Prediction of Cardiorespiratory Fitness Level of Young Healthy Women Using Non-Exercise Variables

Abstract

Cardiorespiratory fitness (CRF) is considered an important indicator of health in children and adults. The main contribution of this paper is an analysis of cardiorespiratory fitness predictive models among a population of healthy and young women, using the non-exercise variables. The study was conducted on a group of 154 healthy women (aged 20.3 ± 1.2) from selected academic centers in Poland. The VO${}_2$max was measured using a Cosmed K4b2 portable analyzer during a 20 m shuttle test. In addition, selected anthropomotor parameters including body composition components were measured for each subject. The participants’ leisure-time physical activity was assessed using the Minnesota Leisure-Time Physical Activity Questionnaire. The Ridge regression was the most accurate model for estimating VO${}_2$max from anthropometric parameters. The most accurate model based on the level of leisure-time physical activity was calculated using stepwise regression for which the prediction error was at the level of 6.68 (mL·kg${}^{-1}·$min${}^{-1}$). The best model calculated from all non-exercise variables (age, anthropometric parameters, and leisure-time physical activity) had only two predictors: waist circumference and total physical activity, and had a prediction error equal to 6.20 (mL·kg${}^{-1}·$min${}^{-1}$).

1. Introduction

Physical fitness refers to certain physical characteristics of a person. In this context, much emphasis is placed on cardiorespiratory fitness (CRF) [1,2], which is considered a strong indicator of health [3,4,5]. Studies conducted by Andersen et al. [6] show that high CRF levels reduce the risk of cardiovascular diseases, obesity, high blood pressure, and insulin resistance. In addition, it confirms that high CRF levels in childhood and adolescence are associated with a healthy cardiovascular profile in adulthood.

The best CRF indicator is VO${}_2$max, defined as the maximum consumption of oxygen during physical exercise [7]. Direct measurement of VO${}_2$max in the form of a progressive test is the most accurate method for evaluating this parameter but involves several difficulties in the form of expensive laboratory equipment and the need for highly qualified personnel. Additionally, the VO${}_2$max measurement tests [8,9,10] have a high risk related to reaching the maximum heart rate during complete exhaustion [11]. Therefore, such tests are not intended for the elderly or individuals in poor physical condition, suffering from asthma or obesity [12].

Because of these limitations, submaximal effort-based methods [13,14,15] and non-exercise methods are also used to calculate VO${}_2$max predictive models [15]. The advantage of the latter is the possibility of using them in a large population and independently of expensive instruments or exercise tests. VO${}_2$max can be predicted based on gender, age, and anthropometric measurement, as well as functional ability and physical fitness assessment questionnaires. One of the most commonly used tools for measuring the perception of physical effort is the Ratings of Perceived Exertion Scale (RPE), used in studies by Coguart et al. [16]. In addition, the authors measured basic anthropometric measurements and, based on them, created a VO${}_2$max prediction model for obese women. Furthermore, Akay [17] included PFA (perceived functional ability) [7] and PAR (physical activity rating) [18] in presented predictive models. Shenoy et al. (2012) used similar methods in their studies. Non-exercise data included the mean PFA, PAR, and body surface area (BSA) scores [19].

Physical activity is a variable that is often used in predictive models of CRF [20]. Among subjective methods of assessing physical activity, various questionnaires are used to evaluate it [21]. The Minnesota Leisure-Time Physical Activity Questionnaire (MLTPAQ) focuses on collecting information on leisure-time physical activity, which is a very important component of total physical activity [22], significantly influencing cardiovascular risk factors in the adult population [23,24].

Maranhao et al. [25] conducted research aimed at, among other things, estimating the norms of CRF values in the Czech population using the non-exercise equation, including physical activity level, smoking status, age, BMI, waist circumference, and resting heart rate. The CRF values in MET units were presented. This method of estimating CRF was also used in a study by Patel et al. [26]. In the case of the studies carried out by Jang et al. [27], the predictive factors for estimating VO${}_2$max were physical activity variables, smoking status, age, gender, and BMI. Similar variables were used in their research by Peterman et al. [28]. The authors compiled non-exercise variables with direct CRF estimation methods. They selected distinct non-exercise prediction equations, i.e., BMI, waist circumference, dyslipidemia, and hypertension. Participants also completed a questionnaire about health history using the BALL ST questionnaire. To predict maximum VO${}_2$max values in healthy individuals, Genc and Akay [29] developed non-exercise models using various machine learning methods. The models included variables such as age, gender, BMI, body fat, lean body mass, and the activity code (AC) questionnaire variable describing the level of physical activity. The predicted VO${}_2$max, measured during a 3-min walk, was determined based on age, sex, and body composition by Cao et al. [30].

