In 1994, Y. Mansour conjectured that for every DNF formula on n variables with t terms there exists a polynomial p with t^{O(\log (1/\epsilon))} non-zero coefficients such that \E_{x \in \{0,1\}}[(p(x)-f(x))^2] \leq \epsilon. We make the first progress on this conjecture and show that it is true for several natural ... more >>>