Quantile Regression is The Most Useful Alternative for Ordinary Linear Regression, because it:
is robust to outliers and influential points
does not assume a constant variance (known as homoskedasticity) for the response variable or the residuals
does not assume normality
but the main advantage of QR over linear regression (LR) is that QR explores different values of the response variable, instead of only the average, and delivers therefore a more complete picture of the relationships between variables.
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