In this study, using necessity analysis, we located a fuzzy regression interval that is possibly included in collected interval data by reducing the effect of fluctuating points. First, we developed a fuzzy regression model with a regression interval that is close to the sum of the radius values of collected interval data. Next, we enlarged the feasible region so that the fuzzy regression interval may be possibly included in the collected data by fuzzifying the constraints of the fuzzy regression model within a given tolerance value. Finally, we derived a satisfactory fuzzy regression equation with maximum possibility. The application of the proposed model is illustrated by means of an example.