Unlock Insights with Quantile Regression

Understanding Quantile Regression

Quantile Regression is a type of regression analysis that allows us to estimate the conditional quantile functions. Instead of focusing on the mean of the conditional distribution of the response variable (as in ordinary least squares regression), quantile regression aims at estimating the median or other quantiles of the response variable.

It is particularly useful when the conditions for least squares regression are not met, or when you are interested in understanding the effect of predictors on the entire distribution of the response variable, not just its mean. For example, while ordinary least squares regression helps understand how the average house price changes with size, quantile regression can tell you how the price of cheaper houses (e.g., at the 0.25 quantile) or more expensive houses (e.g., at the 0.75 quantile) changes with size.

Key concepts include:

• Quantile Level (τ): Represents the quantile of interest, ranging from 0 to 1. τ = 0.5 is the median, τ = 0.25 is the first quartile, and τ = 0.75 is the third quartile.
• Coefficients: Similar to linear regression, these indicate the change in the specified quantile of the dependent variable for a unit change in the independent variable.
• Loss Function: Quantile regression minimizes a different loss function (pinball loss) compared to ordinary least squares (squared error loss), making it robust to outliers and non-normal errors.

For further reading, you can explore resources like: Wikipedia on Quantile Regression or statistical textbooks covering regression analysis.