What is Yield beta vs future?

Just gave Kaplan mock exam, one of the questions required us to calculate number of future contracts to adjust duration of the fixed income portfolio. I know the forumula and then we multiply with conversion factor, but the solution to this problem also mutiplied the answer with yield beta vs future actor.

Can someone explain me that what is yield beta vs futures factor?

all explained in the book … (but in an section marked optional)