A Linearity Test for a Simple Regression Model with LR Fuzzy Response

A linearity test for a simple regression model with an imprecise response is investigated. The values of the imprecise response are formalized through LR-fuzzy numbers, and the stochastic variability through probability spaces. The linear regression model and the least squares estimators of the regression parameters are briefly recalled. The nonparametric model to be employed as reference in the testing approach is also presented. The statistic compares the variability explained by the linear regression with the one explained by the nonparametric regression, since in case of linearity, both quantities should be similar. The problem is approached by bootstrapping. A simulation study has been. carried out in order to check the performance of the procedure.