The literature review presented here demonstrates the important role of predictive models in the estimation of maximal oxygen ceiling as an indicator of health. Most of the models presented were based on either maximal or submaximal tests. The use of non-exercise models, which by definition are simpler models to use, provides new opportunities for health monitoring. To the best of the authors’ knowledge, no models have yet been determined for the female student population based on anthropometry parameters and the level of declared physical activity. Additionally, this is the first study on such a large group of female students (N = 154) using direct measurement of VO${}_2$max.

The main objective of this study was to calculate predictive models of cardiorespiratory fitness for healthy and young women using the non-exercise variables. The calculated model was based on age, anthropometric parameters, and level of leisure-time physical activity.

2. Methods

2.1. Subject

The study was conducted on a group of 154 healthy women (aged 20.3 ± 1.2) studying in selected large academic centers in Poland. The women participating in the study were recruited from among female students in various fields of study participating in obligatory physical education classes. Inclusion criteria were voluntary consent to participate in the study and a negative history of starting exercise readiness, after completing the Physical Activity Readiness Questionnaire (PARQ). The exclusion criteria were medical contraindications to participation in the test assessing cardiorespiratory fitness (CRF) and malaise before or during the exercise test. The study was conducted in two stages. The first stage involved 610 women who completed the 20 m SRT. Finally, 154 women randomly selected from among the first-stage participants entered the second stage of the study, and completed a 20 m shuttle test with direct measurement of maximal oxygen uptake (VO${}_2$max).

Predictive models were calculated for the variables presented in Table 1. The analysis included 15 independent variables ($x_1$–$x_{15}$) and only 1 dependent variable (y). Input variables include age ($x_1$), somatic features ($x_1$–$x_5$), body composition ($x_6$–$x_8$), somatic indexes ($x_9$–$x_{11}$), and results of the physical activity questionnaire (described in Section 3.2) ($x_{12}$–$x_{15}$). The value of VO${}_2$max is a dependent variable (y), and it was measured using the 20 m shuttle run test [31].

2.2. Anthropometric Parameters

Body height (BH), waist (WC), and hip (HC) circumferences were measured according to the accepted measurement procedure in anthropometry [32]. Women’s body height was measured without shoes in the so-called Frankfort Horizontal Plane position, using a SECA 213 stadiometer (Hamburg, Germany) with an accuracy of 0.1 cm. Hip circumference (HC) and waist circumference (WC) were measured using a constant tension tape. Hip circumference (HC) was measured through the largest buttock protuberance (at the maximum circumference over the buttocks). WC was measured in the midsection between the lower edge of the last palpable rib and the top of the iliac crest. Body weight and components of body composition (body fat, fat-free body mass, total body water) were measured by bioimpedance analysis (BIA) using a TBF 300 body mass composition analyzer (Tanita Corporation, Tokyo, Japan). In addition, the following anthropometric indices were calculated using formulas: BMI = BW/BH${}^2$—body mass index, WHR = WC/HC—waist–hip ratio, and WHtR = WC/BH—waist-to-height ratio.

2.3. Minnesota Leisure-Time Physical Activity Questionnaire

The Minnesota Leisure-Time Physical Activity Questionnaire (MLTPAQ) is an energy expenditure assessment tool that focuses on gathering information on various forms of leisure-time physical activities. The questionnaire was presented in 1978 by Taylor et al. [33]. It is a recognized subjective method [34,35,36] used in studies into the leisure-time physical activities of adults in various regions of the world [37,38,39], including Poland [40,41,42,43]. The MLTPAQ included leisure-time physical activity in kcal per week, and the final result of energy expenditure (total activity) was presented in terms of exercise intensity of high (≥6 MET), moderate (4.5–5.5 MET) and light (≤4 MET). The examination of student leisure-time physical activity using the MLTPAQ questionnaire was conducted in direct contact with the respondents (face to face).

