I'm looking for a model to predict CTR (click-through-rate)
I have the following data: For each ad I know the number of impressions, clicks and some other attributes (which are mainly dummy variables).
The CTR per ad is calculated as follows: #clicks / #impressions.
I have two questions regarding predicting CTR:
I am wondering which model should be used to predict the CTR. I tried a linear regression, but the R-squared is very low (around 10%-15%). A logistic regression is not an option as my dependent variable is not a 0/1 variable.
When I run a linear regression with clicks as dependent variable and impressions, etc. as explanatory variables, my R-squared suddenly is around 85-95%. How is it possible that this differs so much from taking CTR as dependent variable?
EDIT: I followed the approach from kjetil, which works perfectly.