Given the following linear regression model as following, with two explanatory variables $x_1$ and $x_2$ and response $y$ $$y_i=a+bx_{i1}+cx_{i2}+\epsilon_{i}$$ We say that $\hat{a}, \hat{b}, \hat{c}$ are the least square estimators for $a,b,c$. I just wonder if we have the sample correlation of the two explanatory variables $x_1$ and $x_2$ is positive, then how can I see that the correlation between $\hat{b}$ and $\hat{c}$ will be negative? Is there a way to show that this is true? I'm trying to understand this and I cannot see why this should be negative since our correlation between the two explanatory variables $x_1$ and $x_2$ is positive?
Amir