基于主成分回归分析的环境因素与学生身高关系的研究

为探讨环境因素对学生身高的影响,对30个城市2010年18岁汉族男女学生身高平均数与相应城市的海拔高度、地理纬度、经度和2010年前18年的年降水量、年平均气温、年平均湿度、年日照时间和年人均GDP等环境指标进行相关分析和主成分回归分析.结果显示:不同纬度、经度地区的城市18岁汉族学生身高的差异明显;除海拔高度外,另7项环境指标与学生身高具有相关关系,但环境指标间相关程度较高,独立性差,存在共线性问题;环境指标主成分分析提取了2个主成分,分别代表气象因素和社会经济因素;用其得分建立了与城市18岁男、女学生身高的主成分回归方程,并将其转换为与原环境指标之间的线性回归方程用于推测2010年和2005年18岁学生的身高,推测精度高.因此,身高与海拔高度无相关,与纬度、经度、年日照时间和年人均GDP呈正相关,与年降水量、年平均气温和年平均湿度呈负相关;若城市的这些环境指标已知,即可预测其学生的身高.

A study on the relationship of environmental factors and the height of students based on principal component regression

To investigate the effect of environmental factors on students＇ height, mad correlation analysis and principal component regression analysis about the relationship of the height of 18 years old Han students in 2010 and altitude, latitude, longitude and the annual averages of precipitation, temperature, relative humidity, sunshine time and per capita GDP of 18 years before 2010 in the capital cities of 30 provinces. Results： the area difference of the height of 18 years old Han students of the cities in different latitude and longitude was great. Except altitude, there was a relationship between the height and the other seven environmental factors, but the factors lacked for independence and had the eollinear problem; established a principal component regression equation of the height of 18 years old students in the cities and environmental factors with the principal component analysis. Converted it to a linear regression equations with the primary indexes for predicting the height of students in 2010 and 2005. The prediction was of high accuracy. Conclusion： the height of 18 years old Han students in city was uncorrelated with altitude, but positively correlated with latitude, longitude, annual sunshine time and per capita GDP, negatively correlated with annual precipitation, annual average temperature and annual mean relative humidity; if these environmental indicators of the city are known, student＇s height could be predicted.