The relationship between the regression ANOVA table and ANOVA Table in Complete Factorial Experiments
by
Rawaa Noori Hussein Al-sheikhly
supervised
Prof. Dr. Awad Kadim AL-Khalidy

Abstract
This dissertation highlights the relationship between the two analysis of variance tables, in the regression analysis and the Complete factorial experiments analysis. Also, What this relationship undertakes to define the degree of the Suitable Polynomial. That is used to build a certain regression equation that can locate a specific range of illustrative Variables to reach the best points of response. The design of the complete factorial experiments has been used to find the total squares belonging to each main factor’s Components, and the components’ reactions of two factors. The information of the design has been used to derive the estimated regression parameters and the total squares of each Component and reaction. A Comparison between the two Anova tables indicate similarly result. So is to say that each Component of the design’s Components, or each Component’s reaction of the design’s factors, points to the Polynomial’s degree. Also Rejecting or not Rejecting any component (defined by its’ sum of square) implies a rejection or not rejection the corresponding regression parameter. A study has been done on an individual factor, with (n) levels. Therefore, the equation has (n-1) of components, which are The linear, the quadratic, and the cubic till the last one With (n-1) degree of freedom. The sum of Squares has been computed using a table of orthogonal Polynomial factors. After finding the total Squares of each source of the variance Sources, the results would be displayed in the Variance analysis table. Then, each Source Would undergo the (F) test to identify its importent. To estimate regression polynomial, the method of Ordinary Least Squares (OLS) has been applied, where our focus is placed upon estimating the unknown parameters and finding the components of any form in this model. The application Section, employing hypothetical data, so that the variance analysis results of the practical application for both methods match perfectly. This Confirms that parameters are reliable in applications, the practical and theoretical. We have concluded that using the complete factorial experiments method in estimating and identifying the regression equation’s degree makes it much easier for the mathematical calculations to find sum of Squares of each component. it would also contribute in identifying the regression equation’s degree. And that is What this paper aimed to.