Editing Lineweaver–Burk plot (section)

== Shortcomings ==

The Lineweaver–Burk plot does a poor job of visualizing experimental error.<ref name=dowd>{{Cite journal|last1=Dowd|first1=John E.|last2=Riggs|first2=Douglas S.|date=February 1965|title=A Comparison of Estimates of Michaelis-Menten Kinetic Constants from Various Linear Transformations|journal=Journal of Biological Chemistry|volume=240|issue=2|pages=863–869|doi=10.1016/s0021-9258(17)45254-9|issn=0021-9258|doi-access=free}}</ref> Specifically, if the errors <math>\varepsilon (v)</math> have uniform standard errors, then those of <math>1/v</math>  vary over a very wide range, as can be seen from the following example:

: If <math>v = 1 \pm 0.1</math> then the range of  <math>1/v</math> is 0.91–1.11, approximately 20%
: If <math>v = 10 \pm 0.1</math> (same standard deviation) then the range of  <math>1/v</math> is 0.0990–0.1001, approximately 1%.

Lineweaver and Burk were aware of this problem, and after investigating the error distribution experimentally,<ref name=Ergeb>{{cite journal | journal = Ergebnisse der Enzymforschung  | volume = 3  | pages = 23–56 | author = Burk, D. | title = Nitrogenase}}</ref> finding a uniform standard deviation in <math>v</math>, they consulted the eminent statistician [[W. Edwards Deming]].<ref>{{cite journal
| author = Lineweaver H, Burk D, Deming, W E
| journal =  J. Amer. Chem. Soc.
| volume = 56
| pages = 225–230
| title = The dissociation constant of nitrogen-nitrogenase in ''Azobacter''
| year = 1934
| doi = 10.1021/ja01316a071
}}</ref> In the light of his advice they used weights of <math>v^4</math> for fitting their <math>1/v</math>. This aspect of their paper has been almost universally ignored by people who refer to the "method of Lineweaver and Burk."{{Fact|date=April 2023}}

The values measured at low <math>a</math>, and hence large values of <math>1/a</math> lead to points on the far right of the plot and have a large effect on the slope of the line, and thus in particular on the value of <math>K_\mathrm{m}</math>.