: My question is different from X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean? because my question is in simple linear regression analysis.

Jeff Lin
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    You should be more specific when you say correlated. In real data, you always have non-zero correlation. You also need to be more specific when you say that something is not significant. Do you mean to say at a specific threshold (alpha = 0.05)? Depending on how you frame and specify correlation and significance, your answer can change. – M Waz Jul 17 '19 at 14:22
  • To @MWaz : r = 0.30 (p = 0.024), beta = 0.07 (95% CI = -0.03, 0.19; p = 0.181) – Jeff Lin Jul 17 '19 at 14:32
  • @JeffLin r = 0.3 is a very weak correlation and the your confidence interval contains zero. The correlation does not suggest that your regression coefficient is significant, which is supported by your p-value. – M Waz Jul 17 '19 at 15:20
  • Assuming you have included an intercept, you have performed a multiple regression and so every conclusion in the duplicate applies in your case, too. – whuber Jul 17 '19 at 17:06

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