Abstract: This study focuses on the outlier detection for Multivariate Multiple Regression in Y-direction however, we propose an alternative method based on the squared distances of the residuals. The proposed method refers to the robust estimates of location and covariance matrices derived from the squared distances of the residuals. The proposed method is compared to Mahalanobis Distance method, Minimum Covariance Determinant method and Minimum Volume Ellipsoid method which are used to detect multivariate outliers. An advantage of the proposed method is that it is an alternative method to solve the complicated problem of resampling algorithm in detecting multivariate outliers in Y-direction in the case of having a large sample size and correlation between the dependent variables.