In ordinary regression analysis, the homoscedasticity of random error is a basic assumption. But the rationality of these assumptions for variance is doubtable. This paper takes the weighted nonlinear regression model as a perturbed version of a homoscedastic regression model and develops the tests for heteroscedasticity based on normal curvature of its influence graph. Based on this fact,the modified score statistic was discussed in detail. Final-[y these new statistics was applied to two concrete numerical examples.