基于逐步回归模型的空气质量数据的校准与统计分析

Calibration and Statistical Analysis for the Data of Air Quality based on Stepwise Regression Model

空气污染破坏生态环境并危害人类健康,通过对“两尘四气”的监测可以掌控空气质量。基于2019年全国大学生数学建模竞赛D题,首先对自建点和国控点“两尘四气”的数据进行探索性分析;然后利用单因素方差分析法研究导致自建点和国控点数据差异的原因,并建立多元逐步回归模型确定绝对误差与气象参数的数量变化规律;最后将气象参数一一对应代入回归方程,得出绝对误差的预测值,再作与真实绝对误差的相对误差,从而实现用国控点数据对自建点数据进行校准。

Air pollution damages the ecological environment and endangers human health.By monitoring“two types dusts and four types gases”,the quality of air can be mastered.To study the data of Section D of China Undergraduate Mathematical Contest in Modeling(2019),first the data of two types dusts and four types gases at the self-built site and the national control site are analyzed in an exploratory way.Then,one-way ANOVA was used to study the different reasons between the two sites,and a multiple stepwise regression model was established to determine the quantitative variation law between the absolute error and meteorological parameters.Finally,the meteorological parameters are substituted into the regression equation to obtain the predicted value of the absolute error,and then the relative error with the real absolute error is made,so as to achieve the calibration of data for self-built site with the data of national control site.