Bootstrap Resampling in Gompertz Growth Model with Levenberg–Marquardt Iteration

Abstract

Soybean plants have limited growth with a planting period of 12 weeks, which causes the observed sample to be very small. A small sample of soybean plant growth observations can be bias causes in the conclusion of prediction results on soybean plant growth. The purpose this study is to apply the bootstrap resampling technique in Gompertz growth model which overcomes residual distribution with small samples, the research data was taken from soybean plant growth in four varieties with four spacing treatments, five replications and twelve weeks (long planting period). Gompertz growth model uses nonlinear least squares method in estimating parameters with Levenberg–Marquardt iteration. The value of the Gompertz model after resampling bootstrap has no significant difference. The adjusted R2 value of 0.96 is close to 1. This means that the total diversity of plant heights can be explained by the Gompertz model of 96 percent. Judging from the graph of predictions of soybean plant growth before resampling and after resampling coincide with each other it can also be seen in the initial growth values before resampling 14, 05 and 14.18, the maximum growth values are 55.13 and 55.60. Bootsrap resampling technique can overcome residual normality in the Gompertz growth model, but does not change the information in the initial data.