A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes

Aerobic capacity refers to the body's ability to consume oxygen during activity, that is, the exchange of carbon dioxide and water in the body. Exercise requires a certain concentration of oxygen, so it is important to test its maximum intensity. Through experiments we can conclude that people in physical exercise is mainly dependent on their own nutrients and energy[1]. The most important point is that the muscles, bones and joints are oxygenated; secondly, the nerve fiber tissue plays a big role in the metabolic process of the body and can improve the metabolic capacity of the body and maintain the function of the respiratory system, thus promoting metabolism and the level of function of the body. The most important thing is that sports performance is directly proportional to physical performance[2]. Therefore, we have to find out the connection between the factors affecting the athletes' health test data and analyze them, and then draw conclusions and make reasonable suggestions to help the coaches to improve themselves in teaching and training; and also focus on the most important and critical sports skills and knowledge possessed by the sports talents themselves[3,4].

Sports science is a long history of research projects, from ancient times to the present, people attach great importance to sports, especially after the Olympic Games is an important benchmark to measure the level of a country and comprehensive national power. Athletes continue to participate in fitness activities to enhance physical fitness and improve the quality of life, by more and more social groups and people from all walks of life widely concerned[5]. In recent years, the overall physical quality of our athletes has been declining significantly and showing a downward trend year by year, which makes them more sensitive to the index of sports performance. Therefore, in order to better understand the most critical factors of athletes' fitness, this paper mainly focuses on the various reasons affecting sports performance as the starting point for research. This paper is an in-depth study of the different factors that contribute to the decline of athletes' fitness and the improvement of their physical health through literature and mathematical and statistical analysis[6,7].

A multifactorial regression model is a multiple linear or multi-causal regression equation that is autocorrelated, mutually exclusive and interdependent and mutually constrained based on the relationships between multiple variables. A large amount of data information is used in athletics. This sample information can be obtained by collecting and organizing it, and therefore requires research methods such as analytical processing and prediction of the raw data. And the use of statistical tools to perform statistical tests on these data is also one of the important tasks, and the expression of the multifactorial regression analysis method is shown in equation (1). (1) Y=a0+a1x1+⋯+apxp+εε∈N(0,σ2) \matrix{ {Y = {a_0} + {a_1}{x_1} + \cdots + {a_p}{x_p} + \varepsilon } \hfill \cr {\varepsilon \in N\left( {0,{\sigma ^2}} \right)} \hfill \cr }

Among them, a0, a1, ..., ap are all unknown parameters that have nothing to do with x0, x1, ..., xp, and are further expressed in the form of a matrix as shown in equation (2): (2) X=[ 1x11⋯x1p1x21⋯x2p⋮⋮⋮⋮1xa1⋯xnp ],Y=[ y1y2⋯yn ],B[ a1a2⋯ap ] X = \left[ {\matrix{ 1 & {{x_{11}}} & \cdots & {{x_{1p}}} \cr 1 & {{x_{21}}} & \cdots & {{x_{2p}}} \cr \vdots & \vdots & \vdots & \vdots \cr 1 & {{x_{a1}}} & \cdots & {{x_{np}}} \cr } } \right],\,Y = \left[ {\matrix{ {{y_1}} \cr {{y_2}} \cr \cdots \cr {{y_n}} \cr } } \right],\,B\left[ {\matrix{ {{a_1}} \cr {{a_2}} \cr \cdots \cr {{a_p}} \cr } } \right]

Transforming equation (2) yields equation (3). (3) XT XB=XTY {X^T}\,XB = {X^T}Y

Then, according to the least squares method, the regression parameters are calculated as shown in Equation (4). (4) B=(XTX)−1 XTY B = {\left( {{X^T}X} \right)^{ - 1}}\,{X^T}Y

The test of the regression model: i.e., to test the effect of any independent variable Xi on the dependent variable Y. The significance issue is the hypothesis test of the regression coefficient B = (b0, b1,..., bp).

