Quantile Regression Calculator

Quantile Regression

Quantile Regression estimates the conditional quantiles of a response variable, providing a more complete picture of the relationship between variables than standard linear regression, which focuses only on the mean.

How It Works

While standard linear regression minimizes the sum of squared residuals to estimate the conditional mean of the response variable, quantile regression minimizes a sum of asymmetrically weighted absolute residuals to estimate a specified quantile.

For a given quantile τ (0 < τ < 1), the quantile regression model finds the parameters that minimize:

Σ ρτ(yi - f(xi))

Where ρτ is the tilted absolute value function:

• ρτ(u) = τ × u if u ≥ 0
• ρτ(u) = (τ - 1) × u if u < 0

Common quantiles include:

• τ = 0.5 (median regression)
• τ = 0.25 (first quartile)
• τ = 0.75 (third quartile)

When to Use Quantile Regression

Use Quantile Regression when:

• You're interested in the full distribution of the response, not just the mean
• Your data has outliers or is heteroscedastic (variance changes with the predictors)
• You want to understand how different parts of the distribution respond to predictors
• You need to estimate conditional quantiles for risk assessment or threshold analysis

How to Use This Calculator

Enter your data below as comma-separated x,y pairs (one pair per line) or upload a CSV file. For multiple features, use format x1,x2,...,y with one data point per line. Specify the desired quantile (between 0 and 1), and the calculator will find the best model and provide statistics.