Regression analysis is used for explaining or modeling the relationship between a single variable Y, called the response, output or dependent variable, and one or more predictor, input, independent or explanatory variables, X1 .... Xp.
from this book https://cran.r-project.org/doc/contrib/Faraway-PRA.pdf
What does independent variables mean in the definition?
Considering Xs to be random variables,does it mean that P(Xi|Xj) = P(Xi). BUt this would be very constrainted for anyone trying to use regression analysis as inputs tend to be dependent in most of the cases.