Abstract： At present， the electronic instruments have been generally utilized to collect the test results of physical fitness of students in China， and we have accumulated a lot of raw data which have characteristics of big data. It may have scientific significance on how to utilize the mathematical model in finding out the correlations among the test items when facing test big data of physical fitness and then describing accurately the strength and weakness of their correlations. In this study， we utilized an innovative model of grey relational analysis in order to analyze the test big data of physical fitness of the 31 198 undergraduate students in a university in western China. The innovative model changes the computational process of traditional Deng’s model and then makes itself suitable for big data. The value of BMI has a great influence on the endurance and the explosive force of lower limbs of the female students， and it is the most important test index of females’ physical fitness; The vital capacity has different influence on the endurance， the flexibility and the explosive force of lower limbs of the male students， and it is the most important test index of male physical fitness; long-distance running that is the 1 000-meter running for males as well as the 800-meter running for females and the standing long jump are not only the two most important indicators of the physical fitness but also exist a strong correlation among them. The innovative model of Grey Relational Analysis provides a new idea for the correlation analysis among the physical measurement indexes under the situation of big data， and it gives a modeling reference for the big data analysis in different fields.

Key words： grey relational analysis; big data; physical fitness test; strong correlation degree

CLC number：F49Document code：AWith the modernization of testing instruments and the standardization of testing indicators for the phy-sical fitness， the amount of data from the test of physical fitness is increasing at a high rate， and then it induces an important research value when re-searchers want to mine the correlation among those test indicators from the big data of physical fitness. Both International Commission on Physical Fitness Research （ICPFR） and International Biological Program （IBP） are the earliest organizations to study the assessment on physical health as well as to formulate their respective evaluation indicator systems in the world. By referring to the two organizations， other countries in the world have made their own evaluation index systems. For example， the testing system of youth physical fitness named FITNESS GRAM was proposed by Cooper Institute for Aerobics Research in USA （CIAR）， the system of labor and defend by Sports Commission on Russian President， the framework and indicators of physical strength test by Ministry of Education in Japan， as well as the Testing Agreements of Student Physical Fitness signed by EU countries， etc. Since 2002， China has also tried out the National Student Physical Health Standard （we may refer to it as Standard） and allowed schools to choose different test indicators based on their actual conditions. Later， China has adopted a renewed Standard and abolished their selection power of testing indicators and since 2014 it has implemented a unified test work and has been helpful for the horizontal comparison among different regions and schools in China.

建模與實(shí)證Since the 20th century， many countries in the world have never given up to study the physical fitness test. Then， a large number of classic literatures have been emerged. Some scholars reviewed the de-velopment process of physical fitness test and the penetration rate of school test. For example， Kim reviewed the content and change process of the physical fitness test in the 1970s. He believed that the government did not consider personal status， nutrition and growth status in the physical fitness test promoted by the government to strengthen school sports［1］. Morrow expounded some factors that affect the penetration rate of physical fitness test in American schools［2］. Other scholars discussed the correlation between the attitude of the physical education teachers and the results of the physical fitness test， and they generally believed that the teacher’s attitude is positively correlated with the test results and viewed that there was greater influence on girls and less influence on boys［3-6］. However， most scholars paid more attention to the correlation between the student attitude and the test results of physical fitness［7-12］， and they viewed that the attitude of most students is positive and then proposed that not only their attitude affected the test results of physical fitness but also the results affected their attitude as well as emotion of physical exercise in the future［13］. In addition， some scholars studied the relationship between the test results of physical fitness and other factors such as the academic performance， the Body Mass Index （BMI）， the daily exercise and the aerobic exercise［14-19］. For instance， LONDON et al. ［20］ analyzed the relationship between physical quality and academic performance through the data set of test results of physical fitness; DAVIS et al. ［21］ believed that BMI was significantly correlated with the test results of physical fitness; DING and ZHU et al. ［22-23］ respectively analyzed the relationships between the physical exercise and the aerobic physical fitness test［22］ as well as between it and the physical fitness test［23］.

Chinese scholars also attached great interests to research on the physical fitness tests and their results mainly focused on four aspects， namely （1） the domestic development status of test standards of physical fitness and the comparative analysis at home and abroad［24-26］; （2） the reform attempt and the countermeasure discussions on test mode of physical fitness［27］; （3） analysis on the test result of physical fitness and management mode of the follow-up service［28-30］; （4） statistical analysis on test data and improvement countermeasures of physical fitness［31-32］ and so forth. However， the local scholars paid more attention to the statistical analysis on the test data of physical fitness and made it to be the key research field. To illustrate a few， some scholars discussed the influence of some external factors on test indexes of physical fitness or on physical health， and they believed that those factors， such as the preparation activities， the test sequence and the cognitive level could affect the test results of physical fitness， and they also viewed that other factors such as the exercise density， had a strong correlation with the test indicators which were BMI， 50-meter running as well as sit and reach［33］. According to the analysis results on test data of physical fitness， some scholars studied the similarities and differences on physical health among different groups， which were usually divided by their regions， gender and age， and they found differences on their physical health by using the corresponding mathematical statistical methods and then explained those reasons or put forward some suggestions［34-35］.