Assume that Equation (5) holds: (5) H0:b0=b1=b2=⋯=bp=0.−b±b2−4ac2a \matrix{ {{H_0}:{b_0} = {b_1} = {b_2} = \cdots = {b_p} = 0.} \hfill \cr {{{ - b \pm \sqrt {{b^2} - 4ac} } \over {2a}}} \hfill \cr }

The corresponding test statistic is shown in Equation (6). (6) MSS/fMSSESS/fESS∼F(fMSS,fESS) {{MSS/{f_{MSS}}} \over {ESS/{f_{ESS}}}}\sim F\left( {{f_{MSS}},{f_{ESS}}} \right)

The meaning of building regression models is to predict, so the regression model must ensure its good predictive performance. In other words, it should not be out-of-fit or over-fit. The goodness of fit (i.e., the coefficient of determination) is a measure of the effectiveness of the regression equation often recorded as Equation (7): (7) R2=SSreturnSStotal=1−MSresidualMStotal {R^2} = {{S{S_{{\rm{return}}}}} \over {S{S_{{\rm{total}}}}}} = 1 - {{M{S_{{\rm{residual}}}}} \over {M{S_{{\rm{total}}}}}}

Aerobic capacity refers to the ability of the body to consume oxygen through breathing, diet and exercise, which ensures that the gases in the body are not oxidized and reduced to carbon dioxide, and that the oxygen content in the cells is increased and maintained in a healthy state[8]. The principle diagram of aerobic respiration is shown in Figure 1.

Figure 1

The most important thing in physical exercise is to systematically test all tissues and organs of human body, among which the main thing is to test the cardiopulmonary function of athletes, and evaluate the sports performance according to the results of cardiopulmonary function test, so as to provide scientific and effective reference basis for athletes and improve the training efficiency. The detection of the cardiopulmonary function of the distance mobilization requires the use of athletes' cardiopulmonary function testing model (as shown in Figure 2). Human cardiopulmonary function is a reflection of the impact of the human heart, respiratory system and circulatory system on the body's exercise process, and this can promote the body's blood and tissue to be fully utilized, thereby improving the survival rate of the living body.

Figure 2

The cardiopulmonary function of the human body is closely related to the metabolites of the body. Therefore, it is important to measure the oxygen intake, heart rate, oxygen pulse rate, respiratory exchange rate and anaerobic valve to determine the status of cardiac vitality and physiological activity. In addition, the role of cortical excitability and stability can be evaluated by detecting the amount of oxygen consumed, oxygen consumption and carbon dioxide concentration in the body using a heart consumption meter. In addition, the test of human cardiopulmonary function can be used to determine whether the athlete has an optimal oxygen source.

Oxygen intake: athletes need to consume a certain amount of oxygen during exercise, and excessive oxygen intake is one of the main causes of the decline in body function and physiological imbalance. The calculation of oxygen intake for athletes is shown in equation (8). (8) VO2max=HRmax×MSV×OPD {V_{{O_2}\max }} = {H_{{R_{\max }}}} \times {M_{SV}} \times {O_{PD}}

Heart rate: is an important indicator of athletic performance, and test data for its effective assessment can help predict the state of the athletes performed in the competition. The specific calculation is shown in equation (9). (9) HRmax=220−Age {H_{{R_{\max }}}} = 220 - {A_{ge}}

Oxygen pulse: It is an important physiological indicator in the human body, which reflects the consumption of oxygen by a variety of living organisms such as the heart and blood vessels, so that we can see whether the oxygen supply in the human body is sufficient. The specific calculation is shown in equation (10). (10) O2P=SV×OPD {O_{2P}} = {S_V} \times {O_{PD}}

Respiratory exchange rate: In competitive sports, the respiratory exchange rate of an athlete affects his or her athletic performance, and the effect of maximizing the training effect is whether the athlete is aerobically capable. The specific calculation is shown in equation (11). (11) RQ=VO2VCO2 {R_Q} = {{{V_{{O_2}}}} \over {{V_{C{O_2}}}}}

Anaerobic valve: The main function of the anaerobic valve is to control the gas to meet certain requirements in aerobic state and keep it constant for a certain period of time[9].

Using the multiple linear regression model (as shown in Figure 3), a detection algorithm can be constructed that can detect the cardiorespiratory function of athletes during aerobic training, so as to realize the dynamic detection of the cardiorespiratory function of athletes after aerobic training. Multiple regression methods can predict, analyze, and evaluate problems on variables. It is conditioned on uncertain factors, and this can obtain a functional relationship (factor) related to it to describe the model or process, so that a reasonable and effective solution can be established by using its inherent laws.

