Formulating of Linear Model from One-Way Classification Model

Abstract

This study introduces a novel approach to formulating a linear regression model using a matrix method for Completely Randomized Design (CRD), a type of One-Way classification. In this approach, treatment is the sole classification, and the formulation utilizes response variables organized into rows and columns. The method yields the number of trials (n), slope, predictor, and regression parameters within the system. To ensure the normality of the response variable and select the appropriate error term distribution, we conducted normality tests (Shapiro-Wilk, Anderson-Darling, Cramér-von Mises, Lilliefors) and exploratory data analysis techniques (histogram, boxplot, QQ-plot). The formulation was validated through illustrations, and the results from the matrix method regression were compared to the ordinary least squares regression, yielding identical values for the regressors, and confirming the robustness of the proposed formulation. Furthermore, we evaluated the performance of machine learning linear regression model, which outperformed ordinary least squares regression in terms of mean absolute error, mean square error, and root mean square error, demonstrating the superior accuracy of the proposed approach.