If we were to view the relationship among test indexes of physical fitness， then we could find their influence degree and know the importance degree between every index and the others by using the correlation analysis. For example， some scholars analyzed the relationship between the BMI index and the other indexes for the college students， and viewed that a certain number of overweight/obese students as well as low-weight ones should exist although the BMI of most students was distributed in the normal range， and then obtained that the BMI of both male and female students was negatively correlated with their vital capacity， as well as the BMI of male students were negatively correlated with their grip strength index［36］. Other scholars analyzed the test data of physical fitness of college students by using both principal component and R-type factor methods， and found that the standing long jump is the first principal component and it followed step by step with shape score， step test index， vital capacity index and grip strength index. Then， they obtained a conclusion that the vital capacity and grip strength index were great negatively correlated with BMI， and that the explosive force of lower limbs of college students was relatively poor correlation with abnormal BMI［37］. However， the above literatures only analyzed the correlation between BMI and other test indicators of physical fitness， and the correlation among other indicators was not been considered. Furthermore， some indexes were adjusted and deleted so that a new test index system of physical fitness was re-defined in the new Chinese Standard. But， few scholars analyzed the effective correlation among the new test indexes of physical fitness and induced the lack research on the index correlation for physical measurement under the big-data situation.

According to the above review results， we will analyze the correlation relationships among various test items of physical fitness by using Grey Relational Analysis under the situation with big data and take the students at one college in western China as our example. Then， we can determine which item in-dicator has greater impact on the test results of physical fitness and how the correlation difference may appear among the male students and among the female students. However， the existing correlation research of test items of physical fitness often may be applied for mathematical statistical methods such as factor analysis， principal component analysis， covariance and regression analysis. These classic statistical methods can only measure the linear correlation between random vectors， and they are still limited to the non-linear correlation that is common in big data. Although some scholars have carried out research on the promotion of correlation analysis from linear to non-linear， and proposed some models that are suitable for big data analysis such as the canonical correlation analysis based on mutual information and the discriminant analysis based on kernel canonical correlation， these models are still restricted by their own methods［38］. For example， the mutual infor-mation method needs to estimate the density function but it is difficult to be obtained; and the kernel method needs to choose the appropriate kernel function and its parameters are obviously faced other research challenges. Although Grey Relational Ana-lysis has simple calculation that is different from the above-mentioned statistical methods and also has no special requirements for the distribution and the sum of samples， it has been widely utilized in various fields［39-40］. On the other hand， the Grey System Theory was proposed according to the poor information with less data. However， we believe that the poor information is unnecessarily related to the amount of data. That is to say， there also exist poor information even for the big data. Although the existed Grey Relational Models do not require the distribution and the number of samples， the mathematical models and their computational process are also suitable for less data. Therefore， we change the selection condition of co-efficient values of Deng’s model and verify it to be suitable for the big data. Then， we give an in-depth explanations and detailed discussions on the correlations among all test items of physical fitness by using the improved model which greatly improves the computational process of Deng’s model of Grey Relational Analysis according to our Python program.

1Materials and methods

1.1Participants

In this paper， we viewed the undergraduates as the research objects at one university in western China who took part in the physical fitness test in 2018. Those data were collected according to the re-quirements of National Student Physical Health Standard（revised in 2014） issued by Ministry of Education of People’s Republic of China. In order to ensure the reliability， authenticity and validity of those data， we excluded some test data that students did not complete all the test indexes of physical fitness and then screened out the test data of 31 198 students comprised of 7 405 seniors， 7 324 juniors， 7 963 sophomores and 8 506 freshmen. Because the phy-sical quality and the test index had significant differences between the male and the female， as well as physical performance was also large difference among them， we divided the samples into two categories by sex， and there were 16 821 male students and 14 377 female students （Tab.1）.

According to the relevant requirements of National Student Physical Health Standard （revised in 2014）， the test indicators of physical fitness of college students included BMI that reflected body shapes， vital capacity that reflected body functions， as well as the other five indicators that reflected physical quality which were 50-meter running， sit and reach， standing long jump， 1 000-meter running （male）/800-meter running （females） and pull-up （males）/one-minute sit-ups （female）. In order to ensure the objectivity， their physical health data werecollected by using relevant test acquisition instruments.

1.2Data collection

In order to ensure the high accuracy of test data of physical fitness， we obtained all data of test indexes by using the Huihai brand’s student test instruments of physical fitness， and the specific names and models of these instruments included Height and Weight Tester whose model was Huihai HHTC100-ST; Vital capacity tester is Huihai HHTC100-FH; Standing long jump equipment was Huihai HHTC100-TY; Running tester was Huihai HHTC100-WP with 40 people test and wireless starting speaker and starting foul; Double Beacon Medium amp; Long Distance Running Tester was Huihai HHTC100-PB; Wireless data acquisition was Huihai HHTC100， etc. In particular， it should be noted that the testing instrument to get the value of Body Mass Index（MBI， IBM） was not given and it could be mea-sured from the height and weight of students by MS Excel according to the calculation formula， IBM = weight （kg）/［height （m）］2 and its unit is kg/m2 （Tab.2）.

