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Your use of R is incidental to this as a statistical question migrated from SO to CV, so let's recast the problem as one for Stata. …

I can't help with your difficulties in deciding how to do it in R, which are not stated specifically and arguably are off-topic here in any case. …

@whuber's comment is to the point and a good succinct summary. But some more can be added to flesh out a slender argument. The transformation mentioned is cube root $x^{1/3}$, written in pseudo- or …

Often people are relaxed about the differences between point and interval data. If I have a hundred annual rainfall totals, in principle they are for intervals not points, and there is a strict logic …

I don't program in R, but I program otherwise, and I see no R-specific issue here. I imagine that most people first write something because they really want it for themselves. … R programmers often seem to require that R users know just as much they do about the technique being implemented and document minimally.... …

If you got all the missing data experts in a room, they probably wouldn't agree on which method is best, although they might agree that what is best depends very much on the precise goal and on what u …

You name yourself as a R user, but your graphs look like to me like Excel defaults. …

As numerous comments have shown, we are having a hard time understanding what you want here, but it seems to me that Your variables have different units of measurement, so even in principle it makes …

Although no doubt functions exist that may be helpful, this is just to underline that what you want is more difficult to do definitively than you imply. Even for the case of a normal (Gaussian) dist …

The question asks about R, but the issue can arise with any other statistical software. …

The documentation says "The entries of x must be non-negative integers". That's not true in your case, yet the function doesn't throw you out. But there's still a question of whether what you are doin …

How to deal with circular data in R (or any other specific software) is off-topic here but there are certainly dedicated packages, and indeed a dedicated book by Arthur Pewsey and friends Testing for …

The question here should be turned around. Consider I am interested in (e.g.) the relationship between height and weight for men and women. A linear model is one way to approach this. Spearman co …

Whatever your sense of how difficult this is, and of how much guesswork is needed about information not given, you are exactly right. The minimum in the previous version of the question (no longer v …

$R^2$ is principle is unit-free and dimensionless, so many people compare $R^2$ before and after logarithmic transformation to judge its success. … lower $R^2$ may arguably be the better model. …