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Research On Partial Correlation Analysis Based On Variables Of Nonlinear Relation

Posted on:2019-03-21Degree:MasterType:Thesis
Country:ChinaCandidate:Y GaoFull Text:PDF
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In the age of big data,it is essential to study the relationship between things.The connection between things is very complex,correlation analysis is one of the most important methods to get useful information from these data.It has gradually penetrated into many fields from simple problems of genetic and height.The partial correlation analysis has attracted the attention of researchers.The partial correlation analysis refers to the analysis of the correlation of two certain variables after excluding the influence of other variables for a plurality of numerical variables.Compared with simple correlation analysis,it can reflect the real and essential correlation between variables more accurately.In statistics,partial correlation coefficient is used to measure the degree and direction of correlation between variables,whose research is based on the normal distribution of variables.In the linear case,the partial correlation coefficient is equivalent to the conditional correlation of other variables under the condition that one variable is constant.But in most cases,the relationship between variables is very complex,which is not linear certainly,and nonlinearity may occupy a large part.In this case,the accuracy of the correlation measured by partial correlation coefficient will be reduced,even there is a big difference with the actual.Since there are few studies on this problem,this paper studies the correlation analysis between variables of nonlinear relation.The accuracy of partial correlation analysis is affected by the neglect of the basic as-sumptions in the use of partial correlation.Conditional correlation cannot be used to explain partial correlation when nonlinear relation exists.Based on this problem,this paper takes the variables with nonlinear relationship as the research object,and focuses on the partial correlation and conditional correlation of these variables.The effect of all components re-lated to control variables is excluded from the essence of partial correlation in this paper,and it is proved that the modified partial correlation and conditional correlation are not only equivalent to each other,but also more robust.In this paper,a new nonlinear relation model which called model 3 is proposed,and the results are in agreement with the above results.Then according to the two indexes of evaluating the fitting quality of the model in nonlinear regression method,the new model is further compared with the existing model.The result shows that the new model is fits better,which reflects the superiority of the new model.This paper consists of five parts:Chapter ?:Introduction.The research background,purpose and significance of partial correlation analysis are briefly stated,and the research status is analyzed,and the main research problems and innovations of this paper are expounded.Chapter ?:The introduction of correlation analysis methods.Some commonly corre-lation methods are introduced,and each method and its scope of application is described,and the definition of partial correlation coefficient is introduced in detail at the same time.Based on the existing models,the main problems to be studied in this paper are pointed out.Chapter ?:Robustness analysis of partial correlation coefficient.For the result that the nonlinear partial correlation is not equivalent to conditional correlation,Further revisions are made in this paper.Combined with the essence of partial correlation coefficient definition,the correction method is proved to be reasonable by theoretical deduction,and so that the partial correlation coefficient has better robustness.Chapter ?:Partial correlation between variable of cubic curve relation.Considering the shortcomings of the existing nonlinear model 2,a new nonlinear model is constructed which called model 3.The partial correlation and conditional correlation between this model and existing model 2 are compared and analyzed,and the results show that they are not equal.Based on this,the correction calculation is carried out,and the correction is proved to be reasonable.Finally,the model is compared and analyzed according to two indicators in nonlinear regression,and the results show that model 3 has better fitting effect.Chapter ?:Conclusions and expectation.The main contents of this paper is summa-rized,and the future research directions are pointed out.
Keywords/Search Tags:Partial Correlation, Conditional Correlation, Nonlinear Relationship, Nonlinear Regression
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