Response surfaces and designs

SUMMARY In this Study, the polynomial approximation is applied by the Taylor expression to the equation of the expected response surface; The equation E(Y) = fT|j= f(x,(3) is effected by one or more variables is expressed by the X vector that is controlled by the experimenters or the researches, and 3 is unknown parameters vector, and the standard errors are under normal distribution assumption. 8~N (0, tf2) As a result, it is shown algebraically that the equation is a general solution of a differential equation in all cases. The least squares method is used, and some of the results that is formed by the matrix equations are proved, and also the simply formed first-order polynomial model is applied, but it is recognised that the lack of fit and the curvature of the surface requires the application of second-order polynomial expressions. First the model is translated then rotated in order to eliminate the pure first-order terms and mixed second-order terms. Consequently, the high order polynomial is geometrically interpreted by the coefficients of the canonical form that is found after, and also some designs are investigated. In the application [KHURI. A. and J.A. CORNEL-1987 Exercises 5-6] that is studied, polynomial models are applied with respect to data, and maximum product is attained at the stationary point and lack of fit is tested.