15.5 Poisson regression with an extra binary predictor

Simulate \(y\) data for a Poisson regression with one continuous predictor \(x_1\) and one a binary predicor \(x_2\). This is Poisson regression with a varying intercept.

Code

dg$y = rpois(n = n, lambda = exp(0 + 0.5*x1 + 1*x2))

g = ggplot(dg, 
           aes(x = x1, 
               y = y, 
               color = as.factor(x2), 
               group = x2)) +
  geom_jitter(show.legend = F, 
              alpha  = 0.1, 
              width  = 0, 
              height = 0.3) +
  geom_smooth(linewidth   = 3)

g %>% 
  pub(xlim = c(0, 1 ), 
      ylim = c(0, 14))

[1] 37.35768
[1] 80
[1] 20
[1] 137.3577