I have continuous data for x (for example "time") and y with several groups. I would like to show/test that the slope of groupC changes over time (is positive and rises) while groups A and B do not. Below is a MRE. I was thinking about using a GAM, but could need some inspiration of how to formulate this in R. Please note that my real data are a lot more variable than the example in case that is relevant, so it's really about using some sort of smoother and then use this as a basic for assessing differences in slope.
library(tidyverse) set.seed(1) data <- rbind(data.frame(x=seq(1, 100), y=rnorm(100, 1, 5), group="A"), data.frame(x=seq(1, 100), y=rnorm(100, 3, 5), group="B"), data.frame(x=seq(1, 100), y=jitter(seq(1, 10, length=100)^3, 1000)/20, group="C")) data %>% ggplot(aes(x=x, y=y, color=group)) + geom_smooth() + # any smoother is fine, loess is just an example for viz geom_point()