Figure 3

The multiple regression discriminant statistic is defined as shown in Equation (12). (12) C(m)=1(N−m)1/2⋅∑i=1N−m(xi−xi+m)3[ ∑i=1N−m(xi−xi+m)2 ]3/2 C\left( m \right) = {1 \over {{{\left( {N - m} \right)}^{1/2}}}} \cdot {{\sum\limits_{i = 1}^{N - m} {{{\left( {{x_i} - {x_{i + m}}} \right)}^3}} } \over {{{\left[ {\sum\limits_{i = 1}^{N - m} {{{\left( {{x_i} - {x_{i + m}}} \right)}^2}} } \right]}^{3/2}}}}

When the athlete performs aerobic training, the maximum oxygen uptake that can best reflect the athlete's cardiorespiratory function is defined as the independent variable, and other cardiorespiratory function test indicators are used as the dependent variable, and the multiple linear regression equation is obtained as shown in Equation (13): (13) xn=φ0+∑i=1pφixn−i+∑j=1pφjxn−j {x_n} = {\varphi _0} + \sum\limits_{i = 1}^p {{\varphi _i}{x_{n - i}}} + \sum\limits_{j = 1}^p {{\varphi _j}{x_{n - j}}}

In order to effectively realize the dynamic detection of the cardiopulmonary function of athletes after aerobic training, it is necessary to define the difference significance index of the multiple linear regression model, as shown in Equation (14): (14) S=| 〈 Qs 〉−Q0 |σs S = {{\left| {\left\langle {{Q_s}} \right\rangle - {Q_0}} \right|} \over {{\sigma _s}}}

Using the least squares method to estimate the parameters in the multiple linear regression, assuming that φ^i {\hat \varphi _i} and θ^j {\hat \theta _j} denote the θ_j least squares estimates of the parameters φ_i and respectively, the observed values of aerobic training cardiorespiratory fitness testing in athletes can be expressed as shown in Equation (15). (15) x^n=φ^0+∑i=1pφ^ixn−i+∑j=1qθ^jxn−j {\hat x_n} = {\hat \varphi _0} + \sum\limits_{i = 1}^p {{{\hat \varphi }_i}{x_{n - i}}} + \sum\limits_{j = 1}^q {{{\hat \theta }_j}{x_{n - j}}}

The particle swarm optimization method is also a multi-factor regression method, and the analysis of the particle swarm optimization method is shown in Figure 4. Its basic idea is to build a mathematical model by imitating the laws and characteristics of various things in nature itself under specific conditions of the research object[10].

Figure 4

Firstly, assume that the solution space is a D-dimensional search domain consisting of h particles. The particle orientation, velocity and position are shown in equations (16), (17) and (18), respectively. (16) si=(si1,si2,⋯,siD),i=1,2,⋯,m {s_i} = \left( {{s_{i1}},\,{s_{i2}}, \cdots ,{s_{iD}}} \right),\,i = 1,\,2,\, \cdots ,\,m (17) vi=(vi1,vi2,⋯,viD),i=1,2,⋯,m {v_i} = \left( {{v_{i1}},\,{v_{i2}}, \cdots ,{v_{iD}}} \right),\,i = 1,\,2,\, \cdots ,\,m (18) li=(li1,li2,⋯,liD),i=1,2,⋯,m {l_i} = \left( {{l_{i1}},\,{l_{i2}}, \cdots ,{l_{iD}}} \right),\,i = 1,\,2,\, \cdots ,\,m

The evolutionary process is shown in equations (19) and (20). (19) vid(t+1)=ωvid(t)+r1(lid−sid(t))+r2(lid−sid(t)) {v_{id}}\left( {t + 1} \right) = \omega {v_{id}}\left( t \right) + {r_1}\left( {{l_{id}} - {s_{id}}\left( t \right)} \right) + {r_2}\left( {{l_{id}} - {s_{id}}\left( t \right)} \right) (20) sid(t+1)=sid(t)+vid(t+1) {s_{id}}\left( {t + 1} \right) = {s_{id}}\left( t \right) + {v_{id}}\left( {t + 1} \right)

The influential indexes of aerobic exercise include: oxygen uptake efficiency (Y, %), age (X1, years), body weight (X2, kg), time required for running 1.5 km (X3, min), heart rate at rest (X,4, beats/min), heart rate at running (X5, beats/min) and maximum heart rate (X4, beats/min). These indexes directly affect the oxygen intake efficiency of human body[11]. Assuming that there is a linear relationship between the above indexes and oxygen intake efficiency, the prediction model of oxygen intake efficiency based on multiple regression was constructed, and the results are shown in Table 1.

