Regression model for a count proces
In R I have data where head(data) gives
day count promotion
1 33 20.8
2 23 17.1
3 19 1.6
4 37 20.8
Now 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$fitted, col="blue")
we get this
Here is another plot that shows the same but where days with 0 promotion are removed.
How should I chose my regression model (should I use lm instead of glm) or is the another better approach to solve this? Because the data is not pretty but more random like this what should one do ?
Updated
Finding the sweet spot
I have done the following for finding a sweet spot. I divide data into 10 groups. 650
group1 is simply a subset where the promotion-value is within 1:10. group2 is data where the promotion-value is between 11:20, and so on for the other groups. So in R we have
group1 <- subset(data, data$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 new_good_users than group1. The same goes for
wilcox.test(group3, group2, alternative="greater")
but for wilcox.test(group4, group3, alternative="greater") I get a p-value at 0.20, ie there is no significant difference in new_good_users between group4 and 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 ? 650