In addition， the original units of 1 000-meter running for males and 800-meter running for females were both minutes and seconds as well as their value ranges are 2 min00 s-9 min00 s. In order to meet the operation requirements during the process of Grey Relational Analysis， we converted their units into seconds and got their value range is between 120 s and 540 s. We classified the students by gender and sorted out test data of their physical fitness. The data of male students are sorted out as shown in Tab.3， and their BMI values are calculated by using the data of height and weight that were measured by the instruments， and the measurement unit of 1 000-meter running was also converted into seconds. The sorted data were not only kept the characteristics of the original data but also fit for the calculation requirements of the selected model later. As the method and process to sort out the female data were basically same as those of male and only the test index is different， we did not repeat them here.

1.3Research method

Grey Relational Analysis was proposed by Professor Deng Julong， and many scholars have systematicly researched it and achieved many remarkable results. The methodology aims to measure the similarity or dissimilarity of system development trend and its quatitative form is named as Grey correlation degree to measure the similar degree among indicators of the system development. There are seven test indexes of physical fitness， and we have obtained about 220 000 valid observation data of these indexes from the 31 198 students. Because these data initially own the numerical characteristics of big data， we made some necessary expansion and innovation on the basis of the classical Deng’s model in order to make Grey Relational model adapt to the calculation characteristics of these big data of the test indicators of physical fitness. Then， we established an improved Deng’s model of Grey Relational Analysis and compiled a computer program to realize the calculation process of the improved model as follows.

（8） Replace another sequence as the reference sequence and the remaining sequences as the comparison ones， and then repeat the steps from （3） to （7）. If all sequences have already been as the reference sequence and have been computed， then the loops stop. At this time， the strong correlation degrees between every pair of sequences are obtained.

（9） The sorting and analysis on Grey correlation. Establish 14 ranking tables of the strong correlation degrees of the seven test indexes for both male and female students. By classifying and summarizing these strong correlation sequences by the gender， we can obtain and analyze the summary tables of the strong correlation.

The above computational steps constitute the im-proved Deng’s model. Obviously， the main differences between the improved model and the traditional Deng’s model are：

Firstly， we introduce the threshold of correlation coefficient and propose some new concepts， such as strong correlation coefficient from the Equation （4） and strong correlation degree from Equation （5）. In fact， we set the value of strong correlation coefficient as 0 when it is less than the threshold because wewant to discard those points in the big data environment. There are a large number of weakly correlated points between the reference sequence and the comparison sequence， and their values are small and non-negative. The cumulative result among those small values does not have much influence on the calculation of the strong correlation but a large number of the non-negative numbers will cause the accumulation error， so we discard those coefficients that are less than the threshold and make the strong correlation between every pair of indexes be more targeted.

Secondly， we introduce an accumulator h to compute the number of those points that have strong correlation coefficient and let the mean value of those strong correlation coefficients be the strong correlation degree from the Equation （5）， and then we realize the correlation analysis on two sequences with a large number of points. In fact， the correlation degree can be computed under the situation with big data.

Thirdly， we introduce the tables of seven text indicators of physical fitness. Those tables let the decision-makers observe their relationship of every pair of indicators from different aspects. Then， the suggestions to improve the students’ health should be greater and more effective.

2Results

2.1Strong correlation ranking

According to the improved model， we let the distinguish coefficient" ρ be 0.8 and the threshold value of correlation coefficient γi0for all i0 be 0.6， and then perform the calculation process by using the computer programming.

Firstly， the index BMI for males is utilized to be the reference sequence and the output of the strong correlation ranking is shown in Tab.4. The results show that the maximum value of the strong correlation degree between the 50-meter running and BMI is 0.862 8 which ranks 1， and the degree between pull-up and BMI is 0.828 1 which ranks 2.After replacing the reference sequence， we calculate them one by one， and get 14 ranking tables of strong correlation degree that are similar to Tab.4. Among those tables， there are 7 tables for males and the other 7 tables are for females. For the sake of simplicity， we do not list them in this paper.

Secondly， we summarize the ranking tables of the strong correlation degree for both males and females in Tab.5 and Tab.6， respectively. The two summarized tables only keep the sorting orders of the strong correlation and no longer list their values of the strong correlation degree， and the columns of the two tables represent the reference sequences and the rows represent comparison sequences. The grid content of the two tables represents the ranking order of strong correlation between every reference sequence and the other comparison sequences. The smaller the order number， the larger the strong correlation degree as well as the stronger correlation between the two sequences. At the same time， the empty grids in-dicate that there is no correlation ranking order between the test index and itself， i.e.， the elements on the diagonal lines in Tab.5 and Tab.6 are all of no values.

