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【2017年整理】数学建模公选课第五讲.ppt

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3、预测与控制 (1)预测 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. (2)控制 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 四、可线性化的一元非线性回归(选讲) (曲线回归) 例2 出钢时所用的盛钢水的钢包,由于钢水对耐火材料的侵蚀, 容积不断增大.我们希望知道使用次数与增大的容积之间的关 系.对一钢包作试验,测得的数据列于下表: Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 散 点 图 此即非线性回归或曲线回归 问题(需要配曲线) 配曲线的一般方法是: Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 通常选择的六类曲线如下: Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 一、数学模型及定义 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 二、模型参数估计 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 三、多元线性回归中的检验与预测 (Ⅰ)F检验法 (Ⅱ)r检验法 (残差平方和) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2、预测 (1)点预测 (2)区间预测 返回 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 四、逐步回归分析 (4)“有进有出”的逐步回归分析。 (1)从所有可能的因子(变量)组合的回归方程中选择最优者; (2)从包含全部变量的回归方程中逐次剔除不显著因子; (3)从一个变量开始,把变量逐个引入方程; 选择“最优”的回归方程有以下几种方法: “最优”的回归方程就是包含所有对Y有影响的变量, 而不包含对Y影响不显著的变量回归方程。 以第四种方法,即逐步回归分析法在筛选变量方面较为理想. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 这个过程反复进行,直至既无不显著的变量从回归方程中剔除,又无显著变量可引入回归方程时为止。 逐步回归分析法的思想: 从一个自变量开始,视自变量Y作用的显著程度,从大到地依次逐个引
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