Abstract
It is necessary to check the linearity of selected covariates in regression diagnostics. There are various graphical methods using residual plots such as partial residual plots, augmented partial residual plots and combining conditional expectation and residual plots. In this paper, we propose the modified pseudolikelihood ratio test statistics based on these residual plots to test linearity of selected covariate. These test statistics which measure the distance between the nonparametric and parametric models are derived as a ratio of quadratic forms. The approximate distribution of these statistics is calculated numerically by using three moments. The power comparison of these statistics is given.