2.2The correlation among physical measure-ment indexesIn order to effectively explain the correlation among the physical measurement indexes， we only analyze the comparison sequences whose ranking orders are the top three， and describe their correlation degrees by using strongest， stronger and strong， respectively. If a strong correlation order in the summarized ranking table is symmetrical along with the diagonal line of the table， then it indicates that the two sequences can maintain the same order when they exchange their role between reference and comparison， and it also means that their strong correlation relationship may be more stable， and we call the relationship as a strictly symmetric re-lationship and show it by the solid double-headed arrow in Fig.1.

From Fig.1， the strongest correlations between 50-meter running and BMI， between 1 000-meter running and vital capacity， as well as between sitting body forward flexion and standing long jump are strictly symmetrical， and they indicate that the correlation between the corresponding two indexes is not only the strongest but also the most stable. By analyzing the above correlation， we can find that the BMI value of males will seriously affect the test result of 50-meter running. Because BMI is an important index to affect the body shape as well as the 50-meter running mainly reflects both the flexibility of nerve response and the coordination of the human body， the correlation between BMI and 50-meter running means that the body shape of male has a great influence on the body coordination. On the other hand， the correlation between 1 000-meter running and vital capacity also shows that the long-distance running for male is a good way to exercise their body endurance and cardiopulmonary function， as well as the relationship between sit-reach and standing long jump reflects that there has an important and mutual influence between the body flexibility of male and the explosive force of their lower limb. Secondly， the stronger correlations between pull-up and BMI as well as between 1 000-meter running and standing long jump are also strictly symmetrical， and they indicate that there is a stronger and stable correlation between the corresponding two indexes. Therefore， the BMI of males has a stronger influence on the development level of the muscle of upper limbs as well as of the strength of waist and abdomen. There is also a stronger correlation between the long-distance running and the explosive force of lower limb for males. It means that the boys who insist on long-distance running not only exercise their endurance but also promote their explosive force of lower limb. Thirdly， the strong correlation in the third order is strictly symmetrical relationship between sit-reach and vital capacity， and it indicates that the correlation between the two indicators is strong and stable， which means that there is also a strong correlation between the body flexibility of males and their vital capacity.

From the solid double-headed arrow in Fig.2， we find that the strongest correlation between 800-meter running and BMI is a strictly symmetrical， and it indicates that the BMI value of females also seriously affects their results of long-distance running. The stronger correlation between 800-meter running and the standing long jump is a strictly symmetrical， and it shows that there is also a stronger correlation between the long-distance race of girls and their explosive force of lower limbs. It indicates that the long-distance race can promote the explosive force of lower limbs for females.

Except for the strictly symmetrical relationship that are mentioned above， there has another non-strictly symmetrical relationship in Tab.5 and Tab.6， which means that the strong correlation between the two indexes is not symmetrical at the diagonal line of the tables. For example， when BMI is served as a reference sequence， the order of strong correlation between vital capacity and BMI is 3. However， when vital capacity is taken as the reference sequence， the strong correlation ranking order between BMI and vital capacity is 4. That is to show the rank of strong correlation between BMI and vital capacity is unsymmetrical at the diagonal line in Tab.5. Although the strong correlation order is different for the same two indexes under the different reference， the correlation relationship can also have a certain representativeness if their rank-position difference does not exceed 1. From the dotted double-headed arrow in Fig.1， we find the ranking order of the correlation degree from strong to weak below：

The strong correlation between pull-up and 50-meter running whose orders are 1 and 2; and the one between standing long jump and vital capacity whose orders are 2 and 3; and the one between 1 000-meter running and sit-reach whose orders are 2 and 3; and the one between BMI and vital capacity whose orders are 3 and 4.

These orders are different and their difference is only 1. On the other hand， there is also the same relationship for the females in Fig.2， which means that the strong correlation order between standing long jump and BMI whose orders are 1 and 2; and the one between 50-meter running and vital capacity whose orders are 2 and 3. Their orders are different but the difference is only 1.

In this paper， we judge the strength of cor-relation relationships that are mentioned above as follows：

The strong correlation orders of two test indexes that are 1 and 2 means that their correlation degree is between strongest and stronger， and the orders of two indexes that are 2 and 3 means that their correlation degree is between stronger and strong， and the orders that are 3 and 4 means that their degree is slightly weaker than the strong.

2.3Comparative analysis

According to the comparative analysis for both males and females， we find that there are certain some similarities on the correlation of test indicators of physical fitness. It indicates that there is a stronger correlation between long-distance running（1 000-meter running for males and 800-meter running for females） and standing long jump， which indicates that the long-distance running and the explosive force of lower limbs are mutually influenced for the teenagers. However， there are also more differences on the correlation of physical indicators between males and females.

Firstly， the BMI of males is the primary factor to affect the performance of 50-meter running and the secondary one to affect the performance of pull-ups， and it also has certain influence on the performance of vital capacity at the same time. The BMI of females is the primary index to affect the performance of 800-meter running and it also has a strong influence on the performance of fixed long jump. The results show that BMI has great influence on the physical coordination and the upper limb strength， and the vital capacity reflects the physical function of the male. However， the vital capacity has also a great influence on the endurance and the explosive force of lower limb for the females.

