最小二乘法的统计学原理及在农业试验分析中的应用

The Least Squares Method of Statistical Principles and Applications in Agricultural Pilot Study

在现实世界中,普遍地存在着变量之间相互联系、相互制约的关系.那么,怎样用一个简单的解析式较为准确地描述和反映变量之间的关系呢?回归分析是最好的数学工具.在回归分析中,估计回归方程经常用到普通最小二乘法.然而,最小二乘法因其抽象常常被大家所忽视,它是从误差拟合角度对回归模型进行参数估计,并在参数估计以及预测、预报等众多农业领域中得到广泛的应用.就最小二乘法的引入,原理的证明,简单的应用进行归纳和总结.探讨了最小二乘法的线性拟合,对非线性拟合作了简要的叙述,使人们对最小二乘法有更为清晰、系统、全面地认识.农业科学研究影响因素多,能产生多种现象,似乎无规律可循,但是,在一定的条件、范围内,是有一定规律可循的,在这里,采用逆向思维的方法,应用普通最小二乘法就能很好地解决这一类问题,它为农业科研分析提供了一种强有力的手段.

Common in the real world, there are linkages between variables, the relationship of mutual restraint. So, how to use a simple analytic formula more accurately describe and reflect the relationship between the variables？ Regression analysis is the best mathematical tool. Frequently used ordinary least squares regression analysis, the estimated regression equation. The least squares method, however, because of its abstract often been overlooked, and it is from the regression model parameter estimation error fitting angle, and has been widely used in the parameter estimation, forecasting and many other agricultural areas. In this paper, the method of least squares introduced proof of principle, a simple application and summarized. Discussed the linear least squares fitting, nonlinear fitting are presented, so that people have more clear, system, comprehensive understanding of the least square method. Effects of agricultural scientific research by many factors, can produce a variety of phenomena, seems to have no rules to follow, but, in certain conditions, scope, has certain rules, here, by using the method of reverse thinking, application of ordinary least squares method can well solve this kind of problem, provides a powerful means of it is agricultural research analysis.