## Two-way ANOVA by using Cholesky decomposition and graphical representation

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.51, no.4, pp.1174-1188, 2022 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 51 Issue: 4
• Publication Date: 2022
• Doi Number: 10.15672/hujms.955559
• Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
• Page Numbers: pp.1174-1188
• Keywords: &nbsp, Cholesky decomposition, aalysis of variance and covariance (ANOVA), linear equations, COVARIANCE-MATRIX, FACTOR MODELS
• Istanbul University Affiliated: Yes

#### Abstract

In general, the coefficient estimates of linear models are carried out using the ordinary least squares (OLS) method. Since the analysis of variance is also a linear model, the coefficients can be estimated using the least-squares method. In this study, the coeffi-cient estimates in the two-way analysis of variance were performed by using the Cholesky decomposition. The purpose of using the Cholesky decomposition in finding coefficient estimates make variables used in model being orthogonal such that important variables can be easily identified. The sum of squares in two-way analysis of variance (row, column, interaction) were also found by using the coefficient estimates obtained as a result of the Cholesky decomposition. Thus, important variables that affect the sum of squares can be determined more easily because the Cholesky decomposition makes the variables in the model orthogonal. By representing the sum of squares with vectors, how the prediction vector in two-way ANOVA model was created was shown. It was mentioned how the Cholesky decomposition affected the sum of squares. This method was explained in detail on a sample data and shown geometrically.