Secondly， the vital capacity is the primary index that affects the performance of 1 000-meter running for the males and it also has a strong correlation with the sit-reach and standing long jump at the same time， which indicates that vital capacity has a great influence on the endurance， flexibility and explosive force of lower limbs for the male. On the other hand， the vital capacity only has a strong correlation with 50-meter running for the females， which shows that the vital capacity only has a certain influence on the explosive force of the females.

Finally， there are strong correlations between sit-each and standing long jump as well as it and 1 000-meter running， and the strong correlation between pull-up and 50-meter running for the males which is different from the females， where it means that there have different characteristics on the indicators of physical qualities between the males and the females.

From both Tab.5 and Tab.6， the sum of the six order numbers in the same row can reflect the importance degree of the test index which corresponds to the comparison sequence among all physical indexes， and the smaller the sum of the six orders of strong correlation the more important the index is. From Tab.5， the importance of test indexes for the males from large to small is as follows：

Vital capacity with 16， 1 000-meter running with 17， BMI with 20， standing long jump with 21， pull-up with 23， sit and reach with 24 as well as 50-meter running with 26. Also from Tab. 6， the importance of the test indexes for the females from large to small is as follows：

BMI with 10， 800-meter running with 14， standing long jump with 16， vital capacity with 22， one-minute sit-ups with 24， 50-meter running with 28 as well as sit and reach with 33. According to the importance ranks above， we find that the vital capacity for the males which reflects physical function and BMI for the females which reflects the physical shape are both at the first position. Because the sum of BMI for the females is smaller than the ones of the vital capacity for the males， the importance of BMI may be more prominent among all test indexes of physical fitness for the females. We also find that the 1 000-meter running for the males and the 800-meter running for the females are ranked the second importance among their respective indicators， which shows that the long-distance running for both boys and girls is the second important indicator among all test indicators. It points out that the long-distance running ranks first position among the five indicators that reflect the physical quality. To sum up， the vital capacity， long-distance running， BMI and standing long jump for both the males and females are the top four important indicators， while the importance of sit and reach， 50-meter running， pull-up for the males and one-minute sit-up for the female ranks the three positions on the bottom. The results show the im-portance of each index.

3Discussion

In this section， we will discuss the physical health of college students from three aspects （body shape， physical function and physical fitness） based on the calculation process and the analysis above.

Firstly， discussion from body shape. According to the previous results， BMI is the most important test index of physical fitness for the females and the third important one for the males. Because the value of BMI has a strong correlation with the achievements of 50-meter running， pull-ups and vital capacity for the males， and it also related to the achievements of 800-meter running and standing long jump for the females， we can determine that BMI is very important for the physical health of college students. The results confirm that BMI is significantly correlated with the endurance and strength of the upper limb which was proposed by literature［21］ as well as it is prominently related with the vital capacity and the standing long jump proposed by literature［36］. On the basis of the correlation between BMI and other test indicators， we perceive that college students should control the value of BMI in order to effectively improve their per-formance of other related test items.

According to the calculation formula of BMI， we have obtained the results that the weight of college students will be the main influence factor on the value of BMI when their height cannot or slightly be changed. Therefore， the college students need to control their own weight to affect their value of BMI. In order to effectively promote the scores of the related test items of physical fitness mentioned above， we suggest that the colleges and universities should set up some corresponding training items in the physical education to encourage their students to control the weight within a reasonable range. Significantly， BMI is the most important test index of physical fitness for the females and has a strong influence on other indexes， and the reason may be that the female students have relatively little exercises. The non-sufficient physical exercise induces that their body functions and physical qualities cannot be effectively improved， and then may cause that their value of BMI in a larger extent affects the results of other test indexes. However， BMI for the males has a relatively weak influence on other indicators because they have relatively large amount of exercise. Therefore， the college administrators should try their best to provide students， especially girls， with enough exercise time， training venues and sports measures to promote them to increase their exercises or practices.

Secondly， discussion from body function. Among the five indexes of body function， vital capacity is the first important test item for the males and the fourth important one for the females. Because vital capacity has strong correlation with 1 000-meter running， sit-reach， BMI and standing long jump for the male， as well as with 50-meter running for the females， we can obtain the results： the college boys like the sports to consume high energy such as basketball and football， and they can improve their vital capacity. At the same time， these exercises not only balance the value of BMI for one’s body but also improve their flexibility and explosive force. Therefore， their test results of physical fitness may show that the vital capacity is related with many test items such as 1 000-meter running and standing long jump. Then， the college teachers can appropriately strengthen some training items with more intense exercises during their physical courses， such as basketball and football， which not only improve the exercise interest for the males， but also promote their achievements of most test indicators of physical fitness. On the contrary， the vital capacity of college girls does not seem to be an important factor that affects the most physical indicators， and its reason may be that the non-abundant of their exercises relatively induces their vital capacity and then cause that the vital capacity cannot reflect the physical health of girls. On the basis of the results， the college teachers should arrange some training programs to promote the enthusiasm of the aerobic exercise during the physical courses of the females， and it should more effectively improve the test scores of physical fitness for the females.

