In this paper , after collecting 57 shell-type galactic supernova remnants data , we first make the statistical result of \Sigma - D relation on these data by applying the linear regression method .
Our statistical result shows that the best fit line slope of \Sigma - D relation is \beta = -2.56 , which is slightly flatter than those proposed by some other authors before .
In addition , comparing with the statistical results of \Sigma - D relation by some other authors , we can find that a transition point is usually introduced in their statistical results .
In order to make a theoretical interpretation for this transition point in the statistical results of \Sigma - D relation , we also analytically investigate the \Sigma - D relations of shell-type supernova remnants at 1 GHz both at the adiabatic phase and radiative phase , which is simply followed the work Duric & Seaquist ( 1986 ) .
Our analytical results show that indeed there can be a transition point at 1 GHz between these two analytical \Sigma - D relations .
Moreover , the analytical transition point is 30 pc , which can be consistent with the statistical results at 1 GHz made by some other authors before , i.e .
32 pc at 1 GHz made by Allakhverdiyev et al .
( 1983 ) .