Back transformation of log transformed data

Hi everyone,

I was wondering if someone can help me out. I am currently writing my thesis and I am in the middle of data analysis. My dependent variable was not normally distributed. Hence, I log-transformed the data (log10(x+1)). I used '+1' in order to prevent the exclusion of 'zeros' in my data. Now my data was normally distributed, so I could run a simple multivariate linear regression. I was able to find out how to back transform the unstandardized coefficient using the following formula: (e(^B)-1)*100. However, now I want to back transform the CI. I do not know how to. Does anybody know? In the figure below you can find the output (with the log-transformed dependent variable).

I also struggle with another thing. I namely want to see what the random effect is of nursing home clusters. Hence, I want to calculate the Intraclass Correlation Coefficient (i.e. ICC) for every individual variable. For the independent variables this is no problem. But I want to calculate the ICC of nursing home clusters together with the log-transformed dependent variable (time spent on activities). So, I get an ICC that includes log-transformed data. How do I back-transform an ICC?

Thank you in advance for your time!



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Who says the independent variable should be normally distributed???
That's a good point. But irrelevant because I don't think OP mentioned the IV should be normally distributed. They did say something about the DV being normally distributed - which is also not an assumption. We just need the error term to be normally distributed. And by "need" what I mean is that if we want to just apply a standard general linear model without worrying about anything and want to do inference then that is one of the assumptions we're hoping to meet.