These problems can be solved with standard statistical
techniques (1). That is mandatory because
analysis of slopes of linear regression can be quite different for the different
approaches.
Domain distribution of muscle tissue is lognormal, as seen so far, but combination of domains with other features must be interpretated with care. The reason is, that domains, overlap areas, and so on, are distributed and cannot be used as fixed variable in a statistical analysis.
Example: capillaries and muscle cells. Often, capillaries here surround a muscle fiber, and how many can be determined by counting the number of domains overlapping the fiber cross section. The objective is, the relation between cell size and number of capillaries: how will the number of capillaries increase with cell size. The first step would be linear analysis. But standard linear analysis (like y = ax+b) is based on a fixed variable (x) and a spreading variable (y) and neither variable is a fixed one. More complicating: the number of capillaries is spread but only can change by a whole unit, e.g., from 4 to 5 instead of from 4 to 4.1.
These problems can be solved with standard statistical
techniques (1). That is mandatory because
analysis of slopes of linear regression can be quite different for the different
approaches.
Example: consider the measuring points (x,y) = (1,1), (2,3), (3,2) - the stars in the figure. Taking x as the independent variable yields the blue line, taking y the orange one. The difference is obvious.