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To the best of our knowledge, only the existing approach (Rabiei et al. in Soft Comput 18(10), 2043–2059, 2014) has been proposed to construct a full interval-valued fuzzy linear regression model [a regression model when the observation of the response, independent variables as well as the regression coefficients are triangular interval-valued fuzzy numbers (TIVFNs)]. However, after a deep study, it is observed that a mathematical incorrect assumption has been considered in this approach. Furthermore, it is observed that to resolve this mathematical incorrect assumption, there is a need to propose the multiplication of an unrestricted TIVFN (regression coefficient) with a restricted TIVFN [observed values of independent variable(s)]. Keeping the same in mind, in this paper, the same type of multiplication is proposed, and with the help of proposed multiplication, a modified approach is proposed to construct a full interval-valued fuzzy regression model. Also, the modified results of some existing real-life problems are obtained with the help of the modified approach. [ABSTRACT FROM AUTHOR]