2.4. VO${}_2$max Measurement

Direct measurement of maximal oxygen uptake VO${}_2$max, breath-by-breath, was performed during a 20 m shuttle running test (20 m SRT) conducted according to Leger [31] description and procedures using a k4b2 analyzer (Cosmed, Roma, Italy). The start speed of the 20 m SRT was 8.5 km per hour. With each next stage of the test, the speed increased by half a kilometer per hour. Before testing, the k4b2 analyzer was warmed up for a minimum of 20 min and then calibrated according to the recommendations, using standard gases (using known gases and room air sampling). Heart rate (HR) per minute during exercise was monitored using a Polar system (Polar Electro Oy, Kempele, Finland), at 5 s intervals. Maximum VO${}_2$max was considered achieved if at least two of four criteria were met: RER (respiratory exchange rate) ≥ 1.10; volitional exhaustion; VO${}_2$ stabilized even with increasing intensity; achieving 90 percent of the maximum target heart rate appropriate for the age of the subject (according to the formula: 220 (bpm)—age (years)) [44,45].

2.5. Predictive Methods

In this study, MISO models for prediction were used (multiple input single output). Ordinary least square regression (OLS), regularized regression, and stepwise regression were used in the calculations of the models. All the methods used are linear.

The implemented methods included OLS regression, in which weights are calculated by minimizing the sum of the squared errors. The study also used stepwise forward regression (OLS–FS) [46,47] where predictor selection based on significance tests is applied, as a result of which only statistically significant input variables remain in the model. This method makes it possible to obtain models with a smaller input structure. Regularized linear models, also known as shrinkage models, which include the Ridge and Lasso methods, were also used to calculate the models. The Ridge model was determined using the criterion which includes a penalty for increased weights. The $\lambda$ parameter decides about the penalty: the greater $\lambda$ the bigger the penalty [48]. The value of $\lambda$ is always positive and for $\lambda =0$ Ridge regression is reduced to OLS regression. LASSO regression similar to Ridge regression, adds to the criterion of performance penalty. In the Lasso model the mechanism facilitates assigning a penalty to variables, and in this way, they are eliminated from equations [49]. This model uses the norm $L_1$ as a criterion of performance.

All predictive models were calculated in R software [50] with additional packages. For Ridge regression, functions from the “MASS” package were used, and for LASSO, the enet function included in the “elastic net” package. To calculate stepwise regression, the “olssr” package was used.

The methods described above were used to calculate predictive models based on all variables (Table 1). In addition, Ridge regression for subcollections of variables received after using the forward selection procedure was calculated. All models were tested using leave-one-out-cross-validation (LOOCV), for which its own functions were prepared. In the process of validation, the ${\mathrm{RMSE}}_{\mathrm{CV}}$ was calculated, which has the form:

(1)${\mathrm{RMSE}}_{\mathrm{CV}}=\sqrt{\frac{1}{\mathrm{n}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}}{\left({\mathrm{y}}_{\mathrm{i}}-{\widehat{\mathrm{y}}}_{-\mathrm{i}}\right)}^2}$

where n—sample size, ${\widehat{y}}_{-i}$—model result calculated after removing the tested pair $({\mathbf{x}}_i,y_i)$.

This paper presents three CRF modeling solutions. In the first part, models calculated only on the basis of anthropometric variables will be presented. In the second, models calculated only for variables describing physical activity will be presented. The third type of models are those calculated for all variables, i.e., anthropometric parameters and physical activity.

3. Results

3.1. Predictive Model Based on Anthropometric Parameters

First, the predictive models were determined, which only included somatic features and the subjects’ body composition (Table 2). The analysis showed that the classic OLS model enabled VO${}_2$max prediction with a relatively large error of 11.51 (mL·kg${}^{-1}·$min${}^{-1}$). The shrinkage regression models have much higher accuracy than the OLS model. The prediction error for the Ridge model is equal to 6.67 (mL·kg${}^{-1}·$min${}^{-1}$), while for the LASSO model, it is equal to 6.71 (mL·kg${}^{-1}·$min${}^{-1}$). The LASSO model rejected the following predictors: BW, WC, and FFM. The most accurate model estimating VO${}_2$max from anthropometric parameters is Ridge regression for a subset of predictors calculated using stepwise regression. This model generates an error of 6.58 (mL·kg${}^{-1}·$min${}^{-1}$) and calculates predictions using four predictors (Age, Fat, TBW, and WHtR).

3.2. Predictive Models Based on MLTPAQ

Another group of models is those estimating VO${}_2$max based on declared physical activity (Table 3). The prediction errors obtained are comparable for all models. The most accurate model was the stepwise regression for which the prediction error was equal to 6.68 (mL·kg${}^{-1}·$min${}^{-1}$). The optimal model contains only one predictor—high-intensity physical activity MLTPAQ${}_H$.

