Abstract: In this paper, we consider two linear models with missing data, where the covariates are not missing, but response variables are missing at random(MAR). The inverse probability weighted imputation is used to impute the missing data of response variables, we can obtain the 'complete' data for two linear regression models. Then we can construct the empirical log-likelihood ratios of quantile differences of response variables. And the difference is that the asymptotic distributions for the empirical log-likelihood ratios of quantile differences of response variables are standard comparing with the results of previous studies. The empirical likelihood confidence intervals for quantile difference of response variables is more accurate because the errors caused right of the coefficient estimates is reduced.