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Suppose I have $10$ exposure variables $a_{1}...a_{10}$ and one dependent outcome $y$.I suspected $a_{9}$ and $a_{10}$ as a possible confounding variables. So at first I performed the multiple linear regression with the $a_{1}...a_{8}$. And got $3$ exposure variables significant$(p<0.05)$. However, again after performing the MLR with all the variables including $a_{9}$ and $a_{10}$. And this time no variables are significant. So my ques is what can I conclude from this result and is the adjustment correct? my best guess is

  1. Those 3 variables have showed relationship with $y$ at first but after adjusting no direct relationship with any exposure variables.
  2. Those 3 variables have showed most important while predicting $y$. However, no variables found more significantly important after adjustment. All are acting same to predict the outcome. Or any other interpretation..... The real results are below:

For 1st regression Model the Outcome is:

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For 2nd regression Model the Outcome is:

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  • $\begingroup$ are a_9 and a_10 significant in the second regression? $\endgroup$ Jun 27, 2020 at 11:32
  • $\begingroup$ No.they were not.. $\endgroup$ Jun 27, 2020 at 11:37
  • $\begingroup$ ok, that is interesting! can you share the sammry of the linear regression model? I mean the p-values of each variable? $\endgroup$ Jun 27, 2020 at 11:53
  • $\begingroup$ I have added the real results. It's actually with 19 exposure variable. $\endgroup$ Jun 27, 2020 at 12:12
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    $\begingroup$ A non-significant variable does not mean that the variable is irrelevant. Use robust standard errors, check the variance inflation factor to detect multicollinearity, look at the mse of different models if your aim is prediction. $\endgroup$
    – Peter
    Jun 27, 2020 at 15:31

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