Consider a Poisson regression. Let \(e_{i}=y_{i}-\widehat{\mu}_{i}\) denote the \(i\) th ordinary residual. Assume that an intercept is used in the model so that one of the explanatory variables \(x\) is a constant equal to one.

a. Show that the average ordinary residual is 0 .

b. Show that the correlation between the ordinary residuals and each explanatory variable is zero.