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I'm a beginner experimenting with machine learning and regression.

I have a dataset that looks like the following, where cost is the target (dependent) variable.

Original scatter matrix

Since the relationships seem skewed and exponential, is it appropriate to take the log of all of them before applying linear regression, like the following figure?

Scatter matrix of the log of variables

Furthermore, only one of the variables, dose, has zero values, is it appropriate to add 1 only to that variable before I take the log or should 1 be added to all of them?

Is there anything else I should check or beware of before applying a logrithmic transformation?

Is there anything else in the shape of the data that is strange that I should investigate?

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    $\begingroup$ You ask a lot of (good) questions here, all of which I believe are answered in other posts on this site (now numbering into the thousands). Please conduct a search. The evident visual fact that the transformations have created a scatterplot matrix all of whose cells exhibit classic elliptical clouds, or nearly so, and have nearly symmetric marginal distributions, answers the question about whether those transformations are advisable. $\endgroup$ – whuber Jan 30 '17 at 16:11
  • $\begingroup$ Thanks, I didn't know the term "elliptical cloud" before, it's a great search term that found other questions that didn't pop up before. However, I haven't yet found any questions that transformed into an elliptical cloud. Only found those who started with one, such as this one and this one Which makes me think that it's an acceptable starting place? $\endgroup$ – edge-case Jan 30 '17 at 18:49
  • $\begingroup$ Often, to sound less technical, people refer to these point clouds as having a shape of a "football" or "cigar." Thus, "cloud" or "point cloud" might make better search terms than "elliptical cloud". $\endgroup$ – whuber Jan 30 '17 at 19:26

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