基于回归理论分析下南瓜估重模型的研究

Model Research on the Problem of Estimating Pumpkin Weight Based on Regression Theoretical Analysis

针对数学建模竞赛南瓜估重问题,主要运用了回归分析理论进行数值模拟。建模前,采用了简单相关分析理论审慎地剔除了线性相关的若干变量,降低了建模的复杂性。然后,分别采用了1种线性回归模型和6种二元高次多项式回归模型对相关数据进行了拟合,并由拟合出的各函数表达式分别求出各模型对应所有数据的误差。通过分析比较所得的误差,对各模型拟合的精度进行了合适地评价,并且挑选出了当前最优模型,也顺利地找到了特殊白南瓜,还为进一步的修正模型剔除了部分不合理数据。最后拟合出最优模型,该模型在假定重量误差允许范围为15.00%的前提下有高达81.25%的拟合准确率,同时又创造性地设计出"查表法"和"卷尺标重法"运用最优模型解决实际估重问题。

According to the problem of how to estimate the pumpkin weight, the regression analysis theory was used to simulate it. Before the mathematical modeling, the simple correlation analysis was used to eliminate linear related variables deliberately in order to reduce the com- plexity of the model. Then a linear regression model and six binary regression models of a polynomial were used to fit the relevant data, and then figure but each function expression and corresponding data error of each model. Through the analysis and comparison of the error, the more suitable model was selected to evaluate the pumpkin weight and select the optimal model. By this way, the special white pumpkin was successfully found and also some unreasonable data were eliminated to further improve the model. Finally, the optimal model was found. This model under the assumption that the allowable error range was within 15.00% pumpkin weight had 81.25% fitting accuracy. Furthermore, according to the optimal model, ＂Look-up Method＂ and ＂Tape Marking Heavy Method＂ were creatively designed to solve practical estimating weight problems.