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I have dependent monetary variable which is a lognormally distributed , i transformed it into log normally distributed using log function in R , after that mean and median has been very close. Now problem with one independent variable which has multimodal distribution. Do i need to convert this independent variable as log normally distributed as well? If yes how can i do this?

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    $\begingroup$ No. There is no requirement that independent variable being normal distributed. $\endgroup$ – user158565 Jul 14 at 17:01
  • $\begingroup$ thanks @user158565 , but what about scaling? After conversion of dependent variable , independent variable is on different scale. Do i need to convert this multimodal to log as well in order to get more linearity? $\endgroup$ – user172500 Jul 15 at 5:41
  • $\begingroup$ Linear transformation (including scaling) on independent variable is meaningless. Non-linear transformation (including log) is needed if you find or know that there is non-linear relationship between dependent variable and independent variable. $\endgroup$ – user158565 Jul 15 at 5:46
  • $\begingroup$ @user158565 make sense , last question if in my model some variable has linear relationship with dependent variable and some has non linear in that what should we chose? $\endgroup$ – user172500 Jul 15 at 9:24
  • $\begingroup$ Keep the variables with linear relationship as they are; make the suitable transformations on variables with non-linear relationship. $\endgroup$ – user158565 Jul 15 at 13:19
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No. There is no requirement that independent variable being normal distributed.

Linear transformation (including scaling) on independent variable is meaningless. Non-linear transformation (including log) is needed if you find or know that there is non-linear relationship between dependent variable and independent variable.

Keep the variables with linear relationship as they are; make the suitable transformations on variables with non-linear relationship.

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