Statistical diagnostic tests of residuals from the Gompertz model used in the fitting of the growth of <i>E. coli</i> measured using a real-time impedimetric biosensor

  • Mohd Shukri Shukor Department of Biochemistry, Faculty of Biotechnology and Biomolecular Sciences, Universiti Putra Malaysia, UPM 43400 Serdang, Selangor, Malaysia.
  • Mohd Yunus Shukor Department of Biochemistry, Faculty of Biotechnology and Biomolecular Sciences, Universiti Putra Malaysia, UPM 43400 Serdang, Selangor, Malaysia.


The development of in situ sensor for measuring bacterial concentrations in biotechnology and the health sciences would allow real-time monitoring of the concentration of bacteria. Kim et al [1] has developed such a method using impedance spectroscopy, and was able to measure in realtime the concentration of E. coli at 0.01 MHz frequency using impedance changes. We modeled the growth kinetics using several nonlinear regression methods and discovered that the modified Gompertz model is the best model for the growth of the bacterium [2]. It is well known that nonlinear regression of a data and further statistical analysis to find the best model relies on the facts that the residuals (difference between observed and predicted data) followed a normal or Gaussian distribution and that the data must be free of outliers. If all of these assumptions are satisfied, the test is said to be robust. In this work we perform statistical diagnostics to the residuals to satisfy the requirements above and found that removal of an outlier allows the residuals to conform to all of the requirements above. The results indicated that remodelling of the Gompertz model using the new set of data should be carried out.


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