# R comparing effect between two regression lines

I'm trying to make sense of how to do something here in R and how to think through a method to answer a business question.

I have an original data frame that has information about advertising money spent on different channels. I also have computed the cost of customer acquisition (cac) which is equal to the money spent / number of customers.

grouped_df_summarizing_cac <- original_df %>% group_by(date) %>% summarize(average_cac = mean(cac))

ggplot(grouped_df_summarizing_cac, aes(x = date, y = average_cac)) +
geom_point() +
geom_smooth(method = "loess") +
labs(title = "", subtitle = "Average Cost of Acquisition")

grouped_df_summarizing_total_spend <- original_df %>%
group_by(date) %>%
summarize(average_spend = mean(actual_spend))

ggplot(grouped_df_summarizing_total_spend, aes(x = date, y = average_spend)) +
geom_point() +
geom_smooth(method = "loess") +
labs(title = "", subtitle = "Average Advertising Spend") +


Here are the two graphs that the code creates:  What is a good way to think about these two graphs together? My theory here is that, given fairly consistent advertising spending overall, the cost of customer acquisition is less at the beginning or middle of the month, for whatever reason. (Maybe it's the paycheck effect.)

In these graphs I intentionally chose the smooth method "loess" instead of "lm" for "linear model" because the localized regressions seems to capture the cycle whereas the linear regression doesn't make that beginning of month / middle of month cycle obvious.

Instead of just eyeballing these two graphs together and saying that it looks like there's a dip in cost of customer acquisition at the beginning or the middle of the month - how can I set up a stats question in order to say that this effect is, in fact, surprising in the data and therefore significant? I'm really also looking for some direction to implement this in R. Any help is really appreciated I don't know how to go forward here.