library(tidyverse)
rounded.data = data %>%
              mutate(MeanTemp = round(MeanTemp*5)/5) %>%
              group_by(MeanTemp) %>%
              summarise(Snow = sum(SnowBinary), NoSnow = n() - Snow)


rounded.model = glm(cbind(Snow, NoSnow) ~ MeanTemp, data = rounded.data, family = binomial())

# Deviance GOF test
pchisq(rounded.model$deviance, rounded.model$df.residual, lower.tail = F)

cut.data = data %>%
  mutate(MeanTemp = cut(MeanTemp,seq(-25,25,5))) %>%
  group_by(MeanTemp) %>%
  summarise(Snow = sum(SnowBinary), NoSnow = n() - Snow)

cut.model = glm(cbind(Snow, NoSnow) ~ MeanTemp, data = cut.data, family = binomial())

snow = tibble::tribble(
  ~MeanTemp, ~SnowBinary,
        3.5,           0,
        3.7,           0,
        2.5,           0,
        4.9,           0,
          5,           0,
       -0.3,           0,
       -2.7,           0,
       -2.8,           0,
       -1.7,           0,
         -4,           1,
       -5.5,           0,
       -6.2,           1,
       -9.8,           1,
      -11.9,           0,
       -9.6,           0,
         -5,           1,
         -6,           0,
       -0.4,           0,
        3.4,           0,
       -0.9,           0,
         -2,           0,
       -2.6,           1,
       -1.7,           0,
       -6.9,           1,
       -9.9,           1,
      -15.9,           0,
        -16,           0,
      -14.9,           0,
      -12.6,           1,
      -15.8,           1,
      -18.4,           1,
      -15.6,           1,
      -13.4,           0,
      -13.4,           0,
      -14.2,           1,
      -18.3,           0,
      -19.9,           1,
      -13.8,           0,
       -1.1,           1,
       -7.4,           1,
       -3.6,           0,
        8.1,           0,
        0.4,           0,
        -12,           0,
      -10.8,           0,
       -9.6,           1,
       -9.2,           1,
      -10.8,           1,
       -7.9,           0,
       -2.6,           0,
        0.8,           0,
       -1.1,           0,
        4.5,           0,
        1.5,           0,
       -6.3,           0,
       -6.9,           1,
        0.1,           0,
        3.4,           0,
        0.7,           0,
       -5.9,           0,
      -10.6,           1,
       -4.9,           0,
       -4.6,           1,
      -11.1,           1,
       -6.6,           1,
       -4.8,           1
  )