The multivariate regression model was proposed by the famous American psychologist Professor LangYin. In his research, the independent combination of the explanatory variable and the dependent variable is called the factor or autocorrelation factor. Each principal component can independently represent one or more influential indicators, which can also be explained by linear functions and nonlinear models. Therefore, the influencing factors of factors or independent variables have multicollinearity, that is, one is controlled and has an influence on the results. According to the development of the fitness level of athletes in sports colleges and universities in our country and the statistical analysis of the establishment of physical health education courses for college students, it is found that the degree of influence of different factors is not the same, and the teaching design of physical education teachers is also very important. big difference. In the regression equation for different factors, there is a positive correlation between aerobic capacity and athletic performance. However, it did not reach the maximization, that is, there was a negative correlation between sports performance and physical fitness indicators. Secondly, athletes may suffer from muscle strain, bone bending and joint damage due to insufficient aerobic capacity, which will affect their overall functional level and ultimately hinder the development of sports.

Oxygen is an indispensable part of human activity, but the increasing demand for oxygen and the continuous development and progress of body functions have led to changes in the internal metabolic system, respiratory muscles and other physiological functions of the human body. Therefore, it is important to understand the different levels of oxygen supply that different athletes have. When people enter a certain stage, they will find that the body needs to replenish oxygen for consumption, and if the body is not able to replenish itself in a timely manner when it is in a state of oxygen deficiency, this will lead to changes in the physiological functions of the body, which will lead to the decline of body organs and systems, and ultimately affect human health. The aerobic respiration process of the human body is shown in Figure 5.

Figure 5

The lungs are the most important organ in the body, providing the energy needed for breathing, supplying nutrients and water. Aerobic exercise can improve the conditions of the exercise environment. In the process of aerobic training, no-load endurance exercises are needed to achieve good results, while attention should be paid to maintaining the health of the organism as well as improving its physical fitness, all of which are inseparable from physical exercise. Therefore, the most important factors in the test are lung capacity, thoracic volume and respiratory rate, which in turn are important factors affecting the athletes' exercise. The cardiorespiratory exercise curve in aerobic exercise is shown in Figure 6.

Figure 6

As can be seen from Figure 6, cardiorespiratory function refers to the metabolism of oxygen and respiratory circulation in all organs and systems of the body. As for fitness, it is mainly determined by measuring the oxygen concentration in the body (COD) to determine whether aerobic exercise is performed. The experimental results of tolerance time and cardiopulmonary peak power ratio index after aerobic training are shown in Table 2.

Through the data analysis of the regression equations of different factors, we can see that there is no significant difference when setting the multi-influence maximization variable and the aerobic capacity test (including personal factors) of the less meeting people. After setting the multi-effect maximization variable, the test data did not show significant differences, so it can be considered that this factor is closely related to the physical fitness level of athletes. In order to make the coaches' training of physical fitness sports more scientific, reasonable, effective and interesting, it is necessary for students to improve their physical quality through their own efforts to achieve the best results.

According to the above results, it is not difficult to conclude that: adding more nutrients to the human cardiovascular system has a very large role; secondly, adding more vitamin B and trace elements in the training process can improve the function of the heart, enhance the function of the heart, and this can improve the circulation of the respiratory system, improve the body's resistance to various toxic substances and harmful gases and irritating odors in the external environment.

Currently, research on health testing of athletes is mainly focused on college physical education students. For general colleges and universities, their own characteristics and faculty strength lead to limitations in making fitness choices. Therefore, the question of how to get more people to participate in sports is a big issue. This also requires the joint efforts of our society, schools and people to achieve the goal. Firstly, it is necessary to strengthen the publicity and educational resources development and construction, secondly, it should improve the comprehensive quality level of coaches and athletes, and again, it is necessary to improve the relevant supporting facilities and equipment, so as to provide a better platform and learning conditions for college sports students and other aspects of improvement. Through the aerobic ability test of our athletes, we can conclude that, firstly, the physiological quality of human body is the most important component in the sports test, and the degree of muscle development directly affects the function of all parts of the body, so we should focus on improving our functions when training. Secondly, before the competition should have a comprehensive and accurate knowledge of all aspects of the sports they want to participate in. Finally, we should choose a scientific and effective method to evaluate and predict the athletes from the perspective of their maximum physical development, so as to improve their physical fitness and athletic ability.