Multiple Linear Regression Assumption Test: Detecting Outlier and Influential Point on Laboratory Measurement Data Using Diagnostic Methods

Abstract

This study aims to test the assumptions of multiple linear regression by detecting the presence of outlier, high leverage point, and influential point in laboratory measurement data using diagnostic methods. The study was conducted using 321 samples of lady finger bananas, including acidity (pH), total dissolved solids (^oBrix), and peel color components (Red, Green, Blue/RGB). The analysis stages include building an initial regression model using the R Studio application, applying diagnostic methods consisting of: R-student for outliers, hat matrix for high leverage point, and DFFITS for influential point, and performing automatic iterations by removing data detected as influential point until a convergent data condition (free from influential point) is obtained. The data iteration process stops at the 17^th iteration, with the final result being 178 data sets free from influential point. The final iteration results for the pH prediction model obtained a regression equation ŷ_i = 5,8096 + 0,0143R – 0,0263G + 0,0138B with a coefficient of determination (R²) of 82,25% and a residual variance (s2) of 0,0138. The final iteration results for the Brix prediction model obtained a regression equation ŷ_i = 22,3332 – 0,0936R + 0,1175G – 0,0521B with a coefficient of determination (R²) of 47.57% and a residual variance (s²) of 0.5424. The presence of outlier and influential point data can damage the assumption of normality and affect the results of regression parameter estimation. The use of repeated diagnostic methods (iterations) is very necessary to clean the model from the influence of unusual data so that a more accurate and reliable regression model is produced.