Human development index modelling in South Kalimantan province using panel regression

Human development is a paradigm and becomes the focus and target of all development activities. Development is a way to improve welfare and a better quality of life. The Human Development Index (HDI) is one indicator to measure the success of a development. The purpose of this research is to describe the factors that are thought to influence HDI in South Kalimantan Province, estimate the parameters of the HDI panel regression model, and determine the best model. The data of this research is sourced from the Central Statistics Agency (BPS) of South Kalimantan Province with a period from 2015-2018. Based on the results of data analysis it can be concluded that the Fixed Effect Model with the time effect is the best model of the HDI panel regression in South Kalimantan Province with an R-Squared value of 99,81.

An analysis of the HDI of the Province of South Kalimantan in 2015-2018 was carried out again in this study using panel regression to measure the outcome of the development that has been carried out in the Province of South Kalimantan in the following year. Research has identified the factors that have a major impact on HDI estimates in the province of South Kalimantan. Other factors, however, may have influenced the HDI score in South Kalimantan Province. Using a panel regression approach, this study will estimate the regression parameters and determine the optimum HDI model in South Kalimantan Province, as well as estimate the parameters of the HDI panel regression model, and determine the best model.

Descriptive Statistics
Descriptive statistics is a strategy for collecting, classifying, and concisely presenting data so that it can be understood more easily [5].

Panel Regression Analysis
Panel regression analysis is a method for modeling the effect of the independent variable on the dependent variable in different research sectors over a period of time. Model of panel regression [6]:

Estimation Panel Regression Model
Three types of estimations can be used to estimate panel regression [7] 2. 3 H 0 is rejected if JB > 2 ( ,2) with meaning the residuals is not normally distributed.

Multicollinearity Test.
In linear regression, the multicollinearity test is used to measure the correlation of independent variables. One method of detecting multicollinearity symptoms is to examine the R2 value of the estimated regression model and analyze it using a correlation matrix of independent variables [6].
Conclusion: If > reject 0 this indicates that the independent variable has a concurrent effect on the dependent variable.
b. Time Effect Model Hypotheses: Test statistics using equation (10) Conclusion: If > reject 0 this indicates that the independent variable has a concurrent effect on the dependent variable.

The t-test (Partial).
The purpose of t-test testing will be how the independent variables in the Fixed Effect Model affect the dependent variable independently [13]. Hypotheses: Conclusion : If | ℎ | > ( 2 , − ) or 0 is rejected, the independent variable has an individual effect.

Coefficient of Determination.
The coefficient of determination is used to estimate how much of the dependent variable's diversity is explained by the independent variable [6].

Descriptive Statistics
The pattern of HDI distribution in South Kalimantan Province, and also the factors that are thought to influence it.

Panel Regression Model
If the probability value for each variable is greater than the significance = 0,05 level in panel regression analysis, the model is not significant. Variables that are not significant will be excluded from the model one at a period, starting with the one with the highest probability value. The following are the results of the model parameter estimation that was repeated, and the results are as follows: The results of the school participation rate variable with a negative coefficient value can be seen in Table  3. This means that as the value of the school participation rate increases, the HDI value decreases or decreases. Meanwhile, HDI is positively influenced by variables such as expected years of schooling, mean years of school, life expectancy at birth, health facilities, and adjusted per capita expenditure.
According to the value of each coefficient, if the projected expected years of schooling, mean years of school, life expectancy, health facilities, and adjusted per capita expenditure are modified to increase, the HDI value will also expand. The following are the results of the individual effects FEM model equations, as can be seen in Table 4 Ŷ it = α i + 0.9335 1 it + 2.1831 3 it + 1.3144 4 it + ε it The value of the variable expected years of schooling, mean years school, life expectancy at birth has a favorable effect on HDI, as according to Table 4. According to the value of each coefficient, if the predicted length of schooling, the average length of schooling, or life expectancy increases, the HDI value will also increase.  The following are the results of the time effects FEM model equations, as can be seen in Table 5 ̂=̂+ 0.7974273 − 0.0569077 + 1.15169314 + 0.63052511 + 0.0017921 + 0.1157241 + The value of the variable expected years of schooling, mean years of school, life expectancy at birth, health facilities, and adjusted per capita expenditure has a favorable effect on HDI, according to Table  5. According to the value of each coefficient, if the projected expected years of schooling, mean years of school, life expectancy at birth, health facilities, and adjusted per capita expenditure are modified to increase, the HDI value will also grow. The school participation rate variable, on the other hand, has a negative value in the equation. This means that as the value of the school participation rate rises, the HDI value decreases.  Table 6 shows that the variables expected years of schooling, mean years of school, and life expectancy at birth all have positive coefficients, which means that when the HDI value rises, the value of each of these variables rises by the coefficient value. While the variable percentage of the poor people has a negative coefficient, the HDI value will fall by the coefficient value if the percentage value of the poor increases. Table 7. Result Chow Test

Method of Regression Panel
The Fixed Effect Model is the best model if the probability value is less than the value of the significance level = 0,05 and it rejects H0, as shown in Table 7.  Table 8 shows that the probability value is less than the significance level = 0,05, so it is rejected, indicating that the Fixed Effect Model is the best selection. The Fixed model was used in the study and was based on the Chow and Hausman tests.

Multicollinearity Test.
The multicollinearity test is used to see if an independent variable in one model correlates with other independent variables. There must be no correlation between the independent variables in a decent regression model. Table 9. Result Multicollinearity Test  X1  X2  X3  X4  X5  X6  X7  X1 1 Table 9 values of the correlation coefficient between the independent variables < 0.9, it is free from multicollinearity symptoms.

4.4.3
Heteroscedasticity Test. Heteroscedasticity testing is used to determine whether there is an inequality of variance between one residual and another observation in the regression model. Determine if the residual variance-covariance structure is homoscedastic or heteroscedastic. The Breusch Pagan value was calculated using the results of the heteroscedasticity test. The Breusch Pagan value is 28,47 < 2 (0,05,19) = 30,1435 and the probability value (0,07878) > α = 0,05. And Accept H0, which indicates that the model's residual variance is homoscedastic.

4.4.4
Autocorrelation Test. The autocorrelation test is used to see if there is a correlation between confounding errors and residuals in the t-1 (prior) period in a linear regression model.

Effect Test
Statistic

4.5.6
Result Coefficient Determination Using Individual Effect Model. The results of measuring the coefficient of determination using the time effect model were obtained from the study's findings value coefficient 0,981or the independent variable in the individual impact model's Fixed Influence Model has a 98.1% effect.

Conclusion
The following conclusions are drawn from the findings and discussion.