Chose the right regression analysis
In R I have data where head(data) gives
day promotion profit new_users
1 105 45662 33
2 12 40662 13
3 44 46800 20
4 203 54102 46
Now day is simply the day (and is in order). promotion is simply the promotion-value for the day, the profit is the profit that day and new_users is the number of new users that day.
I want investigate the relationships between promotion to profit and new_users. We see a clear positive correlation between promotion and profit, and there is also a positive correlation between promotion and new_users. In R I simply test correlation
cor.test(data$promotion, data$profit, method="kendall", alternative="greater" )
cor.test(data$promotion, data$new_users, method="kendall", alternative="greater")
which both gives a low p-value, ie we have a positive correlation.
I want to find a point where where the increase of promotion don't increase profit or new_users that must, ie a sweet spot.
Here is 2 plots and the R code for these
plot(data$promotion, data$profit, col="brown")
plot(data$promotion, data$new_users)
How should this be done?
My thoughts where to make a regression model. For the first one "promotion vs. 650
new_users" one could use a poisons model because it's a count-process, so a model like this would be a good chose?
glm(formula= data$new_users ~ data$promotion, family="poisson", data=data)
Next what regression model should one chose for the next one. Is it fair to say that this regression model is a good chose ? (I use sqrt command)
glm(formula=data$profit ~ sqrt(data$promotion) , data=data)
Or maybe it's not even necessary to use a regression model at all to find a sweet spot?
Thanks.
I have now looked at 'good' new users. For each day we have a promotion value and we have a count value which is the number of new good users. This plot shows us the number of good new users we get for a promotion for each day. For example for promotion value 90 we have a day where we got 8 new good users and a day where we got 14 new good users.
What would be the right approach to find a sweet spot for the use of promotion ? 587