Multiple Linear Regression

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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.

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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 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

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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:

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

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FAQs on Multiple Linear Regression

What is 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.

What is the difference between multiple linear regression and simple linear regression?

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.

What is the formula for multiple linear regression?

The formula for multiple linear regression is as follows;

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

What are some assumptions of multiple linear regression?

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

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