In the field of ecology, the relationship between the concentration of available dissolved organic substrate and the rate of uptake (velocity) of that substrate by heterotrophic microbial communities has been described by the Michaelis-Menten model. The velocity \((y)\) and concentration \((x)\) data shown in the following table were collected by the Department of Biology at Virginia Tech.

Fit the Michaelis-Menten model to the data. Investigate the adequacy of this model.

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Observation y x 1 0.0773895 0.417 234 4557 2 0.0688714 0.417 3 0.0819351 0.417 0.0737034 0.833 0.0738753 0.833 6 0.0712396 0.833 0.0650420 1.670 8 0.0547667 1.670 9 0.0497128 3.750 10 0.0642727 3.750 11 0.0613005 6.250 12 0.0643576 6.250 13 0.0393892 6.250