From a sample of \sim 50 , 000 early-type galaxies from the Sloan Digital Sky Survey ( SDSS ) , we measured the traditional Fundamental Plane in the g , r , i and z bands . We then replaced luminosity with stellar mass , and measured the “ stellar mass ” Fundamental Plane . The Fundamental Plane , R \propto \sigma ^ { a } / I ^ { B } , steepens slightly as one moves from shorter to longer wavelengths : the orthogonal fit has slope a = 1.40 in the g band and 1.47 in z , with a statistical random error of \sim 0.02 . However , systematic effects can produce larger uncertainties , of order \sim 0.05 . The Fundamental Plane is thinner at longer wavelengths : it has an intrinsic scatter of 0.062 dex in g and 0.054 dex in z . We have clear evidence that the scatter is larger at small galaxy sizes/masses ; at large masses measurement errors account for essentially all of the observed scatter ( about 0.04 dex ) , suggesting that the Plane is rather thin for the very massive galaxies . The Fundamental Plane steepens further when luminosity is replaced with stellar mass , to 1.54 or 1.63 when stellar masses are estimated from broad-band colors or from spectra , respectively . The intrinsic scatter also reduces further , to 0.048 dex on average . Since color and stellar mass-to-light ratio are closely related , this explains why color can be thought of as the fourth Fundamental Plane parameter . However , the slope of the stellar mass Fundamental Plane remains shallower than the value of 2 associated with the virial theorem . This is because the ratio of dynamical to stellar mass increases at large masses : M _ { dyn } / M _ { * } \propto M _ { dyn } ^ { 0.17 \pm 0.01 } . This scaling is the edge-on projection of the stellar mass \kappa -space . The face-on view suggests that there is an upper limit to the stellar density for a given dynamical mass , and this decreases at large masses : M _ { * } / R _ { e } ^ { 3 } \propto M _ { dyn } ^ { -4 / 3 } . All these trends can be used to constrain early-type galaxy formation models . We also study how the estimated coefficients a and B of the Plane are affected by other selection effects , whether in apparent or absolute quantities . For example , if low luminosity objects are missing from the sample , and one does not account for this , then a and B are both biased low from their true values . If objects with small velocity dispersions are missing , then a is biased high , although this matters more for the orthogonal than the direct-fitted quantities . These biases are seen in Fundamental Planes which have no intrinsic curvature , so the observation that a and B scale with L and \sigma is not , by itself , evidence that the Plane is warped . On the other hand , we show that the Plane appears to curve sharply downwards at the small-size/mass end , and more gradually downwards as one moves towards larger sizes/masses . Whereas the drop at small sizes is real , most of the latter effect is due to correlated errors .