3.3. Predictive Models Based on Anthropometric Parameters and MLTPAQ

The last group of models is based on the entire set of variables, that is, based on anthropometric parameters and declared level of leisure-time physical activity (Table 4). The model with the smallest error was the Ridge model for the subset of predictors calculated using stepwise regression. This model has a prediction error of 6.20 (mL·kg${}^{-1}·$min${}^{-1}$) and is based on two predictors: waist circumference (WC) and total physical activity MLTPAQ${}_T$. This model has higher accuracy than models calculated from only anthropometric parameters (Table 2) and only from declared physical activity (Table 3).

4. Discussion

The main contribution of this study was to calculate models for the prediction CRF among healthy and young women using the non-exercise variables. The presented regression models for predicting VO${}_2$max, which is the best indicator of CRF, based on non-exercise variables. Predictive models of VO${}_2$max based on non-exercise data applied to apparently healthy individuals have their limitations; however, they allow rapid assessment of CRF without the need for a maximal exercise test. Such models are inexpensive, require no specialized equipment, and are time-efficient and feasible for large groups in epidemiological and population-based studies [28]. Non-exercise regression models give relatively accurate results and are a convenient way to predict VO${}_2$max in both adult men and women [51]. Comparing the errors of calculated models with those of other presented solutions in the literature is difficult and in some cases impossible. This is due to the fact that direct comparison of errors is possible only when the same maximum test was used, models were calculated for a similar sample of subjects, and using cross-validation for evaluation predictive ability [52].

All models in this study were developed and cross-validated using data from 154 healthy young women. The models obtained were compared with models presented in other studies. The models determined by the other authors are calculated from a sample that includes men and women. Gender is differentiated by the input variable. Thus, there are models for both men and women, which allows comparison with the model calculated in this work. Direct comparison of the calculated model with other authors’ models is very difficult. The models presented in Table 5 are models for which a different evaluation criterion was used. For most of the models, the SSE or SE fitting error was calculated, while in the present study, a critical approach was taken by evaluating the models with the LOOCV cross-validation. The exception is the model presented in work [53], where the same criteria and the same database were used, except that the model was based on the maximum test. However, when comparing these two models, it is noted that the use of non-exercise variables results in an error gain of only 2.13 (mL·kg${}^{-1}·$min${}^{-1}$). Thus, it can be concluded that non-exercise models have big potential and can be used for CRF estimation.

The analysis showed that in a model based solely on age and anthropometric parameters, the following predictor’s age, body fat, total body water, and WHtR indicator were significant. The predictors obtained are not random, and their significance on VO${}_2$max levels is found in earlier studies [53]. CRF is strongly related to the level of individual components of body composition. Low CRF levels in young adults with high body fat may be a factor in the development of cardiovascular disease in middle age and old age [56]. In addition, an important aspect in assessing the risk of cardiovascular disease, among other things, are indicators of body composition, especially those related to fat distribution such as WC, WHR, and WHtR [57].

For models based on age and leisure-time physical activity rates, MLTPAQ${}_H$ activity proved to be the only significant predictor. A cross-sectional study conducted in a group of healthy men and women over a wide age range showed that the level of leisure-time activity positively shaped peak VO${}_2$. The strongest correlation was observed for high-intensity leisure-time activity [58], which is consistent with the obtained model. Physical activity and CRF play an important role in preventing cardiovascular disease and risk factors [59,60]. Previous studies have also shown that individual CRF levels depend mainly on the level of physical activity [61]. Other studies have also emphasized the importance of lifelong physical activity in enhancing or maintaining CRF [62,63,64].

The model obtained from all analyzed variables (age, anthropometric parameters, and leisure-time physical activity level) has two significant predictors: waist circumference and total physical activity level. The significance of the obtained predictors can be found in other scientific studies. Waist circumference is also a predictor of visceral fat and an indicator of central obesity [65]. Lakoski et al. research [66] confirm the desirability of maintaining a healthy body weight to achieve greater CRF in a healthy population of men and women. Lifestyle changes to increase physical activity, reduce body weight, and improve eating habits are effective in reducing the risk of metabolic syndrome in young adults [67,68]. A World Health Organization document shows that, worldwide, one in four adults and three in four adolescents (ages 11–17) do not meet the recommended health-promoting dimension of physical activity [69]. Physical activity is important for a healthy lifestyle, weight control, and fitness development [70,71]. Studies suggest that increasing physical activity intensity or volume impacts CRF. Even moderate-intensity physical activity at a level of 40–55% VO${}_2$max is sufficient to improve CRF [72,73]. A significant decline in CRF is observed after the age of 30, and the rate of decline significantly accelerates with decreasing physical activity and weight gain [74]. In addition, lower leisure-time physical activity increases the risk of metabolic syndrome, especially in women over 40 years of age [37,38].

