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Residual-by-predictor plots from a properly specified median regression model including a quadratic term (top row) and from a model ignoring the quadratic term (bottom row). From left to right, the residuals are OMER, PSR using only information obtained from median regression, PSR with fitted distribution estimated using quantile regression (QR), and PSR with fitted distribution properly specified as a mixture of normals. Smoothed curves using lowess are added.
