Suppose $$Y_i = \beta_1 + \beta_2 X_i + u_i$$ is our population regression function with $\beta_1$ the population regression line intercept, $\beta_2$ the population regression line slope, $u_i$ the disturbance term, $X_i$ the regressor and $Y_i$ the regressand.
How can I explain this relationship $\operatorname{E}(\hat \beta_2 u_i) = \operatorname{Cov}(\hat \beta_2,u_i)$ graphically? (where $\hat \beta_2$ is the OLS estimator of $\beta_2$).
I would assume that $(u, \hat{\beta_1})$ follow the normal bivariate distribution and would draw $n$ pairs $(u_i, \beta_{1i})$ from this function, plot it and draw $u=\frac{S_u}{S_{\beta_1}}r(b_1-\beta_1)$ to illustrate $\mathbb{E}[u|\beta_1=b_1]$. Where the parameters for the bivariate distribution you can take as the MLE estimators of $\sigma^2, \beta_1, \rho...$
Not sure that this is the best way, but for illustrative purpose it should work.