Alternative approach to fitting first-order model to the response surface methodology

In this paper, we present the computational procedure of the First-Order Model in Response Surface Methodology (RSM) in a new dimension. Firstly, we fit the First-Order Model to a 2k design by applying Yates' technique to calculate the sum of squares of main effects and their interactions. Secondly, we prove that SS regression and SS linear are equivalent. Thirdly, we give a new idea for computing SS quadratic under the concept of unbalanced Completely Randomized Design. The formula used in this technique is numerically and mathematically equivalent to the existing technique. Lastly, we split the total variation in the responses into all possible sources with the help of a diagram.