suppose you have Standard & Poor 500, and a portfolio to hedge. The portfolio does not eactly mirror the index. We then use B (beta).

I always studied beta as a measure of the sensitivity of the portfolio to mkt movements, but the definitin provided by th book is this one:

" Beta is the slope of the best-fit line obtained when excess return on the portfolio over the risk-free rate is regresses against the excess return of the mkt over the risk-free rate"

which I do not really get. What does "regressed" mean?

does this simply mean that beta= covariance/variance starting from the assumption of a linear affine relation that the excess return for a certain stock is equal to the excess return for the mkt plus an error?

I am trying to be as clear as possible but the confusion in my mind does not guarantee a great result...

Thanks for any help.