The study showed that 1) the PA score obtained using m-WLAQ, rather than sitting times, was associated with measured VO2max; 2) the equation models that included age, sex, body fat-related values, and PA score obtained using m-WLAQ had favorable validity for estimating VO2max; 3) no appreciable difference was observed in estimated VO2max among the three models with regard to BMI, WG, and %fat; and 4) favorable reliability values were shown for sitting times and the PA score obtained using m-WLAQ.
Consistent with the findings of a previous study , significant negative correlations were observed between sitting times and measured VO2max (Table 3). However, sitting times were not accepted as an effective explanatory variable for estimating VO2max in our regression analyses. In contrast, questionnaire-based PA data, such as frequency, duration, and intensity, were significantly correlated with measured VO2max (Table 3), and the regression model identified the PA score to be the principal explanatory value for the equation models. The PA score was calculated for precise VO2max prediction in reference to the HUNT study by Nes et al.  and a previous exercise intervention study . Nes at al . used some question items regarding PA frequency, duration, and intensity for estimating VO2max and relative weightings of different responses were set on the basis of their relation to VO2max. In their estimation, PA intensity was weighted more heavily than PA duration and frequency on the PA score. Further, an exercise intervention study  emphasized the primacy of PA intensity rather than PA duration and volume in improving VO2max. We followed these studies to develop the PA score, i.e., the questions regarding intensity, such as Q6, Q10, and Q15, were weighted more heavily than other questions (Table 2). The PA score was strongly correlated with VO2max (Table 3) and functioned well for estimating VO2max (Table 4). The results of previous studies and the present study suggest that PA intensity can have a potential role in estimating VO2max.
Age, sex, and body fat-related values were significantly correlated with measured VO2max (Table 3), and these three factors accounted for 43–51% of the variance in measured VO2max (Table 4). These percentages increased by 11–16% following to addition of the PA score obtained using the questionnaire in the model (Table 4). Jackson et al.  suggested questionnaire-based VO2max prediction models including age, sex, body fat-related values, and the PA score obtained using the questionnaire, demonstrating SEEs of 5.35–5.70 ml·kg− 1·min− 1. Similarly, Wier et al.  suggested questionnaire-based VO2max prediction models including age, sex, body fat-related values, and the PA score obtained using the questionnaire, demonstrating SEEs of 4.72–4.90 ml·kg− 1·min− 1. Furthermore, Malek et al.  developed a VO2max prediction equation including age, body weight, height, and questionnaire-based exercise values, which had an SEE value of 4.12 ml·kg− 1·min− 1. The present study showed results similar to these previous studies, with prediction model SEEs of 4.13–4.29 ml·kg− 1·min− 1. These SEE values can be replaced with %SEE values of 10.8–11.2%. Other types of VO2max estimation studies reported %SEE values of 11.4% in the 20-m shuttle run test study  and 10–15% in wearable device studies [13, 27, 28]. The SEE values in the present study seem to be favorable when compared with those calculated in other VO2max prediction studies.
Regarding the method to validate a regression equation, although the data-splitting method is well known, in which the entire data are divided into a fitting group and validation group, the PRESS method  is particularly recommended for studies with a small sample size. This method can provide useful diagnostics while avoiding the disadvantages of the data-splitting method such as lack of equation stability due to diluted sample size. In fact, studies with a large sample size, such as those of Jackson et al. (1999 participants)  and Nes at al. (4637 participants)  used the data-splitting method. However, the PRESS method has not only been used in studies with a large sample size such as in that of Matthews et al. (799 participants)  and Wier at al. (2801 participants)  but also in studies with a small sample size such as those of Malek et al. (115 participants)  and Cao et al. (148 participants) . The PRESS method appeared to be appropriate for the present study on 198 participants.
Jackson et al.  recommended questionnaire-based VO2max prediction models including age, sex, the PA score obtained using the questionnaire, and body fat-related values such as %fat (skinfold method) and BMI, and they demonstrated SEE values of 5.35 ml·kg− 1·min− 1 for the %fat model and 5.70 ml·kg− 1·min− 1 for the BMI model. Wier et al.  also recommended questionnaire-based VO2max prediction models including age, sex, the PA score obtained using the questionnaire, and body fat-related values such as %fat (skinfold method), WG, and BMI and they showed no considerable differences in accuracy among the three models using WG (SEE value of 4.80 ml·kg− 1·min− 1), %fat (SEE value of 4.72 ml·kg− 1·min− 1), or BMI (SEE value of 4.90 ml·kg− 1·min− 1). The present study obtained results similar to those of previous studies, i.e., no considerable difference was observed in accuracy among the three body fat-related variables, i.e., BMI, WG, and %fat (bioelectrical impedance analysis). Although the SEE value of the BMI model (4.29 ml·kg− 1·min− 1 or 11.2%) was relatively higher than those of the WG (4.17 ml·kg− 1·min− 1 or 10.9%) and %fat (4.13 ml·kg− 1·min− 1 or 10.8%) models, which are consistent with the findings reported by Wier et al. , the BMI model could be more convenient than the other models because BMI is a basic and less burdensome assessment item in adult health checkups. Therefore, the following equation model is suggested for VO2max estimation in the present study (using sex = 0 for women and 1 for men): VO2max = 59.96 + (− 0.23 × age) + (7.39 × sex) + (− 0.79 × BMI) + (0.33 × PA score).
There are some limitations to the present study. First, response bias may have occurred because the participants had advance knowledge of the experimental procedure, i.e., they could decide to participate in this study after viewing our research advertisement, which may have led to greater inclusion of participants preferring PA or exercise. Second, CE analyses (Table 5) and scatter graphs (Fig. 1) showed that the CRF evaluation model derived in the present study significantly underestimated VO2max in participants with high fitness and overestimated VO2max in those with low fitness. This systematic error usually occurs in VO2max estimation studies [15, 17]. As pointed out by other researchers [15, 17], while underestimation in individuals with high fitness may not be a pressing problem because high fitness relates to low disease and mortality risks, overestimation in individuals with low fitness may be more problematic because low fitness relates to increasing disease risks. A correction method such as a compensation formula or including a convenient stress test should be considered to correct the error, particularly in individuals with low fitness. Third, we could not include approximately 50% of the participants in test–retest reliability analyses because they did not participate in the second round of m-WLAQ. Participant selection bias could have occurred because the selection was not conducted at random but in accordance with participant convenience. Fourth, in recent public health research, moderate-to-vigorous intensity PA (MVPA) has been treated as an important terminology separately from SB [30, 31]. MVPA and SB are defined as accelerometry-measured PA of ≥3.0 metabolic equivalents (METs) and PA of ≤1.5 METs, respectively . m-WLAQ can assess SB but not MVPA.