How to start from the fitness needs of people and effectively improve the precision of the supply of public fitness services everyone is an important issue that needs to be solved first at the current stage. This requires us to proceed from the reality, conduct accurate research, and find a method that can match the current problem. In this paper, taking basketball projects in national fitness as an example, by introducing a proposition about the development of small basketball events, the corresponding big data modeling and analysis methods are studied. The research methods and research objectives involved in this paper are based on the relevant parameters of the multivariate statistical model. First, the article introduces the calculation principle of the multiple linear regression model. We introduce the concept of variance inflation factor involved in this principle and carry out the modeling and analysis of big data based on this variable. In order to illustrate the application effect of big data in this kind of research, this paper introduces three different big data technologies, including immune selection optimization algorithm, particle swarm optimization algorithm, and Elman neural network, to predict and analyze the variance inflation factor (VIF) corresponding to the small basketball project. The analysis results show that the Elman network exhibits certain advantages in terms of computing convergence time. And, as the number of calculation steps increases, the superiority of the Elman network is more obvious. As far as the prediction performance is concerned, the square of the correlation coefficient corresponding to the immune selection optimization algorithm is the largest and the sum of the squares of the residuals is the smallest, showing superior prediction performance.
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