How can I measure correlation when my observations grow closer to the mean in both directions? I'm not sure how to explain it. I'm measuring time passed (not normal) against my dependent variable (a grade, with distribution close to normal). What I can see from the scatter plot is almost triangular. That is, I have both low and high grades when less time has passed and it becomes flatter as time passes.
I'm not sure if it´s linear because it seems both positive and negative. I'm also not sure is monotonic. I've recently heard about "distance correlation". Is that the case here?

 A: The phenomenon you think you are seeing is called heteroscedasticity. That, for the more extreme values of time on the $X$-axis, the apparent variability in GPA ($Y$-axis) seems to go down. The issue in this case isn't how to measure correlation: the usual measures can be used. Rather, it's how you estimate the uncertainty. Putting that aside, I actually don't see much evidence of heteroscedasticity in this plot.
The problem with the default settings on a plot like this is that it doesn't show point density.
Between time 30 and 40 I can easily count the sample size. However there are too many points to even count at time 0. Our eye tends to impute the sample size somewhat conservatively in these cases.
Some better plotting choices can help you to see the sample size more apparently:

*

*Use transparent points so that slightly overlapping points can be seen as distinct values rather than one blob

*Do not use scatterplots if there are more than, say, 300 points. Rather, use hexagonal binning, or using a partition of the $X$ domain, create box-and-whisker plots or violin plots

*Mark quantiles or deciles or other percentiles as appropriate on the X-axis or include the cumulative $N$ at each $X$-axis tick mark

*Include a smoothed estimate of mean trend as a function of the $X$ such as lowess or smoothing spline

