Why does econometrics assume X’ε=0? While the sum of εi should clearly be zero, why should products of random x values and random ε values sum up to zero?

Answer 1

When you regress some dependent variable Y on independent variables,X You will gat a potion of the variation in Y "Explained" by X and the balance is "unexplained.". If X'Esplison were not equal to zero. Then knowing X would help you know epsilon