Validity of Polynomial Regression Analysis of Body Fat Percentage in Relation to BMI in Japanese Junior High School Girls

Abstract

BMI (Body Mass Index) is simple and convenient for determining the hypertrophy degree, but because the degree of fat mass accumulation differs in relation to the physique, the physical ability (physical fitness and athletic ability) of the obese and the slim may be misjudged. In order to solve this problem, it is necessary to establish a methodology that can verify the physical fitness of people by categories, after they are categorized according to their degree of fat mass accumulation in relation to BMI. The methodology is to apply polynomial regression analysis of body fat percentage to BMI and to verify its validity. This method was applied to 750 junior high school girls in Osaka City, from which 341 girls with no missing values in the measurement data were selected. Measurements were taken from April to June 2022. Body size and body composition were measured using a body composition analyzer (InBody 3.2, Biospace). Height was measured using a digital height scale; BMI was calculated by dividing weight (kg) by the square of height (m). Physical fitness was measured in grip strength, upper body sit-up, seated long forward bend stretch, repeated side-to-side jump, and 20-m shuttle run. Athletic ability was measured in 50-m run, standing long jump, and handball throw. The results showed that for each hypertrophic group classified by BMI, the cubic polynomial regression curve of BMI for body fat percentage further classified morphological quality into three categories: overfat, normal, and underfat, according to the degree of fat accumulation relative to BMI. The reason why the cubic polynomial regression was valid was due to statistical logic and the logic that the relationship between BMI and body fat percentage is a sigmoid-shaped composition. In addition, the logistic model of sigmoid shape can be applied to the increase in body fat percentage in response to the increase in BMI, and the marginal body fat percentage hypothesis can be proposed for the female junior high school students in this study, in which body fat percentage stabilizes from a BMI of around 30.