We formulate a model in which the direction angle influences the ratio of road distance on a rectangular grid network to the Euclidean distance between the endpoints. We used trigonometric regression analysis to test the null hypothesis using an F-test and estimated the parameters of the model in each quadrant around railroad stations in the Tokyo Metropolitan Area. The F-tests show the significance of the model in many regions. The direction angle and the parameters for each region enable the estimation of each road distance from the Euclidean distance between the endpoints.
