Reliability and validity analysis of the questionnaires
In order to avoid wrong inference, the homogeneity test was carried out prior to questionnaire data integration. Since the data were all categorical variables, SPSS24.0 was used. The chi-square test assessed the contribution of gender, grade, ethnicity, and school of study of the research subjects in affecting the answers to the questionnaire. The P values of the test results were all higher than 0.05 (as shown in Table 3). Therefore, the null hypothesis was not rejected, that is, there was no difference in the sampling and expected frequencies of different genders, grades, ethnicity, and school of study. AMOS24.0 was used to conduct confirmatory factor analysis on all questions of the questionnaire, and its convergence validity and discriminated validity are shown in tables 4 and 5.
Table 4 indicates that in the case of non-standardization, the P values of significance estimates of all parameters were less than 0.01, suggesting that all questions in the questionnaire were authentic. In the standardized condition, the factor load was higher than 0.6 and the SMC value of the question reliability was higher than 0.36. Moreover, the CR value of the composition reliability was higher than 0.7, indicating that the questionnaire exhibited internal consistency. The convergence validity was higher than 0.5, indicating that each dimension could be accurately measured.
In Table 5, the characters in bold correspond to the open square root value of the dimension convergence validity AVE, whereas the other values are Pearson correlation coefficients between the two dimensions. The square root value of AVE was compared with the Pearson's correlation coefficient as follows: 0.871 was higher than 0.626, 0.744, 0.251, and 0.513, indicating a significant difference between college students' exercise behavior and other dimensions. 0.838 was higher than 0.626, 0.738, 0.364, and 0.644, indicating a significant difference between college students' exercise attitude and other dimensions. Similarly, exercise conditions, support for family exercise, and family members' behavior were also significantly different from other dimensions.
Structural equation regression model analysis
In order to verify the theoretical hypothesis, the regression model was used for analysis, and the results are shown in Figure 4.
Evaluation of regression model
In order to determine the accuracy of the model, the non-standardized parameters, standardized parameters, and model fit were evaluated respectively, and the results are shown below.
The null hypothesis in Table 6 indicates that there is no difference in the influence of non-observed and observed variables on the observed values. The statistical results were as follows: The residuals of all variables were positive, and a P<0.05 was obtained, rejecting the null hypothesis. It was noted that each variable had an error term and that the influence of the unobserved variable on the observed value was non-significant. The data further indicated that every observed variable in the regression model was real and had a significant effect on the observed value.
The null hypothesis in Table 7 is the following: In the case of non-standardization, the load of one factor is set as 1 and it is assumed that the influence of other factors on the dimension is not significant. The statistical results indicated that the P values of all other factors were less than 0.05, rejecting the null hypothesis. Therefore, in the case of non-standardization, other factors exhibited a significant influence on the dimension. In the case of standardization, it was generally considered that factor load higher than 0.6 was acceptable and factor load greater than 0.7 was ideal. Therefore, it was considered that all factors (including the factor with a load of 1) had a significant effect on the dimension.
Table 8 indicates that the running results of the fitness indicators of the regression model were all within the ideal range, indicating that the model exhibited optimal fitness. It should be noted that the null hypothesis used in the analysis (Table 8) was the following: There is no correlation between the latent variables. P>0.05 indicates no significant correlation between potential variables, that is, there is a correlation between potential variables, and the null hypothesis is rejected. In addition, a correlation test was also required for external latent variables. The pair correlation coefficients of the college students' exercise behavior, exercise attitude, and exercise conditions were 0.63, 0.36, and 0.25 respectively. Since these values were less than 0.7, the data suggested no collinearity problem among the three.
Regression model results and analysis
The regression model of the standardized family behavior in Figure 4 was reported from two aspects of model path coefficient and model explanatory power, as shown in Table 9.
In Table 9, under non-standardized conditions, the P of "MC-- > SU"=0.318>0.05, indicating that family exercise conditions exhibited no significant impact on family exercise support and that hypothesis H3 was not valid. The result "MC-- > CA" P=0.303>0.05 indicated that family exercise conditions exhibited no significant influence on family exercise behavior, suggesting that hypothesis H7 was not valid. The P-value of other assumptions was less than 0.05, indicating that the other assumptions were true. It was concluded that H3 and H7 were not tenable, while H1, H2, H4, H5, and H6 were tenable. The results indicated that family exercise conditions exhibited no significant influence on family exercise support and family exercise behavior, while college students' exercise behavior and attitude exhibited significant influence on family exercise support, and college students' exercise behavior, while attitude exhibited significant influence on family exercise behavior.
According to the standardized path coefficient value, the most influential factor on family exercise support was college students' exercise attitude (0.509), followed by college students' exercise behavior (0.178). The most direct influence on family exercise behavior was caused by college students' exercise behavior (0.403), followed by support for family exercise (0.329) and the least was college students' exercise attitude (0.257). According to the non-standardized and standardized data, the college students' attitude and behavior of exercise had a mediating effect on their family members' exercise support when they could influence their family members' exercise behavior.
The analysis demonstrated the following results: 0.19<SMC≤0.33 indicating that the explanatory power of the model was weak. When 0.33<SMC≤0.67 a medium explanatory power of the model was achieved and when 0.67<SMC a good explanatory power of the model was evident. Therefore, the regression model exhibited a moderate explanatory power for family exercise support (0.44) and good explanatory power for family exercise behavior (0.74).