**3. Results**

The average BMI *Z*-score of the sample was 2.45 ± 0.46, with 212 participants classified as obese (88%) and 29 (12%) considered overweight. For a more detailed description of the sample characteristics, see Table 1.

For reference, the six baseline multiple linear regression models explaining HRQOL and the dimensions of self-concept (scholastic competence, social competence, physical appearance, behavioral conduct, and global self-worth) adjusting for all independent variables are shown in Table S1 in the supplementary material. Table 2 summarizes the resulting final models after the removal of all insignificant variables using backward stepwise multiple regression analysis.


**Table 1.** Descriptive Sample Characteristics.

<sup>1</sup> High, both parents have completed secondary school; Low, only one parent/neither mother nor father have completed secondary school; HRQOL, Health-Related Quality of Life; *n*, number of participants; SD, Standard Deviation; Min, Minimum; Max, Maximum; ◦ Subdomains of Self-Concept; Psychosocial variables are based on scores ranging from 0 (lowest) to 100 (highest).



\* After removal of all insignificant variables. Significance was set at *p* < 0.05; HRQOL, Health-Related Quality of Life; *β*, Standardized Coeffecient Beta; s.e., Standard Error; Adj, Adjusted; ◦ Subdomain of Self-Concept; Reference Categories: <sup>a</sup> low parental educational level (only one parent/neither mother nor father have completed secondary school/*Abitur*), <sup>b</sup> Non-German.

After all other factors had been accounted for in the final models explaining HRQOL, scholastic competence, and social competence, relative physical fitness remained the only significant predictor. Participants with high levels of relative physical fitness (W/kg) showed higher HRQOL (*β* = 0.216, *p* = 0.011; Adj. R<sup>2</sup> = 0.040, *p* = 0.011) and perceived scholastic (*β* = 0.228, *p* = 0.008; Adj. R<sup>2</sup> = 0.045, *p* = 0.008) and social competence (*β* = 0.197, *p* = 0.023; Adj. R<sup>2</sup> = 0.031, *p* = 0.023). Relative physical fitness explained approximately 3.1–4.75% of total variability in each of these first three models.

We found BMI *Z*-score and physical activity to be significantly associated with only one of the dependent variables investigated. More precisely, BMI *Z*-score (*β* = −0.334, *p* < 0.001) and self-reported physical activity (*β* = −0.164, *p* = 0.040) significantly predicted physical appearance. Jointly with age (*β* = −0.276, *p* = 0.001), the three predictors accounted for approximately 17% of the total variability in the final physical appearance model (Adj. R <sup>2</sup> = 0.171, *p* < 0.001).

In the fifth model explaining behavioral conduct, high parental educational levels (*β* = 0.204, *p* = 0.016) and migration background (No/German; *β* = 0.169, *p* = 0.045) showed a positive association to this subdomain of self-concept and explained a significant proportion of variance (Adj. R<sup>2</sup> = 0.057, *p* = 0.008). Higher parental education was also positively associated with global self-worth (*β* = 0.224, *p* = 0.008), and together with age (*β* = −0.186, *p* = 0.028) accounted for approximately 6% of total variability in the final global self-worth model (Adj. R<sup>2</sup> = 0.063, *p* = 0.005).