The limitations of this research are related to the data used for calculating models. Estimation of VO${}_2$max by the proposed models will be most accurate for a similar group as the one used to calculate the models. This study was unable to externally validate this model and therefore it is not known how it will perform in a different setting and a different population.

The use of presented models makes it possible to evaluate the level of CFR without using specialized and expensive equipment, and which is the most important without the exercise test. The application value of the results is that the prediction is made using data from a physical activity questionnaire and based on basic anthropometric parameters. The prediction of the VO${}_2$max parameter may be useful as an element of monitoring the health and physical performance of young women. The results in the form of predictive model equations will be implemented in the StudentFit application in the future.

Author Contributions

Conceptualization, E.Z., Z.B., M.Z.-D. and K.P.; Data curation, K.N.-C. and M.H.; Investigation, E.Z., Z.B., M.Z.-D., E.N.-B., T.H., K.N.-C. and M.H.; Methodology, E.Z., K.H.P., J.I., É.R.G. and K.P.; Project administration, E.N.-B., T.H. and K.N.-C.; Supervision, E.Z. and K.P.; Visualization, K.P.; Writing—original draft, K.H.P., M.Z.-D. and K.P.; Writing—review and editing, E.Z., J.I., É.R.G. and K.P. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Written informed consent was obtained from all subjects. The project and used methods were approved by the Bioethics Committee of Rzeszow University, Poland, which noted the absence of any contraindications and ethical violations (Resolution No. 20/12/2015). The research was conducted according to the guidelines laid down in the Declaration of Helsinki.

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to privacy.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

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Tables

Table 1

The basic statistics of variables used to calculate predictive models (N = 154).

Variable	Description	$\overline{\mathit{x}}$	$\mathit{sd}$
y	VO${}_2$max (mL·kg${}^{-1}·$min${}^{-1}$)	44.9	7.0
$x_1$	Age (years)	20.3	1.2
$x_2$	Body weight—BW (kg)	58.9	9.8
$x_3$	Body height—BH (cm)	165.0	5.7
$x_4$	Waist circumference—WC (cm)	75.1	8.1
$x_5$	Hip circumference—HC (cm)	95.7	7.5
$x_6$	Body fat—FAT (%)	23.2	7.0
$x_7$	Fat-free mass—FFM (%)	76.7	7.0
$x_8$	Total body water—TBW (%)	56.1	5.2
$x_9$	Body mass index—BMI (kg/m${}^2$)	21.6	3.2
$x_{10}$	Waist-to-height ratio—WHtR	0.46	0.05
$x_{11}$	Waist–hip ratio—WHR	0.78	0.05
$x_{12}$	Light intensity—MLTPAQ${}_L$	488	497
$x_{13}$	Moderate intensity—MLTPAQ${}_M$	386	493
$x_{14}$	High intensity—MLTPAQ${}_H$	932	1798
$x_{15}$	Total activity—MLTPAQ${}_T$	1806	2071

$\overline{x}$—mean value; $sd$—standard deviation; MLTPAQ—Minnesota Leisure-Time Physical Activity Questionnaire.

Table 2

Weights and RMSE${}_{CV}$ errors for models based on anthropometric parameters.

Method	OLS	Ridge ($\mathit{\lambda }=302$)	LASSO ($\mathit{s}=0.2$)	OLS–FS	Ridge–FS ($\mathit{\lambda }=0.1$)
Intercept	244.46	51.20	158.00	167.61	161.48
$x_1$—Age	0.4529	0.2347	0.5481	0.5978	0.6010
$x_2$—BW	$-0.9773$	$-0.0163$	0	0	0
$x_3$—BH	$-0.6820$	$-0.0044$	$-0.1828$	0	0
$x_4$—WC	1.7479	$-0.0363$	0	0	0
$x_5$—HC	0.8833	$-0.0442$	0.1529	0	0
$x_6$—Fat	$-2.0482$	$-0.0419$	$-1.2268$	$-1.3818$	$-1.3201$
$x_7$—FFM	2.9933	0.0267	0	0	0
$x_8$—TBW	$-6.5526$	0.0360	$-1.4244$	$-1.6247$	$-1.5414$
$x_9$—BMI	3.5957	$-0.0728$	0.7615	0	0
$x_{10}$—WHtR	$-573.2857$	$-6.1956$	$-128.0183$	$-23.3978$	$-23.7046$
$x_{11}$—WHR	146.64	$-1.4372$	53.0944	0	0
RMSE${}_{CV}$	11.51	6.67	6.71	9.63	6.58

OLS—ordinary least squares regression; $\lambda$—Ridge regression parameter; s—LASSO regression parameters; Ridge–FS—Ridge regression mogel with input variables calculated by forward regression; RMSE${}_{CV}$—root mean squared error.

