The regression analysis model is a multivariate analysis model used to illustrate the relationship between independent and dependent variables. Regression models include interval regression models that illustrate the possibilities under analysis. Because measurements usually contain errors, the regression coefficients are determined to minimize errors and vagueness. However, in interval regression, errors in the observed values may be reflected in the vagueness of the regression. Therefore, research results have been reported to reduce the vagueness of interval regression. We assume that errors in the observed values make the predictions vague and reduce the vagueness of the regression. In this study, a Type-2 (T2) fuzzy regression model is constructed by extending the membership function of interval regression to a T2 fuzzy set. In the numerical example, a two-layered T2 fuzzy regression is obtained, with the conventional interval fuzzy regression as the upper membership function and vagueness-adjusted fuzzy regression as the lower membership function. This study constructs an interval fuzzy regression with T2 membership functions, and discusses the results of applying the proposed model to numerical examples.