The simple answer is no. Take a look at the following example. It shows a simple linear regression results between two variables $X$ and $Y$. The only difference between the black points and regression line, and the red ones, is that in the second case I changed $Y$ to $Y + 5$. In the "black scenario, the parameters are $\beta_0 = 0.1256, \beta_1 = 4.9122$, while in the "red" scenario $\beta_0 = 5.1256, \beta_1 = 4.9122$. Answer yourself: did the amount of unaccounted biases changed by five between the two scenarios?
Check also When is it ok to remove the intercept in a linear regression model?
I guess that what you are looking for is rather the $R^2$ statistic, but beware that it can be misleading as describes in Is $R^2$ useful or dangerous?