Many authors, for example Greco and Hakala, have claimed that non-linear regression is always superior to regression of the linear forms of the Michaelis–Menten equation. However, that is correct only if the appropriate weighting scheme is used, preferably on the basis of experimental investigation, something that is almost never done. As noted above, Burk carried out the appropriate investigation, and found that the error structure of his data was consistent with a uniform standard deviation in . More recent studies found that a uniform coefficient of variation (standard deviation expressed as a percentage) was closer to the truth with the techniques in use in the 1970s. However, this truth may be more complicated than any dependence on  alone can represent.
Uniform standard deviation of . If the rates are considered to have a uniform standard deviation the appropriate weight for every  value for non-linear regression is 1. If the double-reciprocal plot is used each value of  should have a weight of , whereas if the Hanes plot is used each value of  should have a weight of .
Uniform coefficient variation of . If the rates are considered to have a uniform coefficient variation the appropriate weight for every  value for non-linear regression is . If the double-reciprocal plot is used each value of  should have a weight of , whereas if the Hanes plot is used each value of  should have a weight of .
Ideally the  in each of these cases should be the true value, but that is always unknown. However, after a preliminary estimation one can use the calculated values  for refining the estimation. In practice the error structure of enzyme kinetic data is very rarely investigated experimentally, therefore almost never known, but simply assumed. It is, however, possible to form an impression of the error structure from internal evidence in the data. This is tedious to do by hand, but can readily be done in the computer.