Thirdly， discussion from physical quality. Among the seven test items， there are five indicators to reflect the physical quality of the human body. According to the results from the above section， the long-distance running （1 000-meter running for boys and 800-meter running for girls） and standing long jump are the top four importance， which shows that the two indicators have strong influence on other indicators， especially the long-distance running of both boys and girls has strong correlation with standing long jump. Furthermore， the 1 000-meter running for the males is also closely related with vital capacity and sit-reach， and the 800-meter running for the females is closely related with BMI. The standing long jump for the males is also closely related with sit-reach and vital capacity， and the standing long jump for the females is closely related with BMI.

In order to improve the physical quality， the physical training is easier than both body shape and body function， then the most direct and effective key index is to strengthen the training of long-distance running and standing long jump when we need to improve the total test scores of physical fitness for both males and females. The results partly verify the conclusion in literature［37］， which viewed that the standing long jump is the first principal component of the six test indexes by using principal component analysis and R-type factor analysis when long-distance running was not included within the test items. Obviously， long-distance running and standing long jump are common training items during the physical courses of college education. Therefore， the college and university teachers should insist on increasing the teaching courses of these training programs in order to effectively improve their total test scores of physical fitness. In addition， the importance of the remaining three indicators of physical fitness that are ranked behind is below： Pull-up for the males and one-minute sit-up for the females， 50-meter running and sit-reach. However， the training of the three items cannot be ignored during the physical courses of college/university education because they are inter-related with other indicators and forms as an integral part of test achievements of physical fitness.

4Conclusion

According to the relevant research results in recent ten years， we find that most scholars paid more attention to the test scores of indicators of various physical fitness that were affected by one or more external factors such as preparation activities， test sequence and cognitive level， etc.， and the scholars may lack to analyze the internal correlation among the test indicators of physical fitness， especially to do the correlation research on physical fitness by using the big data. In this paper， we have studied the physical situation by using the test data of one university students in western China on the basis of the improved model of the traditional Grey relational analysis according to the big data characteristics of physical achievement， and then we obtained the conclusions as follows：

Firstly， BMI is the first important test index of physical fitness for the females and it has great influence on their endurance and explosive force of lower limbs;

Secondly， vital capacity is the first important test index of physical fitness for the males and it has different influences on their endurance， flexibility and explosive force of lower limbs;

Thirdly， long-distance running and standing long jump will not only be the two most important indicators of physical fitness but also have strong correlation between each other. On the basis of these conclusions， we also put forward some teaching suggestions for the physical courses during the college/university education. On the other hand， the improved model of Grey Relational Analysis provides a new idea to analyze the correlation of test indexes of physical fitness under the big-data situation， and also gives a new big-data model of Grey Relational Analysis in other fields. Especially， the research results in this paper do provide not only a certain theoretical basis for the related training or teaching reforms of physical health but also give a certain reference basis for the government departments and corresponding organizations to formulate as well as improve their standards of physical health.References：

[1]KIM M. The aspects of 1970s physical education policy by reviewing the physical fitness tests［J］. The History Education Review， 2017， 25： 43-74.

［2］ MORROW J R， FULTON J E， BRENERN D， et al. Prevalence and correlates of physical fitness testing in US schools-2000［J］. Research Quarterly for Exercise and Sport， 2008， 79 （2）： 141-148.

［3］ FREDRICK R N， SILVERMAN S. Relationship between urban middle school physical education teachers’ attitudes toward fitness testing and student performance on fitness tests［J］. Measurement in Physical Education and Exercise Science， 2020， 24 （4）： 273-281.

［4］ KEATING X D， STEPHENSON R， HODGES M， et al. An analysis of Chinese preservice physical education teachers’ attitudes toward school-based fitness testing in physical education settings［J］. Physical Education and Sport Pedagogy， 2020， 5（1）： 1-14.

［5］ KEATING X， LIU X L， STEPHENSON R， et al. Student health-related fitness testing in school-based physical education： strategies for student self-testing using technology［J］. European Physical Education Review， 2020， 26（2）： 552-570.

［6］ BLACKSHEAR T B， BARTON A T， MOXLEY J. The evaluation of student fitness levels in exercise science and physical education teacher education programs［J］. Quest， 2019， 71（1）： 21-41.

［7］ O’KEEFFE B T， MACDONNCHA C， DONNELLY A E. Students’ attitudes towards and experiences of the youth-fit health-related fitness test battery［J］. European Physical Education Review， 2021， 27 （1）： 41-56.

［8］ MERCIER K， SILVERMAN S. High school students’ attitudes toward fitness testing［J］. Journal of Teaching in Physical Education， 2014， 33 （2）： 269-281.

［9］ MERCIER K， SILVERMAN S. Validation of an instru-ment to measure high school students’ attitudes toward fitness testing［J］. Research Quarterly for Exercise and Sport， 2014， 85 （1）： 81-89.

