基于线性回归模型、马尔萨斯人口增长模型及logistic模型的全国人口预测

Population forecast nationwide based on linear regression model,Malthus Population Growth Model and logistic model

目的为了更好地认识我国人口的数量变化规律,并对我国未来人口进行预测。方法根据国家统计局官网公布的1949-2019年人口数据,计算人口增长率,分析人口增长规律;利用1949-2014年的人口数据依次建立线性回归模型、马尔萨斯人口模型及logistic模型,利用相对误差对3种模型进行评价,预测我国2020-2040年人口数,分析未来人口发展变动趋势。结果我国人口增长率呈下降趋势,1960、1961年出现人口负增长,其余年份均为正增长;通过模型拟合,对比发现:线性回归模型存在较大误差,马尔萨斯人口模型预测误差最大,logistic模型比线性回归模型及马尔萨斯模型有很大的改善。结论logistic模型更适合长期的人口预测,误差更小,模拟精度更好,所预测的结果可信度更高。

Objective To have a better understanding of the change laws of Chinese population and predict the future population of China.Methods The population growth rate was calculated and the law of population growth was analyzed according to the population data from 1949 to 2019 published on the official website of the National Bureau of Statistics.The linear regression model,Malthusian population model and logistic model were established by using the population data from 1949 to 2014,which were evaluated with relative errors to predict the population in 2020-2040,and analyze the change trend of future population development.Results The population growth of China showed a downward trend,with negative population growth in 1960 and 1961,and positive growth in the rest years.It was found through model fitting and the comparison that the linear regression model had large errors,the Malthus population model had the largest prediction error,and the logistic model was much better than the linear regression model and Malthus model.Conclusion Logistic model is more suitable for longterm population prediction,with smaller error,better simulation accuracy and more reliable prediction results.