In the empirical analysis, we must first determine the research problems and objectives, and then choose the appropriate data sources and methods for data collection. The quality and integrity of data are very important to the results of empirical analysis, so it is necessary to carefully screen and process the data. Next, statistical methods or machine learning algorithms can be used to analyze the data to verify the hypothesis and prediction ability of the model. Commonly used statistical methods include descriptive statistics, regression analysis and variance analysis. Machine learning algorithms such as linear regression, logical regression and decision tree are also commonly used in empirical analysis.
When checking the model, you can evaluate the performance of the model by the following methods:
1. Cross-validation: divide the data set into training set and test set, use the training set to build the model, then use the test set to predict the model, and calculate the error or accuracy between the predicted result and the actual result.
2. Sensitivity analysis: change the values of parameters or input variables in the model, observe the changes of model output, and evaluate the sensitivity of the model to parameter changes.
3. Residual analysis: calculate the residual between the predicted value of the model and the actual observed value, analyze the distribution and correlation of the residual, and evaluate the fitting degree of the model.
4. Comparative analysis: Compare with other existing models, and evaluate the performance of the model on the same data set.
In a word, empirical analysis and model test are indispensable links in the national competition paper of mathematical modeling. Through reasonable data collection and analysis methods and scientific model checking means, the validity and accuracy of the model can be effectively evaluated, and the scientificity and credibility of the paper can be improved.