Multiple Regression Analysis Apparatus Stratification Method
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Solution Overview
Problem
The existing multiple regression analysis techniques face challenges in accurately performing analysis when the number of explanatory variables is large, leading to reduced generalization performance due to the 'curse of dimensionality'.
Innovation Solution
A multiple regression analysis apparatus and method that involves determining a stratification explanatory variable, dividing data sets into layers, performing multiple regression analysis on each group, and acquiring an integrated regression equation, while using non-linear regression methods and random forests to calculate contribution rates and reduce the number of explanatory variables.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If new differential explanatory variables are added to improve prediction accuracy, then the accuracy of predicting the objective variable is improved, but the number of explanatory variables increases causing reduced generalization performance
Solution Approach 1:
The patent segments the data sets into multiple groups based on stratification explanatory variables, and performs multiple regression analysis separately on each group. This segmentation approach allows the model to capture different relationships in different data segments without being overwhelmed by the total number of explanatory variables, thus maintaining generalization performance while improving prediction accuracy within each segment.
Solution Approach 2:
The patent extracts and identifies effective explanatory variables through contribution rate calculation and selects appropriate stratification explanatory variables from the original set. By extracting only the most relevant variables for stratification and using them to divide data into manageable groups, the method reduces the effective dimensionality while preserving predictive power.
2Quantity of substance
If the number of explanatory variables is large, then more information is available for analysis, but regression cannot be efficiently performed due to the curse of dimensionality
Solution Approach 1:
The patent divides the data sets into multiple groups using stratification explanatory variables and performs regression analysis on each group separately. This segmentation reduces the effective number of variables to handle in each regression model, making computation more efficient while still utilizing the information from all explanatory variables through the stratification process.
Solution Approach 2:
The patent introduces a new dimension of stratification by using stratification explanatory variables to divide the data into layers. This dimensional approach transforms the problem from handling all explanatory variables simultaneously to handling fewer variables within each stratified group, effectively reducing dimensionality while preserving analytical capability.
3Measurement precision
If automatic stratification is performed to improve analysis accuracy, then the accuracy of multiple regression analysis is improved, but the complexity of the analysis process increases
Solution Approach 1:
The patent implements automatic stratification where the system automatically identifies effective explanatory variables, calculates contribution rates, selects stratification variables, and divides data sets without requiring manual intervention. This self-service approach handles the complexity internally while providing accurate analysis results, shielding the user from the underlying computational complexity.
Solution Approach 2:
The patent uses contribution rate calculation to automatically identify and select appropriate stratification explanatory variables based on their importance to the objective variable. By changing the parameter selection process from manual to automated based on contribution rates, the method reduces the operational complexity while maintaining or improving analysis accuracy.
Data Source
AI summary
A multiple regression analysis apparatus capable of accurately performing a multiple regression analysis is provided. A multiple regression analysis apparatus includes a determination unit, a division unit, an analysis unit, and a regression equation acquisition unit. The determination unit determines one of a plurality of explanatory variables that is effective as a parameter when stratification of a plurality of data sets is performed to be a stratification explanatory variable. The division unit divides the plurality of data sets for each layer using the stratification explanatory variable. The analysis unit performs a multiple regression analysis on each of groups of the plurality of data sets that have been divided. The regression equation acquisition unit acquires an integrated multiple regression equation in which results of the multiple regression analysis are integrated.