<p>Conformal prediction provides a distribution-free framework for constructing interval estimates of response variables with guaranteed coverage probabilities. This study introduces a missing weighted split conformalized quantile regression (M-WSCQR) method to address challenges associated with missing response variables, assuming a Missing at Random (MAR) mechanism. M-WSCQR employs covariate shift adjustment to account for the MAR mechanism, ensuring robust and reliable predictions with specified coverage guarantees. The proposed method exhibits double robustness and scalability, making it adaptable to a broad range of problem settings by modifying the weighting function or quantile regression model. Simulation studies conducted under varying missing rates, as well as both homoscedastic and heteroscedastic conditions, confirm the effectiveness and robustness of M-WSCQR. Additionally, its practical utility is demonstrated through analyses of two real-world datasets, highlighting its applicability in diverse inference contexts. In contrast to traditional methods that assume independent and identically distributed observations, M-WSCQR integrates information from both observed and missing groups. This approach accommodates covariate shifts arising from the MAR mechanism and differences in covariate distributions between observed and missing responses. By incorporating these considerations, M-WSCQR achieves enhanced robustness and versatility, offering a valuable solution for addressing missing data challenges in statistical modeling.</p>