Is the assumption of constant variance violated in the following?
I am measuring point in a 3D coordinate system (X,Y,Z) using 10 different methods. One method is the golden standard (reference). The measurements are done at the same time for 40 different subjects repeated 2-3 times per subject. I end up with 105 measurements for each of the 10 methods. I am then interested in the length of the error compared to the reference (|Xerror| = |Xref-Xmethod|) in the X, Y and Z direction and the total error as the Euclidian distance (=sqrt(X^2+Y^2+Z^2)).
I want to see which method gives the smallest error in each of the directions (X,Y,Z) and also the lowest Eucledian distance. I have been using linear regression for this. With a model in for example the X direction as: |X| ~ 1+ method, where method is a categorical variable representing the 9 different methods tested (not including the reference). I have 9 x 105 = 945 observations.
Some different diagnostic plots can be seen below. I have used square-root transformation of the data to get a decent QQ-plot. My biggest concern is on the assumption of constant variance? But is there anything else which should concern me?
Additional info: the measurements are discrete (can only be integer numbers).