In R I have
day new_users promotion 1 33 20.8 2 23 17.1 3 19 1.6 4 37 20.8
day is simply the day (and is in order).
promotion is the promotion-value for the day - it's simply the cost of advertisements on television.
new_users is the number of new users we got that day.
The plot indicate that we have a positive correlation, ie more promotion we get more new users. In R I test for positive correlation:
cor.test(data$promotion, data$new_users, method="kendall", alternative="greater")
which gives us a very low p-value, ie we have positive correlation.
Finding the sweet spot
I want to find a sweet spot, that is a point where the increase of
promotion don't effect (or don't increase)
# Setting the promotion-value to 24 promotion_rate = 24 # Sub setting data so we only have promotion-value higher than 24 data_new = subset(data, data$promotion > 24) # Testing for positive correlation cor.test(data_new$promotion, data_new$new_users, method="kendall", alternative="greater" )
I have done this for different values for
promotion_rate. The results are
for all promotion-values below 24 we get a low p-value, ie we have positive correlation in these cases. For promotion-values higher than 24 we get a p-value higher than 0.05, ie we do not have a positive correlation in these cases.
Now is it valid to conclude that 24 is the sweet spot ?
I have now plotted the cumulative sum of
new_users - in R I type
plot(cumsum(data$new_users), xlab="days", ylab="cumulative sum of new_users", col="darkred")
Similar I plotted the cumulative sum for
promotion. The blue is
new_users and the orange is
plot(cumsum(data$new_users),xlab="days",col="blue") points(cumsum(data$promotion), col="darkorange")
But this looks like a straight line so is it even possible to find a sweet spot?