Research On Sample Statistics-Based Regression Method

Regression analysis is a statistical analysis method to determine the quantitative relationship between two or more variables,which is widely used.The reliability of the regression model is strongly dependent on the reliability of the sample data.It is worth noting that in the process of realistic prediction,it is often difficult for us to obtain complete data,and there will be some subjectivities in the selection and processing of data.Since the data itself is not complete,there will be deviations in the reflected facts,and the unreliability of the data directly leads to the deviation in the predicted results.Although there are a lot of researches and modifications on the classical regression model,most of them are based on the integrity and reliability of the data,without considering the reliability of the prediction from the data itself.However,data missing is a form that is often encountered in the process of practical prediction.Therefore,it is of great theoretical significance and application value to study regression prediction model in consideration of data missing.Based on sample size and sample variance,this dissertation mainly does the following work: 1)Based on the statistical theory and the analysis of the function characteristics of sample size on the prediction results,a measurement strategy of sample credibility based on sample size was developed,a sample aggregation method based on mean was developed,and a weighted regression prediction model based on sample size was established,which is simply called SR-CRM.Then,the application process of the method is analyzed in combination with specific cases.Compared with the classical regression prediction model,the method simplifies the calculation through data integration,and the obtained prediction results have high credibility,which provides a new method for regression prediction and has strong practicability in practical prediction problems.2)For the heteroscedasticity of regression model,the weighted least square method is difficult to determine the weight.This dissertation proposes the idea of stratifying the samples according to the sample variance so as to eliminate the heteroscedasticity of each layer of samples.The weight function was established,and the sample regression function at each layer was fitted.Finally,the weighted regression function based on sample stratification was obtained,which was simply denoted as CPM-SD.Then,the practicability of the model was verified by a case.Compared with the weighted least square method,the method not only reduces the amount of calculation,but also gives a higher credibility to the predicted results,which provides a new idea for solving the heteroscedasticity problem and has a higher practicability in the real heteroscedasticity problem.