Regression Models by Gretl and R Statistical Packages for Data Analysis in Marine Geology

Gretl and R statistical libraries enables to perform data analysis using various algorithms, modules and functions. The case study of this research consists in geospatial analysis of the Mariana Trench, a hadal trench located in the Pacific Ocean. Technically, data modelling was performed using multi-functional combined approach of both Gretl and R libraries. The study aim is modelling and visualizing trends in the variations of the trench’s properties: bathymetry (depths), geomorphology (steepness gradient), geology, volcanism (igneous rocks). The workflow included following statistical methods computed and visualized by Gretl and R libraries: 1) descriptive statistics; 2) box plots, normality analysis by quantile-quantile (QQ) plots; 3) local weighted polynomial regression model (loess), 4) linear regression by several methods: weighted least squares (WLS) regression, ordinary least squares (OLS) regression, maximal likelihood linear regression and heteroskedasticity regression model; 5) confidence ellipses and marginal intervals for data distribution; 6) robust estimation by Nadaraya–Watson kernel regression fit; 7) correlation analysis and matrix. The results include following conclusions. First, the slope angle gradient has a correlation with the geological settings of the trench and distribution of volcanic igneous rocks. Second, the sediment thickness varies by the tectonic plates showing unequal distribution in space. Third, there is a correlation between the slope gradient and aspect degree. Forth, geospatial analysis of the bathymetry shows that the deepest part of the trench is located in the south-west.