Establish relationship between two variables with scatter plot like a trapezoid What transformation can be used to establish relationship between two variables whose scatter plots looks like the plot below?
I have applied log Y, log X, exp Y, exp . But a relationship could not be established with high R-squared.


Based on that $x$ feature alone, the relationship seems pretty clear: increasing conditional mean of $y$ as $x$ increases, with the conditional variance of $y$ also increasing as $x$ increases.
I do not see any transformations or expansions of the $x$ feature (e.g., polynomials or splines) that will do much for you.
You say that you want a high $R^2$, but I do not believe you to have the features to achieve that goal with any kind of generalizability (e.g., out of sample performance, adjusted $R^2$). You are missing some component that drives $y$.
