When it comes to finding the best fit of nonlinear curves to acceptable models, linear regression with least squares is the most effective technique. Because residuals (the difference between observed and predicted data) must follow a normal distribution and the data must be free of outliers and uniform variance, statistical tests are used to identify the most appropriate model for a given situation (homoscedasticity). If all of these characteristics are satisfied, the system is said to be robust. In parametric nonlinear regression, one of the numerous assumptions is that the within-group variances of the groups are all the same, which is one of several assumptions (exhibit homoscedasticity). If the variances vary from one another (show heteroscedasticity), then the model is not statistically competent to describe the data as a whole. Data on the detection of Vibrio cholerae DNA with polystyrene-coacrylic acid composite nanospheres as modelled using the nonlinear four-parameter logistic (4PL) regression was preliminary check for homogeneity of variance using the Bartlett’s and Levene’s tests. It was found that the critical value of 2 was 28.869, according to Bartlett's test findings. Excel's CHIDIST function yielded a probability of 0.389 (not significant), suggesting that the variances of the residuals did not change significantly. The p-value for Levenes's test was 0.917, indicating that there were no distinct changes between the residual variances meaning that the use of the 4-PL model in fitting the data was adequate statistically.
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