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Estimates from confidence intervals are more powerful than point estimates, because there are intervals for parameter values used to estimate populations. In relation to global conditions, involving issues such as type 2 diabetes mellitus, it is very difficult to make estimations limited to one point only. Therefore, in this article, we estimate confidence intervals in a truncated spline model for type 2 diabetes data. We use a non-parametric regression model through a multi-variable spline linear estimator. The use of the model results from the irregularity of the data, so it does not form a parametric pattern. Subsequently, we obtained the interval from beta parameter values for each predictor. Body mass index, HDL cholesterol, LDL cholesterol and triglycerides all have two regression coefficients at different intervals as the number of the found optimal knot points is one. This value is the interval for multivariable spline regression coefficients that can occur in a population of type 2 diabetes patients.

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In this paper, we study an extracellular process of a biochemical system such as batch ethanol fermentation system by considering an unstructured kinetic model with four different wellknown models for the specific growth rate of the yeast cells. Then, we fit the unstructured models to the experimental data for determining the appropriate model that can capture the dynamic behaviour of the batch ethanol fermentation experimental data. The fitting procedure is proceeded by minimising a least-squared error between the model solutions and the experimental data using a direct search method. Our simulations show that the unstructured model with Aiba-type structured model for the specific growth rate of the yeast cell has the best approximating ability to describe the dynamic of the batch ethanol fermentation data.