Table 3

Weights and RMSE${}_{CV}$ errors for models based on MLTPAQ.

Method	OLS	Ridge ($\mathit{\lambda }=178$)	LASSO ($\mathit{s}=0.1$)	OLS–FS	Ridge–FS *
Intercept	37.7737	39.2731	38.0141	43.6790	–
$x_1$—Age	0.2726	0.2197	0.2608	0	–
$x_{12}$—MLTPAQ${}_L$	$-7.4786$	0.0002	$-0.7479$	0	–
$x_{13}$—MLTPAQ${}_M$	$-7.4785$	0.0002	$-0.7477$	0	–
$x_{14}$—MLTPAQ${}_H$	$-7.4779$	0.0004	$-0.7471$	0.0013	–
$x_{15}$—MLTPAQ${}_T$	7.4791	0.0003	0.7483	0	–
RMSE${}_{CV}$	6.91	6.77	6.88	6.68	–

*—For Ridge, “x” must be an array of at least two dimensions. OLS—ordinary least squares regression; $\lambda$—Ridge regression parameter; s—LASSO regression parameters; Ridge–FS—Ridge regression mogel with input variables calculated by forward regression; RMSE${}_{CV}$—root mean squared error.

Table 4

Weights and RMSE${}_{CV}$ errors for models based on anthropometric parameters and MLTPAQ.

Method	OLS	Ridge ($\mathit{\lambda }=190$)	LASSO ($\mathit{s}=1$)	OLS–FS	Ridge–FS ($\mathit{\lambda }=10$)
Intercept	225.8640	55.3396	225.8640	65.9761	64.6133
$x_1$—Age	$-0.0432$	0.1527	$-0.0432$	0	0
$x_2$—BW	$-0.8807$	$-0.0195$	$-0.8807$	0	0
$x_3$—BH	$-0.5568$	$-0.0080$	$-0.5568$	0	0
$x_4$—WC	1.3967	$-0.0435$	1.3967	$-0.3098$	$-0.2897$
$x_5$—HC	0.8201	$-0.0485$	0.8201	0	0
$x_6$—FAT	$-1.7537$	$-0.0459$	$-1.7537$	0	0
$x_7$—FFM	6.2698	0.0247	6.2698	0	0
$x_8$—TBW	$-10.7272$	0.0327	$-10.7272$	0	0
$x_9$—BMI	2.7528	-0.0870	2.7528	0	0
$x_{10}$—WHtR	$-464.4435$	$-7.3139$	$-464.4435$	0	0
$x_{11}$—WHR	118.3648	$-2.4083$	118.3648	0	0
$x_{12}$—MLTPAQ${}_L$	$-3.0242$	0.0003	$-3.0242$	0	0
$x_{13}$—MLTPAQ${}_M$	$-3.0240$	0.0003	$-3.0240$	0	0
$x_{14}$—MLTPAQ${}_H$	$-3.0238$	0.0004	$-3.0238$	0	0
$x_{15}$—MLTPAQ${}_T$	3.0250	0.0003	3.0250	0.0012	0.0011
RMSE${}_{CV}$	12.54	6.37	12.54	6.21	6.20

OLS—ordinary least squares regression; $\lambda$—Ridge regression parameter; s—LASSO regression parameters; Ridge–FS—Ridge regression mogel with input variables calculated by forward regression; RMSE${}_{CV}$—root mean squared error.

Table 5

Error comparison of non-exercise predictive models.

Author	Method	Criteria
Our study	Ridge–FS	RMSE = 6.20
Bradshaw et al. 2005 [51]	OLS	SE = 3.63
Akay et al. 2009 [17]	SVM	SE = 3.53
Nielson et al. 2010 [54]	OLS	SE = 3.56
Akay et al. 2017 [55]	OLS	SSE = 5.14
Przednowek et al. [53]	RBF	RMSE = 4.07

RMSE—root mean squared error; Ridge–FS—Ridge regression model with input variables calculated by forward regression; SVM—support vector machine; OLS—ordinary least squares regression; RBF—artificial neural network with radial basis function.

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