Help on understanding these plots I am very weak in the english language and I need to understand how I can describe my plots. It's the best way for me to learn, understand plots and memorize the phrases. 



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*So my first question is, the x variable is skewed and should be log-transformed since it's positive. But the y variable is also skewed and positive and should be log-transformed. Is my assumption correct?

*There is a no clear liniear relationship between x and y but there is a clear liniear relationship between log y and log x. Is this the correct way to phrase it for this plot?

*This question is more about understanding the transformation of the plots. In the book it says "The variables cannot be log transformed because they contain negative values." What does this exactly mean? Does it speak about the histogram or the scatterplot? I do not see a negative value in the histograms, so it should be possible to be log transformed. Or is my understanding wrong? 
 A: Welcome to Cross Validated! :)


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*In practice, whether or not do conduct a certain preprocessing step highly depends on your problem and (just according to my experience) there is no 'general answer'. I.e. it is neither always good to log-transform variables nor is it always good not to do so.


If you are interested in the relationship between x and y (as it seems to be the case in your example) then doing the log-transform is totally correct. Why? Well, because after transforming the variables in that way, you see the linear relationship. The fact that x and y are distributed in that 'skewed' way is a 'hint' that it might be useful to log-transform them.


*This seems to be a fine explanation. Nothing to add here :-)

*Whatever you are showing us, the book (at the point you quote) seems to have a different dataset. Why? Because you are showing us two distributions that express that there are no negative values (the histograms start at 0 at the x-axis). If there are negative values then there are different ways of dealing with that:
a) just skip them
b) violently push them to 0
You should only do these things if there are only a few negative values. For example: If some sensor is measuring the length of a certain process in seconds then there may not be negative values. Every negative value is an error and can safely be ignored (provided that there are only few errors ;-)).
If there are many negative values (for example, if the data is normally distributed around 0) then actually the histograms do not look like the ones you showed us and a log-transform is simply not applicable (right away). However, what people then usually do it to change the data (move it towards the right so that everything becomes positive). In the end: A linear relationship between log(x+10) and log(y) is as interesting as a linear relationship between log(x) and log(y) is (because both allow you to model y in relationship to x much better than just applying any learning algorithm).