［10］JAAKKOLA T T， SAAKSLAHTI A， MANNINEN M， et al. Student motivation associated with fitness testing in the physical education context［J］. Journal of Teaching in Physical Education， 2013， 32 （3）： 270-286.

［11］GRAO-CRUCES A， RACERO-GARCIA A， SANCHEZ-OLIVA D， et al. Associations between weight status and situational motivation toward fitness testing in physical education： the mediator role of physical fitness［J］. International Journal of Environmental Research and Public Health， 2020， 17（13）： 4821-4833.

［12］DYRBYE L N， SATELE D， SHANAFELT T D. Healthy exercise habits are associated with lower risk of burnout and higher quality of life among US medical students ［J］. Academic Medicine， 2017， 92（7）： 1006-1011.

［13］SIMONTON K L， MERCIER K， GARN A C. Do fitness test performances predict students’ attitudes and emotions toward physical education？［J］. Physical Education and Sport Pedagogy， 2019， 24 （6）： 549-564.

［14］KAUFMANN S， BENEKE R， LATZEL R， et al. Meta-bolic pofiles of the 30-15 intermittent fitness test and the corresponding continuous version in team-sport athletes-elucidating the role of inter-effort recovery［J］. International Journal of Sports Physiology and Performance， 2021， 16（11）： 1634-1639.

［15］VANHELST J， BEGHIN L， DRUMEZ E， et al. Physical fitness levels in French adolescents： the BOUGE program［J］. Revue D’ épidémiologie Et De Santé Publique， 2016， 64（4）： 219-228.

［16］PACHOLEK M， ZEMKOVA E， ARNOLDS K， et al. The effects of a 4-week combined aerobic and resistance training and volleyball training on fitness variables and body composition on STEAM students［J］. Applied Sciences-Basel， 2021， 11（18）： 1-10.

［17］ASKE D B， CHOMITZ V R， LIU X， et al. Relationship between cardiorespiratory fitness， weight status， and academic performance： longitudinal evidence from 1 school district［J］. Journal of School Health， 2018， 88（8）： 560-568.

［18］GIURIATO M， KAWCZYNSKI A， MROCZEK D， et al. Allometric association between physical fitness test results， body size/shape， biological maturity， and time spent playing sports in adolescents［J］. Plos One， 2021， 16（4）： 1-13.

［19］SASAYAMA K， NONOUE K， TADA T， et al. Cross-sectional and longitudinal relationship between physical fitness and academic achievement in Japanese adolescents［J］. European Journal of Sport Science， 2019， 19（9）： 1240-1249.

［20］LONDON R A， CASTRECHINI S. A longitudinal examination of the link between youth physical fitness and academic achievement［J］. Journal of School Health， 2011， 81 （7）： 400-408.

［21］DAVIS S， ZHU X H， HAEGELE J. High school student fitness test attributions： does BMI or performance matter？［J］. Journal of Teaching in Physical Education， 2021， 40 （1）： 49-57.

［22］DING C， JIANG Y M. The relationship between body mass index and physical fitness among Chinese university students： results of a longitudinal study［J］. Healthcare， 2020， 8 （4）： 1-15.

［23］ZHU X H， CHEN S L， PARROTT J. Adolescents’ interest and performances in aerobic fitness testing［J］. Journal of Teaching in Physical Education， 2014， 33 （1）： 53-67.

［24］孫雙明， 葉茂盛. 美、俄、日和歐盟學(xué)生體質(zhì)健康測試概述［J］. 北京體育大學(xué)學(xué)報(bào)， 2017， 40（3）： 86-92.

［25］ZHANG F， BI C J， YIN X J， et al. Physical fitness reference standards for Chinese children and adolescents［J］. Scientific Reports， 2021， 11（1）： 1-12.

［26］ZHANG T， DENG A Q， CHEN A. The missing link？ middle school students’ procedural knowledge on fitness ［J］. Journal of Teaching in Physical Education， 2021， 40（3）： 474-483.

［27］WANG J L. Thoughts about problems existing in student physical health test［J］. Journal of Physical Education， 2015， 22（1）： 70-74.

［28］BAO D W， XIAO Z X， ZHANG Y Y， et al. Mandatory physical education classes of two hours per week can be comparable to losing more than five kilograms for Chinese college students［J］. International Journal of Environ-mental Research and Public Health， 2020， 17（24）： 1-12.

［29］CAI T P， LONG J W， KUANG J， et al. Applying machine learning methods to develop a successful aging maintenance prediction model based on physical fitness tests［J］. Geriatrics amp; Gerontology International， 2020， 20（6）： 637-642.

［30］WANG J L. The association between physical fitness and physical activity among Chinese college students［J］. Journal of American College Health， 2019， 67（6）： 602-609.

［31］LI H C， SHEN S F. Construction of college students’ physical health data sharing system based on Django framework［J］. Journal of Sensors， 2021， 2021： 3859351.1-3859351.7.

