Linear vs Logistic Regression: Where’s the Difference?

Linear vs Logistic Regression: Where's the Difference?

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If you thought you left statistics behind in college, then you better think again. As it turns out, statistics are frequently used in the predictive analytics of many domains – especially those involved in the niche world of data mining and machine learning. If you’re about to write code for predictive modeling, then you should brush up on your statistic basics. As a refresher, two of the most common statistics techniques are linear regression and logistic regression. If you also forgot the exact difference between linear vs logistic regression, don’t worry; we have you covered with a quick crash course in predictive statistic techniques.

Before you get started on writing the analytics for your code, study up on linear vs logistic regression. Depending on which technique you use, the interpretation of your data can be vastly different. It’s vital to your project that you are using the right predictive technique. Otherwise you will find grave errors in the results of your work, which means more work down the line.

Now that you understand the importance of using the correct technique, let’s go back to the basics.

What Is Linear and Logistic Regression?

As we mentioned before, linear and logistic regression are two of the most common techniques used in statistics. The point of both of these techniques is to predict the relationship between independent and dependent variables.

Linear Regression

You might have guessed it, but linear regression tends to predict a linear relationship between independent and dependent variables. If you were to look at linear regression on a chart, you would see that the line on the chart will ascend toward the top of the chart in a single straight line. Linear regression shows an equalized relationship between independent and dependent variables. If the independent variable is x, then the dependent variable will have a corresponding x at a near-equal value as the ascension climbs.

Linear regression shows linear relationships.

Logistic Regression

Unlike the previous technique, logistic regression is a predictive statistical analysis that is not necessarily predictable. A linear regression will churn out a linear line if the data is correct. A logistic regression, on the other hand, will create an analysis that is unique. If you were to look at logistic regression on a chart, the first thing you will notice are the curves – sometimes, logistic regression will curve in a sideways S shape, and other times it will slope at the beginning of the chart or at the end of the chart. Logistic regression is used to show the complex relationships between a single dependent variable and one or more independent variables.

Logistic regression shows an explanation for the relationships between variables.

Linear Vs Logistic Regression: Is There a Difference?

By now, it should be obvious that there is a definite difference in linear vs logistic regression. Not only is there a difference in the exact formula that are used for either of these regression techniques, but there are also differences in the types of variables that are used, the algorithm theories, the curve of the regression, and the statistical distributions of the data. To make it clear, although both are used for predictive analytics, these are two vastly different statistical techniques.

Let’s break it down.


Linear regression is all about numbers. In fact, the only data that can be used for linear regression is numerical values. On the other hand, logistic regression can be for nominal, interval, ordinal, or ratio variables – that is to say, non-numerical values that are represented by numbers.

Of the two, logistic regression is the one that is perhaps slightly more useful for coded functions – and this is because the data that is analyzed by logistic regression is binary. For logistic regression, binary does not refer to the binary language of computers (although it could). Rather, binary data in logistic regression is the simple choice between two options, such as yes/no, pass/fail, or win/lose. If you have data that can be interpreted through a binary choice, then logistic regression is the best technique.

Algorithm Theories

Linear regression uses least square estimation, which suggests that there should be a minimized sum of the square distances of the regression coefficients. Least squares is a theory that tries to find the smallest value for the sum of every residual in each equation. Basically, least squares is a way of estimating how data will fit within a linear regression.

Logistic regression uses maximum likelihood estimation that maximizes the likelihood of the coefficients. The goal of maximum likelihood is to find values that maximize the likelihood of making correct predictions under a certain set of parameters set by the logistic regression. Basically, maximum likelihood is the mathematical equivalent of a self-fulfilling prophecy.


Linear vs logistic regression use two very different formulas to analyze data. For linear regression, the formula is Y= a + bX, where Y is the dependent variable, b is the curve, and X is the independent variable. The logistic regression formula is much more complex and is typically already a function in most statistic software. For logistic regression, the formula is P(y=1) = 1 / (1+ exp -(b0+b1x1+ b2x2)), where P is the target, Y is the dependent variable, b0 is the intercept of the curve, and b1 and b2 are the predictor coefficients of independent variables.


As we discussed earlier, one of the most obvious differences between linear vs logistic regression is the way the curves of these techniques look when they are shown on a chart. Linear regression shows a straight linear line with an ascending or descending direction depending on the data. Logistic regression shows a distinct S or C shaped curve to illustrate the complexity of the relationships between dependent and independent variables. Even looking at plain data will show a clear steady increase or decrease of values for linear regression, while the data for logistic regression will be more scatter-shot.

Statistical Distribution

Distribution is an important part of statistics, as the distribution that is used for a formula will determine how the results of the formula are interpreted. Linear regression uses normal distribution, while logistic regression uses binominal distribution. You can usually interpret statistical distribution by comparing your results to a distribution chart or by relying on statistic software to analyze and compare your results to distribution rules.

As you can see, there are distinct differences between linear and logistic regression at a basic level. These differences, especially the differences between the variables, is why you can only use on regression technique with a set of data – and that’s why choosing the right technique is important.

When to Use Linear vs Logistic Regression

When should you use linear or logistic regression? Well, outside of an actual statistic class, it’s very common to use these regression techniques in work involving research studies and work with computers. In fact, these regression techniques are commonly used in data mining and other predictive analytics that are done with computers. To some extent, these regression techniques are also used in the code of domains.

But which one should be used for certain projects? We have the answer.

Data Science

Linear regression is used often in data science related to coding. Think about it like this: while data science is all about interpreting data, linear regression is all about finding relationships between two variables. It makes sense that data scientists would use linear regression to interpret raw data, especially when the dependent variable is numerical.

Data scientists typically code in Python, a computer programming language, to create charts and reach a conclusion about the data. If you need to find relationships between two or more numerical variables, then linear regression is the best technique.

Machine Learning

Linear regression is used in machine learning, usually for the purpose of supervised learning or making sure that the artificial intelligence can perform basic linear functions independently. Many consider linear regression to be fundamental to computer science for this reason.

However, there is no doubt that logistic regression is used far more often in machine learning than any other statistical technique. Logistic regression in machine learning is used for binary classification, or sorting data based on non-numerical data. For machine learning, logistic regression can be incredibly complex. If artificial intelligence is taught the logistic regression of a certain set of data, it can then make future predictions based on similar data. For example, a computer can be taught how to predict gender based on height and weight.


There are undoubtedly many differences between linear vs logistic regression. As statistic techniques that are used for predictive analytics, you will find that both linear and logistic regression are used frequently in computer science – especially in machine learning, which is regarded as the most cutting edge of computer development to date.

However, there are appropriate times to use each technique, so it is important to understand the basics of statistical regression before moving on to coding. After you have a solid grasp on the application of linear and logistic regression, you can then confidently interpret and predict data – or teach a computer to do it for you.

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