It is said in Wiley that “when the independent variables do not explain any variation in the dependant variable, the predicted value of the dependant variable is its mean”. Can someone explain why?

What they mean to say is that, in the absence of any statistically significant predictors of the dependent variable, the best method for us to predict the dependent variable is to use it’s mean value.

Another way to look at it is that if the independent variable(s) do not explain any of the variation in the independent variable (i.e., R² = 0), then all of slope coefficients (b1, b2, . . ., b_n_) are zero, and the regression equation is: