Multiple Linear Regression Multiple Linear Regression

Multiple Linear Regression

SHARE THE ARTICLE ON

Table of Contents

Introduction

Before we can delve into understanding multiple linear regression, let’s first understand the concept of linear regression. Linear regression is an approach used to model the linear relationship between two variables. There are two main types of linear regression, namely; 

  • Single Linear Regression: Single linear regression is used to study the relationship between a single independent variable (x) and a single dependent variable (y). 
  • Multiple Linear Regression: Multiple linear regression is used to study the relationship between a two or more independent variables (x) and a single dependent variable (y). 

Within this article, we will specifically explore multiple linear regression to understand what it is, its uses, and its applications in research. 

Transform your insight generation process

Create an actionable feedback collection process.

online survey

What is Multiple Linear Regression?

Multiple linear regression (MLR) is a statistical technique that involves using two or more independent variables to predict or explain the outcome of a single dependent variable by modelling the linear relationship between them. 

Consider the following example; you want to model 

Multiple Linear Regression Multiple Linear Regression

Multiple Linear Regression Formula

The formula for multiple linear regression is as follows: 

Y = a + b1X1 + b2X2 + b3X3 + … + btXt + u

Where,

  • Y = the variable that you are trying to predict (dependent variable).
  • X = the variable that you are using to predict Y (independent variable).
  • a = the intercept.
  • b = the slope.
  • u = the regression residual
Multiple Linear Regression Multiple Linear Regression

Download Market Research Toolkit

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

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

Multiple Linear Regression Assumptions

In order to use multiple regression, you must ensure that your data can actually be used to conduct multiple regression. When using multiple linear regression, the data must pass the following eight assumptions:

  1. The dependent variable must be measured on a continuous scale (it must be on the interval or ratio scale). 
  2. There must be two or more variables, which can be continuous (on the interval or ratio scale) or categorical (on the ordinal or nominal scale). 
  3. There must be independence of observations. 
  4. The relationship between the dependent variable and every one of the independent variables must collectively be linear. 
  5. The data must reflect homoscadasticity, which means that the variables must have the same finite variance along the line of best fit. 
  6. The data must not reflect muticollinearity, which means the data must not depict high intercorrelations among the independent variables.
  7. There shouldn’t be any significant outliers, high leverage points, or highly influential points within the data. 
  8. Residual errors must be (approximately) normally distributed.

See Voxco survey software in action with a Free demo.

FAQs on Multiple Linear Regression

Multiple linear regression is a statistical technique used to model the linear relationship between two or more independent variables and a single dependent variable.

 Simple linear regression involves modelling the linear relationship between a single independent variable and a single dependent variable, while multiple linear regression involves modelling the linear relationship between two or more independent variables and a single dependent variable.

The formula for multiple linear regression is as follows; 

Y = a + b1X1 + b2X2 + b3X3 + … + btXt + u

A few key assumptions that are made when using multiple linear regression are; 

  • Assumption of homogeneity of variance
  • Assumption of normality
  • Assumption of linearity 
  • Assumption of independence of observations

Explore all the survey question types
possible on Voxco

Read more

Shopping Basket
Great Research
Fast Insights
Best-in-class ROI

Voxco’s platform helps you gather omnichannel feedback, measure sentiment, uncover insights and act on them.

Join 500 + global clients across 40+ countries

Great Research
Fast Insights
Best-in-class ROI

Voxco’s platform helps you gather omnichannel feedback, measure sentiment, uncover insights and act on them.

Join 500 + global clients across 40+ countries