Simulating From Poisson Regression

In R we can simulate $n$ Poisson random numbers using rpois(n, lambda).

Recall, we have $\text{log}({\lambda }_i)={\beta }_0+{\beta }_1{x}_i$

Then ${\lambda }_i=e^{{\beta }_0+{\beta }_1{x}_i}$

We are using $i$ to emphasize observations

If we already know ${\beta }_0$ and ${\beta }_1$ from our glm(...) call from earlier, we can produce $\lambda$.

lambda_vector <- exp(3.55 - 0.00166 * d)
n <- nrow(cigbutts)
simcounts <- rpois(n, lambda = lambda_vector)