I know that we have previously discussed how the use of standardized coefficients may obfuscate results rather than shedding more light. I completely agree!

However, I am curious to really understand how one can use these coefficients, if one had to. Consider we run an OLS on standardized y and x, which yields the standardized coefficient beta.

std(y) = 0.191 std(x)

One may interpret this as 1SD change in X is associated with 0.191SD change in y. Consider the s.d of the unstandardized variables are sd(Y) = 27.37 and sd(X) = 0.094. In this case, would it be reasonable to infer that 1SD change in X (sd=0.094) is associated with 1.8% change in Y (0.094*0.191)?

Thanks in advance!