A number of statistical implications of empirical scaling laws in form of power products obtained by linear regression are analysed. The sensitivity of the error against a change of exponents is described by a sensitivity factor and the uncertainty of predictions by a "range of predictions factor". The sometimes small value of the former and corresponding large value of the latter are related to the existence of inner relations in the statistical material used. A procedure for identifying inner relations is outlined. The relations can be of physical nature or can be due to a deliberate or incidental selection of data. In the latter case finding inner relations can help the experimentalist in choosing the experimental variables with necessary and sufficient density in parameter space. Also discussed are the consequences of discarding variables, in particular the effect of eliminating the inner relations by a corresponding reduction of parameter space. Finally a recipe is given for the computations to be done. The whole is exemplified by considering scaling laws for the electron energy confinement time of ohmically heated tokamak plasmas.