+13236381128
+15199002991
+61480040096
Book a Demo
TRY A SAMPLE SURVEY
en_US Englishfr_FR French
en_US Englishfr_FR French
+13236381128
+15199002991
+61480040096
en_US Englishfr_FR French
Quantile Regression Quantile Regression

Quantile Regression

SHARE THE ARTICLE ON

Table of Contents

What is Quantile Regression?

Before we can delve into quantile regression, let us first understand what exactly a quantile is. A quantile is a point in a distribution that relates to its rank order of values within that distribution. The middle value within the sample is known as the median, or middle quantile.

Quantile regression allows us to quantify the association of explanatory variables with a conditional quantile of a dependent variable even when the data does not satisfy the assumption of normality (when the distribution of sample means across independent samples is normal). Quantile regression is generally used when the data does not satisfy the assumptions for linear regression. 

Transform your insight generation process

Create an actionable feedback collection process.

Download Now
online survey
Read More

When is Quantile Regression Used?

Quantile regression is often used for the following reasons: 

  • If there are outliers present in the data.
  • If the residuals don’t follow a normal distribution.
  • If the key assumptions of linear regression are not satisfied. 
  • If an increase in the error variance of the data is occurring with an increase in the outcome variable. 
Start collecting insights at scale!

Quantile Regression Formula

The quantile regression model equation is as follows:

Where, 

p = the number of regressor variables

n = the number of data points

Uncover high quality insights with Voxco

Download Market Research Toolkit

Get market research trends guide, Online Surveys guide, Agile Market Research Guide & 5 Market research Template

Download Now
Making the most of your B2B market research in 2021 PDF 3 s 1.png

Linear Regression vs. Quantile Regression

  • Outcome: Linear regression predicts the conditional mean while quantile regression predicts conditional quantities. 
  • Applicability: Linear regression can be applied even when n is small. Quantile regression, on the other hand, requires sufficient data to be applied. 
  • Assumption of Normality: Linear regression makes the assumption of normality while quantile regression is distribution agnostic. 
  • Outliers: Linear regression is sensitive to outliers while quantile regression is robust to outliers.
  • Computations: Linear regression is computationally acute while quantile regression is computationally intensive.

Advantages of Quantile Regression

These are a few advantages of quantile regression:

  • Facilitates the understanding of relationships between outliers: Quantile regression can be used to understand the relationship between variables that are outside the mean of the data. This helps us understand outcomes that are not normally distributed and have non-linear relationships with predictor variables. 
  • Helps Discover Useful Predictive Relationships in Ecology: Quantile regression is used in ecology to uncover the predictive relationships between variables even when there is no relationship or a weak relationship between their means. 
  • Can be Used to Identify Key Determinants: Quantile regressions allows us to discard the assumption that variables operate at the upper tails of the distribution so that we can uncover the factors that are significant determinants of the variables.

See Voxco survey software in action with a Free demo.

Book a Free Demo

FAQs on Quantile Regression

A quantile refers to a point in a distribution that relates to its rank order of values within that distribution.

Quantile regression is a kind of regression analysis used in statistics to estimate the conditional median of the response variable.

Quantile regression is generally used when the data does not satisfy the assumptions of linear regression.

A few strengths of quantile regression are; 

  • Can be used to understand the relationship between outliers. 
  • Can be used to uncover predictive relationships in ecology even when there is no relationship or a weak relationship between the variables.

The key differences between quantile regression and linear regression are; 

  • Linear regression makes the assumption of normality while quantile regression is distribution agnostic and can be used even when the data does not satisfy the assumptions of linear regression. 
  • Linear regression is sensitive to outliers while quantile regression is robust to outliers.

Net Promoter®, NPS®, NPS Prism®, and the NPS-related emoticons are registered trademarks of Bain & Company, Inc., Satmetrix Systems, Inc., and Fred Reichheld. Net Promoter Score℠ and Net Promoter System℠ are service marks of Bain & Company, Inc., Satmetrix Systems, Inc., and Fred Reichheld.

Explore all the survey question types
possible on Voxco

Try a Sample Survey

Explore Voxco Survey Software

Online page new product image3 02.png 1

+ Omnichannel Survey Software 

+ Online Survey Software 

+ CATI Survey Software 

+ IVR Survey Software 

+ Market Research Tool

+ Customer Experience Tool 

+ Product Experience Software 

+ Enterprise Survey Software 

Get a Free Demo

Read more