Probit Approximation in R

start_time <- Sys.time()

probit_model <- stats::glm(chinstrap_bool ~ flipper_length_mm + bill_length_mm,
                      data = penguin_class_df,
                      family = binomial(link = "probit")) #makes probit approx
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
end_time <- Sys.time()
print(end_time - start_time)
## Time difference of 0.003956079 secs

R code 
# https://stats.stackexchange.com/questions/6206/how-to-plot-decision-boundary-in-r-for-logistic-regression-model
beta_0 <- coef(probit_model)[1]
beta_1 <- coef(probit_model)[2]
beta_2 <- coef(probit_model)[3]
boundary_slope <- -1.0 * beta_1 / beta_2
boundary_intercept <- -1.0 * beta_0 / beta_2

penguin_pred_df <- penguin_class_df |>
  mutate(species_pred = ifelse(
    bill_length_mm > boundary_intercept + boundary_slope * flipper_length_mm,
    1,0)) |>
  mutate(across(species_pred, as.factor))

penguin_pred_df |>
ggplot(aes(x = flipper_length_mm, y = bill_length_mm, 
           color = chinstrap_bool)) + 
  geom_point(size = 3) + 
  geom_abline(intercept = boundary_intercept,
              slope = boundary_slope,
              color = adelie_color,
              linewidth = 2,
              linetype = 2) +
  labs(title = "Probit Approximation",
       subtitle = "<span style = 'color:#fb7504'>decision boundary</span>",
       caption = "Data Science Learning Community") +
  scale_color_manual(values = c("gray70", chinstrap_color)) +
  theme_minimal() +
  theme(plot.title = element_markdown(face = "bold", size = 24),
        plot.subtitle = element_markdown(size = 16))
penguin_pred_df |>
  janitor::tabyl(chinstrap_bool, species_pred) |>
  janitor::adorn_totals(c("row", "col"))
##  chinstrap_bool   0  1 Total
##               0 258  7   265
##               1   8 60    68
##           Total 266 67   333