To extract the main characteristics of the original psychological assessment data, we first set up random variables in this paper. The probability values of the parameters are obtained based on significance tests after decomposing the covariance moments. The regression coefficients of the data are predicted using logistic regression after normalization. The accuracy of the assessment was improved by optimizing the parameters of different assessment indicators. Ninety-five children in a kindergarten were selected, and the highest score in the hyperactivity test based on multivariate statistical analysis intervention was 4, and the score indicators of the undesirable factors test all decreased substantially. Implementing psychological assessment of young children based on multivariate statistical analysis can effectively improve their adverse psychological problems and thus improve their psychological health.