Designing an experiment with linear regression analysis: more categories or more observations per category? During the design of my experiments I encountered the following question: When doing a linear fit (least squares), does it make more sense to have more categories or more observations per category. In other words: what will give the highest confidence of the fit? The image below illustrates my options (not actual data).

Background:
During the experiment I will be doing a Fitt's law experiment. Here I will ask users to move their mouse cursor from a specific position to a target. This target has a specific size (W) and is positioned a certain distance (D) from the starting position.

Fitt's law states that the difficulty of this task (Index of Difficulty (ID)) can be captured in the following formula:
$\mathrm{ID}=\log _{2}\left(\frac{2 D}{W}\right)$
The average time it takes to move to the target (movement time(MT)) can be captured by a linear relationship:
$\mathrm{MT}=a+b \cdot \mathrm{ID}$
Design of the experiment
During the experiment with a participant I have a finite amount of time and a can choose to do a small amount of ID's with a lot of repetitions per ID ór a lot of different ID's with less repetitions per ID. Let's say that the total number of trials per participant is fixed, what would be my best option?
Does this change the R^2 values? And what will give the highest confidence of the fit?

With a lot of work you could develop a Bayesian adaptive scheme that allows you to dynamically select test points for each subject based on previous responses.  Short of that, the experimental design (DOE) literature extensively covers your question.  The short answer is that if you are very sure about linearity, you can assign half the values at the lowest point and half at the highest, to get a minimum variance slope estimator.  To hedge your linearity bet you can put a few observations in the middle.  In DOE there are formal design optimality criteria you can use to select the test points.
