Reference sample size for multiple regression in corn

Abstract: The objective of this work was to determine the number of plants required to model corn grain yield (Y) as a function of ear length (X1) and ear diameter (X2), using the multiple regression model Y = β0 + β1X1 + β2X2. The Y, X1, and X2 traits were measured in 361, 373, and 416 plants, respectively, of single-, three-way, and double-cross hybrids in the 2008/2009 crop year; and in 1,777, 1,693, and 1,720 plants, respectively, of single-, three-way, and double-cross hybrids in the 2009/2010 crop year, totaling 6,340 plants. Descriptive statistics were calculated, and frequency histograms and scatterplots were created. The sample size (number of plants) for the estimate of the β0, β1, and β2 parameters, of the residual standard error, the coefficient of determination, the variance inflation factor, and the condition number between the explanatory traits of the model (X1 and X2) were determined by resampling with replacement. Measuring 260 plants is sufficient to adjust precise multiple regression models of corn grain yield as a function of ear length and ear diameter. The Y = -229.76 + 0.54X1 + 6.16X2 model is a reference for estimating corn grain yield.

摘要：本研究旨在确定以穗长（X1）和穗粗（X2）为自变量构建玉米籽粒产量（Y）多元回归模型（multiple regression model）时所需的植株样本量，所用模型形式为Y = β0 + β1X1 + β2X2。2008/2009生长季，分别对单交、三交和双交杂交种的361株、373株和416株植株测定了Y、X1、X2性状；2009/2010生长季则分别测定了1777株、1693株和1720株上述三类杂交种的对应性状，总样本量共计6340株。研究计算了各性状的描述性统计量，绘制了频数直方图与散点图。通过放回式重抽样法，确定了模型β0、β1、β2参数估计、残差标准误（residual standard error）、决定系数（coefficient of determination）、方差膨胀因子（variance inflation factor）以及模型自变量（X1与X2）间条件数对应的样本量。结果表明，测定260株植株即可拟合精度优异的玉米籽粒产量随穗长、穗粗变化的多元回归模型。本研究得到的Y = -229.76 + 0.54X1 + 6.16X2模型可作为玉米籽粒产量估算的参考模型。

搜集汇总

背景与挑战

背景概述

该数据集研究了玉米产量与穗长、穗径的多元回归模型，基于两个作物年度的6340株玉米测量数据，确定260株样本即可建立精确模型，并提供了参考回归方程Y = -229.76 + 0.54X1 + 6.16X2。