Linear Regression Vs. Logistic Regression: Difference Between Linear Regression & Logistic Regression

The world of machine learning would not be complete without the presence of two of the simplest machine learning algorithms. Yes, both Linear Regression and Logistic Regression are the most straightforward machine learning algorithms you can implement. Before discussing any of the differences between linear and logistic regression, we must first understand the basics on which the foundation of both of these algorithms is laid.

First up, both of these algorithms are supervised learning in nature. Meaning, the data that you will feed into both of these algorithms should be well labeled. Another critical thing to note is the use cases. Right off the bat, one glaring difference between these two algorithms is the use cases of both. Linear Regression is used whenever we would like to perform regression. Meaning, we use linear regression whenever we want to predict continuous numbers, like the house prices in a particular area. 

However, the use of logistic regression is done in classification problems. Meaning, if we want to predict whether a particular house is expensive or inexpensive (instead of the price), we use the algorithm of logistic regression. Yes, even though logistic regression has the word regression in its name, it is used for classification.

There are more such exciting subtleties which you will find listed below. But before comparing linear regression vs. logistic regression head-on, let us first learn more about each of these algorithms.

Linear Regression

Linear regression is the easiest and simplest machine learning algorithm to both understand and deploy. It is a supervised learning algorithm, so if we want to predict the continuous values (or perform regression), we would have to serve this algorithm with a well-labeled dataset. This machine-learning algorithm is most straightforward because of its linear nature. To successfully predict future values, linear regression tries to a straight line through the data fed into the algorithm.

So, whenever any information is fed into a linear regression algorithm, it takes the data and takes the equation of a straight line, randomly selecting the slope and intercept until it finds the line of best fit. If the data that we feed into this algorithm only contains a single independent variable, then it is called simple linear regression.

On the other hand, if the data has multiple independent variables, then the regression becomes a multiple linear regression. The mathematical form of linear regression is simply that of a straight line, which is shown below.

y= a0+a1x+ c

Here, y is the dependent variable, the a0 and a1 is the coefficient which this algorithm is tasked to find, x is the dependent variable, and c is the intercept value of this straight line.

Logistic Regression

It is needless to say that logistic regression is one of the most straightforward yet very powerful classification machine learning algorithms under the umbrella of a supervised learning algorithm. This algorithm can be used for regression problems, but it is mostly used to solve classification problems instead. The output which we get from this algorithm is always between 0 and 1 due to which it becomes effortless to classify instances into classes by using a threshold classification value.

The word logistic in the name refers to the activation function, which is used in this regression. The activation function or the logistic function, in this case, is actually nothing but the sigmoid function. It is the property of this sigmoid function, which keeps the logistic regression’s value always between zero and one. The sigmoid function looks something like this:

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Here, y is the output through the sigmoid function, and x is the independent variable. In the case of logistic regression, the variable x would actually be the entire linear regression equation. Hence, the equation for logistic regression can be developed, which is written below:

Here, the meaning of the variables is similar to the one in the logistic regression, x is the independent variable, and y is the dependent variable, b0, b1, b2, etc., are the coefficient which this algorithm determines. 

Difference between linear and logistic regression

Listed below, you will find a comprehensive comparison of linear regression vs. logistic regression side by side:

It requires well-labeled data meaning it needs supervision, and it is used for regression. Thus, linear regression is a supervised regression algorithm.  It also requires the data that is fed into it to be well labeled. However, this algorithm is used for classification instead of regression. So logistic regression is a supervised classification algorithm.
The prediction gained through the linear regression algorithm is usually a value that can be in the range of negative infinity to positive infinity.  The prediction that is gained through the logistic regression is actually in the range of just zero to one. This feature allows for an easy classification with the help of a threshold value.
Linear regression requires no function of activation. Here we need a function of activation. In this case, that function is the sigmoid function. 
There is no threshold value in linear regression. In logistic regression, a threshold value is needed to determine the classes of each instance properly.
The dependent variable in the case of linear regression has to be continuous in nature. Meaning we cannot pass in the variable, which is categorical and expect continuous value in the prediction.  The dependent variable in the case of logistic regression has to be categorical. Meaning it should have different categories (not more than two).
The goal of this algorithm is to find the line of best fit through the training data points. Thus, the resultant straight line, which we draw, should touch almost all the training points if the fit is neither over nor under. If we make any changes to the logistic regression curve’s coefficient, then the entire plot of it would change its shape. 
For predicting the values, the algorithm of linear regression makes a fundamental assumption. It assumes that the values which are passed into this algorithm follows the standard normal distribution or are distributed in accordance with the gaussian distribution. The algorithm of logistic regression also makes an assumption of the distribution of the data that is being passed into the sigmoid function. It assumes that the data follows the binomial distribution.

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