for CLRM the OLS or ordinary least Squares-estomators(or the betas) arre BLUE (Best Linear Unbiased Estimator) when:
1.the regression is linear in the coefficients,it is correctly specified and has an additive error term.
2.mean of the error term is zero.(Include a constant term in the regression(B0 which will force the mean to be zero)
3.the independent variables are not correlated with the erroe term.(if they are correlated then the betas will be biased)
4.observations of the error term (the residuals)are not correltaed with each other.
5.the erroe term has a constant variance(Homoskedasticity)
6.no independent variable is a perfect linear function of any of the other independent variable.(if this is true-multicollinearity will occur)