［32］WANG J J， XIE Z X， LI Y， et al. Relationship between health status and physical fitness of college students from south China： an empirical study by data mining approach［J］. Ieee Access， 2020， （8）： 67466-67473.

［33］蔡瑞金， 季瀏， 尹杰， 等. 運(yùn)動(dòng)密度對青少年運(yùn)動(dòng)能耗與體質(zhì)健康的影響［J］. 上海體育學(xué)院學(xué)報(bào)， 2019， 43（1）： 93-102.

［34］LI Q， JIANG X G， JIANG H. A comparison of the physical health of university students in Guangdong-measurement based on Gini coefficient and factor analysis［J］. Journal of Physical Education， 2017， 24（4）： 106-110.

［35］孫玉金， 劉黎明， 侯迎鋒， 等. 城市高?！秾W(xué)生體質(zhì)健康標(biāo)準(zhǔn)》測試結(jié)果的分析與研究[J]. 北京體育大學(xué)學(xué)報(bào)， 2007， 30（12）： 1702-1703.

［36］吳新宇， 付曉春. 大學(xué)生體重指數(shù)與體質(zhì)健康指標(biāo)關(guān)系的研究［J］. 北京體育大學(xué)學(xué)報(bào)， 2006， 22（8）： 1087-1088， 1093.

［37］蔡忠建， 袁建國. 大學(xué)生體質(zhì)健康指標(biāo)的權(quán)系數(shù)及關(guān)聯(lián)分析［J］. 上海體育學(xué)院學(xué)報(bào)， 2009， 33（2）： 74-78.

［38］LIU H M， GAO Y Y， ZHANG J H， et al. Epilepsy EEG classification method based on supervised locality preserving canonical correlation analysis［J］. Mathe-matical Biosciences and Engineering， 2022， 19（1）： 624-642.

［39］YUAN C Q， YANG Y J， CHEN D， et al. Proximity and similitude of sequences based on grey relational analysis［J］. Journal of Grey System， 2014， 26（4）： 57-74.

［40］ZHENG S， SHI J L， LUO D. A grey correlational analysis method based on cross-correlation time-delay［J］. Journal of Grey System， 2020， 32（2）： 104-118.

（責(zé)任編輯：周曉南）

：建模與實(shí)證李橋興*1，2，楊勇1，吳俊芳3

（1.貴州大學(xué) 管理學(xué)院，貴州 貴陽 550025；2.貴州大學(xué) 數(shù)字化轉(zhuǎn)型與治理協(xié)同創(chuàng)新實(shí)驗(yàn)室，貴州 貴陽 550025；

3.貴州大學(xué) 體育學(xué)院，貴州 貴陽 550025）

摘要：目前，中國普遍采用電子儀器采集學(xué)生體質(zhì)測試結(jié)果，積累了大量具有大數(shù)據(jù)特征的原始數(shù)據(jù)。在面對體質(zhì)測試大數(shù)據(jù)時(shí)，如何利用數(shù)學(xué)模型找出測試項(xiàng)目之間的相關(guān)性，從而準(zhǔn)確描述其相關(guān)性的強(qiáng)弱，具有科學(xué)意義。采用改進(jìn)的灰色關(guān)聯(lián)分析模型，對西部某高校31 198名大學(xué)生體質(zhì)測試大數(shù)據(jù)進(jìn)行分析。該模型改變了傳統(tǒng)鄧氏模型的計(jì)算過程，使其適用于大數(shù)據(jù)。結(jié)果表明：BMI值對女生下肢耐力和爆發(fā)力有較大影響，是女生最重要的體質(zhì)測試指標(biāo)；肺活量對男生的耐力、靈活性和下肢爆發(fā)力有不同的影響，是男生最重要的體質(zhì)測試指標(biāo)；長跑，即男子1 000 m跑、女子800 m跑和立定跳遠(yuǎn)，不僅是身體素質(zhì)的2個(gè)最重要的指標(biāo)，而且它們之間存在著很強(qiáng)的相關(guān)性。改進(jìn)的灰色關(guān)聯(lián)分析為大數(shù)據(jù)環(huán)境下體質(zhì)測量指標(biāo)之間的相關(guān)性分析提供了新的思路，為不同領(lǐng)域的大數(shù)據(jù)分析提供了建模參考。

關(guān)鍵詞：灰色關(guān)聯(lián)分析；大數(shù)據(jù)；體能測試；強(qiáng)相關(guān)性

李橋興，男，1973 年生，管理學(xué)博士，教授，博士生導(dǎo)師，兼任中國人工智能學(xué)會可拓學(xué)專業(yè)委員會副主任。主持國家自然科學(xué)基金、貴州省軟科學(xué)項(xiàng)目和貴州省哲學(xué)社會規(guī)劃課題等國家和省部級項(xiàng)目6項(xiàng)。獲貴州省哲學(xué)社會科學(xué)優(yōu)秀成果獎(jiǎng)勵(lì)二等獎(jiǎng)和三等獎(jiǎng)各1項(xiàng)；在國內(nèi)外高水平學(xué)術(shù)期刊發(fā)表論文50余篇。