# How would you interpret this Binomial Logit GLM?

I ran the binomial logit GLM which predicts whether a claim occurs in a policy or not. My estimated coefficients are as follows:

Intercept: -2.68

Car Type (Saloon is base level) SUV: -0.07 Bus: 0.15

Use (Private is base level) Commercial: -0.09

Am i right to assume here, that if a car is Saloon and is used as a Private car, the odds of claim occurrence are exp(-2.68) = 6.86%? And the probability of claim occurrence would be exp(-2.68)/(1+exp(-2.86)) = 6.42%?

What if a car is a Bus and is used for Commercial reasons? What would be the probability of claim occurrence then?

I think its like this

``````library(tidyverse)
Intercept <- -2.68

car_type <- c(
saloon = 0,
suv = 0.07,
bus = 0.15
)
use <- c(
private = 0,
commercial = -0.09
)

(result <- expand_grid(
Intercept, enframe(car_type, name = "cartype", value = "ctval"),
enframe(use, name = "use", value = "uval")
) %>% mutate(
description = paste(cartype, use),
logodds = Intercept + ctval + uval,
odds = exp(logodds),
probability = odds / (odds + 1),
prob_percent = paste0(round(probability * 100, 2), "%")
))

result %>% select(description,prob_percent)
# # A tibble: 6 x 2
# description       prob_percent
# <chr>             <chr>
# 1 saloon private    6.42%
# 2 saloon commercial 5.9%
# 3 suv private       6.85%
# 4 suv commercial    6.3%
# 5 bus private       7.38%
# 6 bus commercial    6.79%``````

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