基于回归分析与灰色预测的中国人口影响因素相关性分析

Correlation Analysis of Chinese Population Influencing Factors Based on Regression Analysis and Grey Prediction

根据国家统计局公布的从1980到2018年人口数量与粮食产量、GDP、人口出生率以及人口死亡率等数据来研究人口数量与这些因素的相关性。首先建立人口数量与这些因素的回归方程模型。然后通过所给的这39年的人口数量及其相关因素数据,训练参数得到回归系数的估计值及其置信区间。从该回归模型的残差图可以看到,某些年份残差距离均值0比较远,剔除这些异常值,利用剔除异常值的数据重新训练该模型,得到新的回归系数估计值及其置信区间,剔除异常值之后的残差平方和更小,并且以更大的可能接受剔除异常值后的回归模型。最后应用灰色预测模型对人口数量观测值进行拟合,残差平方和明显大于回归模型改进前与改进后的残差平方和,这进一步验证了人口数量与粮食产量、GDP、人口出生率以及人口死亡率具有高度相关性。

According to the data released by the national bureau of statistics from 1980 to 2018 on population quantity,grain yield,GDP,birth rate and death rate,the correlation between population and these factors is studied.Firstly,the regression equation model of population quantity and these factors was established and then the estimated value of regression coefficients and their confidence interval are obtained through the population and related factors data given in the 39 years.From the residual diagram,it can be seen that residuals in some years are far from the mean of 0.Subsequently,these outliers are removed and the new regression coefficient estimation and their confidence interval are obtained by retraining the model with the data of removing outlier elimination.The sum of squares of residuals after removing outlier is smaller and the regression model after removing outlier is more likely to be accepted.Finally,the grey prediction model is applied to fit the observed values of population quantity in which sum of squares of residuals is obviously larger than the sum of squares of residuals before and after the improvement of regression model,which further verifies that the population quantity is highly correlated with grain output,GDP,birth rate and death rate.