Inside of the Linear Relation between Dependent and Independent Variables

Abstract

Simple and multiple linear regression analyses are statistical methods used to investigate the link between activity/property of active compounds and the structural chemical features. One assumption of the linear regression is that the errors follow a normal distribution. This paper introduced a new approach to solving the simple linear regression in which no assumptions about the distribution of the errors are made. The proposed approach maximizes the probability of observing the event according to the random error. The use of the proposed approach is illustrated in ten classes of compounds with different activities or properties. The proposed method proved reliable and was showed to fit properly the observed data compared to the convenient approach of normal distribution of the errors.

Evaluation of a Gluten-Based Edible Film Incorporated with Beetroot Extract and ZnO Nanoparticles as an Active Food Packaging System

“…The application of simple models suggested the statistical procedures for many situations involve a degree of correlation between two variables to better understand the linear relationship among the explanatory variables. 38,39 Table 1 outlines the experimental design using a constant amount of gluten and constant volumes of both ethanol and glycerin while varying the compositions of the GBEF matrix in terms of the amount of BE ranging from 0.5 to 1.5% and ZnONPs ranging from 0.1 to 0.4%.…”

“…The experimental design coded by the symbols A, B, C, D, E, F, G, H, and I was aimed to represent the different compositions of GBEF incorporated with various amounts of BE as high as 0.5, 1.0, and 1.5% and ZnONPs as high as 0.1, 0.2, and 0.4% (Table ). The application of simple models suggested the statistical procedures for many situations involve a degree of correlation between two variables to better understand the linear relationship among the explanatory variables. , Table outlines the experimental design using a constant amount of gluten and constant volumes of both ethanol and glycerin while varying the compositions of the GBEF matrix in terms of the amount of BE ranging from 0.5 to 1.5% and ZnONPs ranging from 0.1 to 0.4%.…”

Key Factors Determining the Expected Benefit of Customers When Using Bank Cards: An Analysis on Millennials and Generation Z in Romania

“…In order to relate the variables, linear association model was used. In the research literature there are many alternate, linear regression methods: Reference [55] proposed an approach for modelling the dependency with exponential, power or inversed equations, while Reference [56] address the multiple linear regressions by maximizing the likelihood under the assumption of generalized Gauss-Laplace distribution of the error. In our research, the Enter method was used for multiple linear regression model, which includes all variables in the analysis, and thus, all variables start with the same initial value.…”

Uji Kelayakan Konstruksi Balok Pt Daeyung Dari Aplikasi Sap2000 Menggunakan Machine Learning Dengan Model Linier Regression

“…Regresi linier merupakan ukuran statistik yang dipakai guna mengetahui kekuatan statistik yang dipakai guna mengetahui kuatnya hubungan antara variabel terikat (dependent) dengan variabel bebas (bebas). Metode peramalan atau prediksi adalah dengan membangun model regresi yang mencari ikatan antara satu atau lebih variabel bebas atau prediktor (X) dan variabel terikat atau respon (Y) (Jäntschi, et al 2015). Regresi linier memodelkan hubungan antara variabel skalar dan satu atau lebih variabel penjelas.…”