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The non-parametric regression model can consider two correlated responses. However, for these conditions, we cannot use the usual estimation process because there are violations of assumptions. To solve this problem, we use a penalized weighted least square involving knots, smoothing parameters, and weighting in the estimation criteria simultaneously. The estimation process involves a weighted criteria matrix  in the estimation criteria. Estimation results show that the estimated two-response non-parametric regression function with penalized spline is a linear estimation class in y response observation and depends on the knot point and smoothing parameter. Furthermore, the use of the model on toddler growth data shows some changes in the pattern of weight and height gain. The pattern segmentation that experienced a gradual increase was age 7-43 months for weight and age 6-54 months for height

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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.