Assuming there is enough data, and all predictors and independent variable are positively correlated, in other words, every possible pairwise correlation is positive. Is it possible to end up with some negative coefficients in a multi-linear model fit? All variables are defined on a continuous scale.
$$ y = \alpha x_1 + \beta x_2 $$ where: $cor(y, x1) > 0$, $cor(y, x2) > 0$, $cor(x1,x2) > 0$
Given the above can either a or b end up being negative?