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二次回归正交旋转组合设计所建立的数学模型一般表达式为二次正交多项式:y=β_0+β_1X_1+β_2X_2…β_p×X_p+β_(12)X_1X_2+β_(13)X_1X_3+…+β_(p-1),_pX_(p-1)X_p+β_(11)X_1~2+β_(22)X_2~2+…+β_(pp)X_p~2+ε上式的p表示自变量的个数,β_1表示X_1的总体偏回归系数,β_2表示X_2的总体偏回归系数,…,β_p表示X_p的总体偏回归系数,β_(12)表示X_1与X_2的交互作用的总体偏回归系数,β_(13)表示X_1与X_3的交互作用的总体偏回归系数,…β_(p-1),_p表示X_(p-1)与X_p的交互作用的总体偏回归系数,β_(11)表示X_1的平方项的总体偏回归系数,β_(22)表示X_2的平方项的总体偏回归系数,…,β_(pp)表示X_p的平方项的总体偏回归系数,ε为试验的随抗误差。上述的数学模
The general expression of the mathematical model established by quadratic regression orthogonal rotation combination design is quadratic orthogonal polynomial: y = β_0 + β_1X_1 + β_2X_2 ... β_p × X_p + β_ (12) X_1X_2 + β_ (13) X_1X_3 + ... + β_ p - 1 p - 1 p - 1 X_p + β 11 X 1 ~ 2 + β 22 X_2 - 2 + ... + β - P x_p ~ 2 + ε p in the above expression represents the number of independent variables , β_1 denotes the overall partial regression coefficient of X_1, β_2 denotes the overall partial regression coefficient of X_2, ..., β_p denotes the overall partial regression coefficient of X_p, β_ (12) denotes the overall partial regression coefficient of interaction between X_1 and X_2, β_ (13) ) Denotes the overall partial regression coefficient for the interaction of X_1 and X_3, ... β_ (p-1), _p denotes the overall partial regression coefficient of the interaction of X_ (p-1) and X_p, β_ (11) denotes the square term of X_1 Β_ (22) denotes the overall partial regression coefficient of the square term of X_2, ..., β_ (pp) denotes the overall partial regression coefficient of the square term of X_p, and ε is the error tolerance of the experiment. The above mathematical model