Meaning of regression coefficients I am having some trouble understanding exactly what is meant by the "true" Regression coefficients. Let's say it is stated that "the true regression coefficients are given as $y=a+bx+e$ where the error term fulfills all the OLS assumptions. Does this mean

a) Given knowledge of the value x takes one would describe their belief about the value y takes with the probability distribution on the right hand side.

b)a one unit change of x in a certain instance would cause the expected value of y to change by b.
a) not sure what exactly you mean here by probability distribution but if you mean the distribution of potential Y given the distribution of estimated coefficient b and a it would be correct, although usually we look at expectation to get single number than on distribution in which case it would be $E(Y|X)$

b) is correct