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OLS Method


Reference: R11. P1.T2_Stock_v5

The three key assumptions of the ordinary least squares (OLS) linear regression model are the following:

1. Assumption # 1: The conditional distribution of the error term, u(i), has a mean of zero. This assumption is a formal mathematical statement about the “other factors” contained in the error term and asserts that these other factors are unrelated to the independent variable, X(i), in the following sense: given a value of X(i), the mean of the distribution of these other factors is zero.

Please can you explain the underlined statements. I understood that there should not be any relationship between u and X but the explanation given in terms of Distribution and Mean is something I am not able to understand.



Well-Known Member
For any value Xi of independent variable the dependent variable value Yi is given by,
Yi=bXi+c+ei where b,c are slope and intercept coeeficients if regression and ei is the error term.For varios values of Yi and Xi which are assumed to be normally distributed the error term values ei are assumed as normally distributed.Take Expected value on both sides of above eqn we get,
E(Yi)=E(bXi+c+ei)=bE(Xi)+c+E(ei) all add up as the terms are ND.
Y=bX+c is regression where Y and X are nothing but exp. Values of x and y, is valid if E(ei)=0 mean of error terms is 0
Thus For regression equation Y=bX+c to be valid the expected value of ei should be 0.