Diabetes Mellitus (DM) is often recognized through an increase in a person's blood sugar level. Factors that can affect the increase in blood sugar levels of DM patients one of which is cholesterol. It usually contains the bookkeeping of several types of cholesterol, including LDL and total cholesterol. DM data are assumed to experience heterokedasticity so that in this study analyzed using regression of weighted cubic spline nonparametric. The estimation method used is weighted least square (WLS). This study aims to obtain a weighted cubic spline model on cholesterol based DM data. The selection of the best model can be seen based on the criteria for the value of generalized cross validation (GCV) minimum. Based on the analysis obtained weighted cubic spline models for cholesterol factors for blood sugar as follows:

In the formation of a regression model there is a possibility of a relationship between one predictor variable with other predictor variables known as multicollinearity. In the parametric approach, multicollinearity can be overcome by the principal component analysis method. Principal component analysis (PCA) is a multivariate analysis that transforms the originating variables that are correlated into new variables that are not correlated by reducing a number of these variables so that they have smaller dimensions but can account for most of the diversity of the original variables. In some research data that do not form parametric patterns also allows the occurrence of multicollinearity on the predictor variables. This study examines the ability of spline estimators in the analysis of the main components. The data contained multicollinearity and was applied to diabetes mellitus data by taking cholesterol type factors as predictors. Based on the estimation results, one main component is obtained to explain the diversity of variables in diabetes data with the best linear spline model at one knot point.

The Poisson hidden Markov model is a model that consists of two parts. The first part is the cause of events that are hidden or cannot be observed directly and form a Markov chain, while the second part is the process of observation or observable parts that depend on the cause of the event and following the Poisson distribution. The Poisson hidden Markov model parameters are estimated using the Maximum Likelihood Estimator (MLE). But it is difficult to find analytical solutions from the ln-likelihood function. Therefore, the Expectation Maximization (EM) algorithm is used to obtain its numerical solutions which are then applied to life insurance data. The best model is obtained with 2 states or m = 2 based on the smallest Bayesian Information Criterion (BIC) value of 338,778 and the average predicted number of claims arrivals is 0.385 per day.

This research aims to describe the parameter estimation of the regression model on the panel data by approaches of Fixed Effects Model with within a group method. This research aims to determine the factors that influence the Human Development Index in South Sulawesi Province in 2011-2017 using Panel Data Regression Analysis. The regression model was obtained from the maximum likelihood estimation using within group approach using a mean for each independent variable and the dependent variable to find out the intercept differences in each city or cross-section that explains the effect of regional differences and to find out the intercept differences for cross sectional or time series. The results showed that the average length of the school variable (𝑋1) and life expectancy variable (X2) significantly affects the Human Development Index (Y) in the Province of South Sulawesi in 2011-2017.