论析因试验的效应重分及其响应曲面的正交多项式回归

THE DECOMPOSITION OF EFFECTS OF FACTORIAL EXPERIMENT AND ORTHOGONAL POLYNOMIAL REGRESSION ANALYSIS OF RESPONSE SURFACE

本文对析因试验的主效应、交互作用及其分解的直线效应、二次方效应、三次方效应和这些效应两两间的交互效应作了明确的阐述,同时对其平方和的分解作了严格的理论推导。文中用正交多项式系数表将这些效应及其平方和计算表格化,从而使统计分析变得简明扼要。最后用正交多项式回归法对达显著的效应作出回归函数,服务于生产实践。

In this paper,the main effect and interaction of factorial experiment are decomposed into linear effect,quadratic effect and cubic effect.At the same time,a proof is given how to divide the sum of squares of the experiment effects.All the effects and the sum of squares of effects can be worked out with an orthogonal polynomial coefficient table.An orthogonal polynomial regression is also given on the significant effects.