In this paper, we study nonparametric estimation of regression quantiles by inverting a weighted Naraya-Watson (WNW) estimator of conditional distribution, which was first used by Hall, Wolff and Yao (1999). %and establish %the asymptotic normality and consistency of the WNW conditional distribution estimator %and $WNW$ conditional quantile estimator. Furthermore, We propose a new test for homoskedasticity of variance in nonparametric regression model based on local empirical likelihood and WNW conditional quantile estimator. Under null hypothesis, the test statistic is asymptotically chi-square distuibution with degree of freedom $m-1$. A simulation study is carried out to illustrate the performance of the new test.