Application of Cramer’s Rule and Digital Computing in Analyzing Multiple Linear Regression

Abstract

This paper examined a multiple linear regression model y=β₀ + β₁x₁ + β₂x₂.The model is a relationship between a dependent variable, body mass (y) and two independent variables, age (x₁) and height (x₂). Multivariate data in terms of y, x₁, and x₂ were generated from fifteen first-year students running National Diploma (ND) programme in Department of Computer Engineering, Captain Elechi Amadi Polytechnic, Rumuola, Port Harcourt. The data were used to digitally compute β₀, β₁ and β₂ of the model through the application of Cramer’s rule and the results were validated by SPSS output. Sampled data were also used to compute the Body Mass Index (BMI) of the students to determine whether they were underweight, normal weight, overweight or obese. Additionally, the sampled data values of x₁ and x₂ were used to estimate y using the already computed values β₀, β₁ and β₂. The results of the study showed that values obtained from Cramer’s rule (use of MATLAB 45.0) for β₀, β₁ and β₂ were consistent with SPSS output. Also, computed results β₀=19.0721, β₁=0.3544 and β₂=18.8728 indicated that height (x₂) was a greater predictor of body mass (y) than age (x₁). Further, students’ BMI results revealed that out of the fifteen students sampled, thirteen were of normal weight while two were overweight. It was concluded that: Cramer’s rule is a reliable method of analyzing multiple linear regression models since its results were consistent with SPSS output; although overweight is not an illness, it may be a potential symptom of health risk. Therefore, it was recommended that individuals regularly know their BMI, engage in physical exercise and stay on diets that do not promote overweight to avoid health risks.