Statistical inferences in bidimensional regression models

This paper proposes formal procedures of significance tests for bidimensional regression models (Tobler 1994): (1) significance tests of estimated parameters, (2) significance tests of bidimensional correlation coefficient, and (3) significance tests for comparison of bidimensional regression models. These tests are demonstrated by reexamination of the cognitive map study in Kanazawa City (Wakabayashi 1994). The empirical results statistically support the systematic distortion in the cognitive map, enlargement and rotation, indicated by the Euclidean model in the previous study, and discern the affine model as a more proper model that can identify more components of systematic cognitive distortion.