Quality evaluation of the regression models plays a key role in making a decision on the suitability of using the constructed models for analyzing the relationships between the studied characteristics and predicting the output characteristic. The presence of fuzzy initial information complicates the task of determining this evaluation, while maintaining its significant importance for further research and conclusions. The objective need to take into account the reliability of fuzzy initial information further complicates the task of determining the quality evaluation of the regression model, but requires its solution in order to avoid the risk of errors. The paper discusses the construction and quality evaluation of the multidimensional regression models under linguistic Z-numbers. For the initial and model Z-numbers, the paper defines a distance based on aggregating indicators. The optimization problem minimizes the sum of the squared distances and allows you to determine the regression model coefficients. The quality indicator of regression models is determined on the basis of aggregating indicators of initial and model information. The significance of the coefficients of the models and the models themselves is determined using criteria for testing hypotheses. The first fuzzy number of predictive output Z-number is determined by substituting the initial first fuzzy numbers into regression model. Reliability recognition of first number is based on a comparative analysis of the aggregating indicators for model Z-number and the aggregating indicators of Z-numbers, the first components of which are first components of model output Z-number, and the second components are formalization of the linguistic values of reliability.