I was just reading an old post and came across this example which I’d like to share with you again:
Here’s a story of R-squared = 1%. Consider a 0/1 outcome with about half the people in each category. For.example, half the people with some disease die in a year and half live. Now suppose there’s a treatment that increases survival rate from 50% to 60%. The unexplained sd is 0.5 and the explained sd is 0.05, hence R-squared is 0.01.