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I was wondering whether it's possible to do simple linear regression with non-normally distributed data. In my data set (n=25) some IVs have a normal distribution and some IVs do not show the normal distribution in the data itself. I want to know whether I can do simple linear regression, with one X variable and one Y variable if the data itself is non-linear (both X and Y) to make interpretation with final R2 values and the p-value. I would be grateful if anyone can have an answer for me. Thank you very much.

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    $\begingroup$ You express common misconceptions. The distribution of the dependent variable is not important for regression, neither is the distribution of independent variables (except that these could result in influential values). What is important is the distribution of the residuals. That is the distribution assumed to be a normal distribution in deriving statistics for ordinary least squares regression models. $\endgroup$
    – Roland
    Oct 12 at 7:01
  • $\begingroup$ Hi Roland, Thank you, now I understand. It helps me to do simple linear regression. But, if my distribution of the residuals are not normally distributed, is that possible to interpret p-value and R2? $\endgroup$ Oct 12 at 7:10
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    $\begingroup$ You can always interpret the Pearson correlation coefficient. You should not interpret p-values if assumptions are violated. I would suggest to fix the model to a model with different assumptions. That could mean simply transforming the DV, using a generalized linear model, ... $\endgroup$
    – Roland
    Oct 12 at 7:21
  • $\begingroup$ Hi Roland, thank you very much for your important explantion. $\endgroup$ Oct 12 at 7:37
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    $\begingroup$ Can you clarify what you mean by "the data itself is non-linear (both X and Y)" ? $\endgroup$
    – Glen_b
    Oct 12 at 13:59

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