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Journals / Hacettepe Journal of Mathematics and Statistics / 2022 / Cilt: 51 - Sayı: 4

Two-way ANOVA by using Cholesky decomposition and graphical representation

Mustafa TEKİN
Haydar EKELİK
Pages
1174–1188
Publication Date
2022-08-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This method was explained in detail on a sample data and shown geometrically.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In general, the coefficient estimates of linear models are carried out using the ordinary least squares (OLS) method.
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Key Findings & Data:Since the analysis of variance is also a linear model, the coefficients can be estimated using the least-squares method.
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Conclusion & Impact:This method was explained in detail on a sample data and shown geometrically.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Cholesky decomposition · aalysis of variance and covariance (ANOVA) · linear equations

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 coefficient 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.

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Cite This Article

TEKİN, M., EKELİK, H. (2022). Two-way ANOVA by using Cholesky decomposition and graphical representation. Hacettepe Journal of Mathematics and Statistics, Cilt: 51 - Sayı: 4, 1174–1188. https://ajindex.com/articles/669186

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