In R I have
day count 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 is simply the number of times an advertisement has been on television.
count is the number of new users we got that day.
I want to investigate the impact the promotion-value has on new users (
count). Since we have a count process I thought it would be best to make a poisson regression model.
model=glm(formula= data$count ~ data$promotion, data=data)
When we type
summary(model) we get
Coefficients: (Intercept) good_users$promotion 13.40216 0.24342 Degrees of Freedom: 793 Total (i.e. Null); 792 Residual Null Deviance: 9484 Residual Deviance: 9325 AIC: 12680
Here is a plot of the data.
But when I plot the fitted values for the model
points(model$promotion, model$fitted, col="blue")
we get this
How should I chose my regression model (should I use lm instead of glm) or is the another better approach to solve this? Because the data is not pretty but more random like this what should one do ?
Finding the sweet spot
I have done the following for finding a sweet spot.
data into 10 groups.
group1 is simply a subset where the promotion-value is within
group2 is data where the promotion-value is between
11:20, and so on for the other groups. So in R we have
group1 <- subset(data, data$promotion %in% 1:10) group2 <- subset(data, data$promotion %in% 11:20) group3 <- subset(data, data$promotion %in% 21:30) ... group10 <- subset(data, data$promotion %in% 91:100)
Now I can use
wilcox.test to test if there is a significantly difference between the groups by typing
wilcox.test(group2, group1, alternative="greater")
which gives a low p-value, ie
group2 has significant higher
group1. The same goes for
wilcox.test(group3, group2, alternative="greater")
wilcox.test(group4, group3, alternative="greater")
I get a p-value at 0.20, ie there is no significant difference in
group3. And the same goes for the rest of the group-pairs up to 10.
So this must mean that if we increase
promotion in the first groups we have an increase in
new_good_users but in the last groups we do not have that increase. This means that we have a sweet spot at
group3 where the promotion-value is
21:30. Is this not correct ?