The dictionary defines a response as a reaction to something. A response variable would be defined as the reaction or effect on a dependent variable as a result of an experimental manipulation of independent variables.

## Response variable

When discussing Design of Experiments (DOE) and Regression, you can talk about independent variables, also known as the X or predictor variables. Or you can talk about the dependent variable, also known as the Y or response variable. The relationship between the X (predictor) and Y (response) variables is denoted as Y = f(X) where the response (dependent) variable is a function of the predictor (independent) variable.

## Overview: What is a response variable?

In both DOE and regression, the estimated value of the response variable is the purpose of developing a prediction equation. By computing the impact or effect of the X’s or independent variables on the response, you will develop a formula which allows you to insert the values of the X’s with the result of the calculations being the estimated value of the outcome or response.

By changing the values of the independent or predictor variables you can observe the change in the computed response variable. In DOE, this is accomplished by running unique combinations of the X values. Any changes in the response variable will allow you to determine whether any of the X’s has a statistically significant relationship, correlation, or impact on the response variable.

The values of the response variable can be continuous data, ordinal data or binary data. For example, in simple linear regression, the response variable may be something measurable like time, weights, viscosity, or speed. In logistic regression you can have the response variable be Yes or No. Or you can have the response be high, medium, or low. The independent variables may be continuous, discrete, or a combination of them.

## An industry example of a response variable

The Six Sigma Green Belt (GB) was seeking to identify which production variables significantly affected whether the product passed or failed a quality test. The variables the GB used were viscosity, temperature, and time of agitation of the liquid. These were the explanatory or predictor variables and were continuous variables.

The response or dependent variable was the liquid either passed or failed the quality test. This was a binary discrete variable. The GB gathered historical production data and used binary logistic regression to predict the probability of passing or failing based on the values of the predictor variables.

### What are other names for a response variable?

A response variable is also known as the Y or output variable. It is also referred to as the dependent variable since its value will be dependent upon the independent, explanatory or predictor variables in the equation.

### Must a response variable be continuous data?

No, it can be continuous data but you may also have applications where the response variable is a binary outcome like pass or fail or an ordinal outcome like hot, warm, or cold.

### Is a response variable and explanatory variable the same?

No. You can think of an explanatory variable as the expected cause that explains the outcome. A response variable is the expected effect and is the response to the explanatory variables.