This question is completely theoretical in the sense that I don't have any real data. Suppose I am designing a study, in which I will go measure N pairs of (X,Y), then the goal is to build a predictive model (say linear regression) between X and Y. i.e. I want good predictive accuracy, but it will also be good to have a prediction interval.
Given the limited resources, I have two choices:
- Increase N, but X will be measured less accurately; or
- Decrease N but measure X more accurately.
The question is, how can I find the balance between the 2 cases?
I understand I haven't provided real data, which is why I am not asking for specific answer. I just want to know what's the line of thought you would follow? What's a good way to approach this question? etc....
Clarification: Don't know why I put it the other way around. X in the dot points above should be Y. I am predicting Y using X. My choice is between increasing N or measuring Y more precisely.
Added: It will be good if your response considers both small sample size and adequate sample size situations.