Linear Regression vs Multiple Regression: Know the Difference

In data science and machine learning, regression is an important modeling algorithm that most individuals learn early on. In fact, people often consider linear regression vs multiple regression in conversations about regression. But first what is regression? Regression is a strong statistical tool for examining the relationship between two or more variables of interest. Regression analysis is a proven approach for determining which variables affect a given subject. Regression analysis helps you confidently decide which factors are most important, which elements can be ignored, and how these factors interact.

Regression analysis is a series of statistical processes used to estimate the relationships between a dependent variable and various independent variables in statistical modeling. 

• Dependent Variable: This is known as the key factor you’re trying to explain or predict. (X-axis)
• Independent Variables: These are the variables that you believe influence the dependent variable. (Y-axis)

You must collect all relevant data for regression analysis to work. It can be represented graphically using an x-axis and a y-axis. There are various types within the regression, with the five most common being; Linear regression, Polynomial regression, Ridge regression, Lasso regression, ElasticNet regression. But due to the sheer volume of each of these, the focus of this post will be on Linear regression and all necessary subsets. When someone asks, ‘what is simple and multiple regression?’, just stick around and you will know what to say.

Linear regression, which can also be referred to as simple linear regression, is the most common form of regression analysis. One seeks the line that best matches the data according to a set of mathematical criteria. In simple terms, it uses a straight line to define the relationship between two variables. So, if we want to estimate the value of a variable based on the value of another variable, we use this formula.

But, in an instance where there are two (2) independent variables, it becomes a multiple linear regression. This means that a multiple linear regression or a multiple regression is when two or more explanatory/independent variables have a linear relationship with the dependent variable. We can start by understanding the difference between simple and multiple regression. 

Simple and Multiple Regression

If you have ever wondered about simple and multiple regression, maybe you’ve wondered about what set them apart, then the simple answer is this;

• There is just one x and one y variable in simple linear regression.
• There is one y variable and two or more x variables in multiple linear regression.

To understand each concept clearly, the first thing to do is to discuss linear regression assumptions and state a linear regression example to make an already theoretical idea much more grounded.

A simple linear regression model usually takes the form of:

 .

Considering the above-stated formula, there are a couple of assumptions or requirements that must be met for a formula to be regarded as a simple linear regression, and they are;

• Linear relationship: The independent variable, x, and the dependent variable, y, have a linear relationship.
• Independent residuals: The residuals are self-contained. In time series results, there is no connection between consecutive residuals in particular.
• Homoscedasticity: At any degree of x, the residuals have the same variance.
• Normality: The model’s residuals have a regular distribution.

If any of these assumptions are broken, any linear regression findings can be inaccurate or even misleading. A typical example of linear regression can be something along the lines of the following;

Assume you own chocolate business. A simple linear regression will entail you determining a connection between revenue and product texture, with revenue as the dependent variable and product texture as the independent variable. 

With multiple regression models, on the other hand, the equation looks more like this:

Here we can see the addition of more variables while leaving a single variable as the independent value. We can take the earlier stated chocolate business and add another variable into the mix. For instance, the relationship between texture, pricing, and the number of employees to revenue can be discovered using multiple variable regression. As a result, simple and multiple regression analysis may be used to investigate various factors on a company’s revenue and income.

Simple Regression vs Multiple Regression in terms of use.

Of course, it is still a bowl of contention when faced with which regression to use and why: many have often pitted the two against each other in a fierce simple vs multiple regression battle. The question of why do we use multiple regression is one that many beginners might ask. So, to answer why multiple linear regression is used, well, it’s like this. In contrast, simple linear regression is a function that allows a statistician or analyst to make assumptions about one variable based on data about another variable. Many explanatory variables are used in a multiple regression model. 

When you’re using multiple linear regression, you want to know whether:

• The extent to which two or more explanatory/independent variables and one dependent variable are related (e.g. how rainfall, temperature, and amount of fertilizer added affect crop growth).
• The dependent variable’s value at a given value of the independent variables (e.g. the expected yield of a crop at certain levels of rainfall, temperature, and fertilizer addition).

So, is multiple regression better than simple regression?

A multiple regression model is a linear regression model that has been expanded to include more than one independent variable. By logic, this means it performs better than a simple regression. Multiple regressions are used for: 

• Planning and monitoring
• Prediction or forecasting. 

The investigator will use multiple linear regression to account for all of these potentially significant variables in one model. The benefits of this approach can include a more accurate and detailed view of the relationship between each particular factor and the outcome. Another great advantage of multiple linear regression is the application of the multiple regression model in scientific research. Researchers may use multiple regression analysis to evaluate the strength of the relationship between an outcome (the dependent variable) and several predictor variables and the contribution of each predictor to the relationship, often with the influence of other predictors statistically eliminated.

So, it depends on what function you need each model to perform when considering linear vs multiple regression models; it’s all a matter of usage in the end. With that out of the way, you should be aware that there are, of course, other matchups that might spark your interest.

Multivariate Regression vs Multiple Regression.

Multivariate regression is known as a supervised machine learning algorithm that analyzes multiple data variables. With one dependent variable and several independent variables, multivariate regression is an extension of multiple regression. Here you can try to predict the outcome based on the number of independent variables. Multivariate regression aims to find a formula that can describe how variables react to changes in others simultaneously.

Like simple and multiple regression, there is an expression for this model, which is;

The clear difference between these two models is that there are several dependent variables with different variances in multivariate regression (or distributions). One or more predictor variables can be used. While, there is only one dependent variable, y, in multiple regression. The predictor variables or parameters, on the other hand, are numerous.

An example of a multivariate regression can be seen with the following illustration;

When you are trying to figure out how much a house would cost. You will gather information such as the house’s location, number of bedrooms, square footage, and whether or not facilities are available. The price of a home can be estimated based on these data and how each variable is interrelated.

Logistic Regression vs Linear Regression.

Logistic regression is known as a mathematical model in statistics for estimating (guessing) the likelihood of an occurrence occurring given any preliminary data. So, what are the two main differences between logistic regression and linear regression? 

One main distinction between the two is that when the dependent variable is binary, logistic regression is used. Linear regression, on the other hand, is used where the dependent variable is continuous and the regression line is linear.

Also, in linear regression, we look for the best fit line, which allows us to predict the outcome with ease. While in logistic regression, we find the S-curve and use it to identify the samples.

To wrap it up!

What is otherwise considered a theoretical concept can very well be applied to several real-time scenarios. You no longer need to think of them as unknowable statistical problems. Once you have your variables, you’re good to go with either the simple, multiple, logistic or multivariate form of linear regressions. You should not forget to subscribe to this blog to stay updated on trends and topics for data science and machine learning tidbits. Share far and wide to friends and family; you might be the reason someone kickstarts their journey into the amazing world of data science.