A Method of Constructing Models for Estimating Proportions of Citrus Fruit Size Grade Using Polynomial Regression

Abstract

Estimating the fruit size is an important factor because it directly influences size-specific yield estimation, which would be useful for pricing in the market. In this paper, it was considered a method of constructing models for estimating the proportion of fruit size grades of citrus using polynomial regression. In order to construct models, curvilinear regressions were performed, utilizing the fruit diameters of a kind of citrus (Citrus junos Sieb. ex Tanaka) in the harvest. The constructed models were validated by comparison with another model, which was constructed using a combination of four datasets obtained from three orchards differing in the number of fruit sets. The estimation model’s accuracy (EMA, defined as the sum of the absolute difference between the actual and estimated proportions of each grade) was used for the evaluation of constructed models. The EMAs of 14 models applied to 28 validation data were ranging from 2.0% to 6.1%. In all validations, the proportions of fruit size grade were insignificant at a 5% level by Pearson’s chi-square test. Additionally, a comparison of EMAs differing in the number of trees by the constructed models showed that most were within EMA ≤ 10.0% in the case calculated by 10 trees. Validation of five farmers’ orchards indicated that the EMA of two was within 10.0%, and the EMA of three was at 11.3 to 12.5%. These results revealed that the constructed models could be applied to orchards for differing numbers of fruit sets. The acceptable accuracy was derived by at least over 10 trees investigated at one time.