# Linear Regression vs. Logistic Regression: Understanding 13 Key Differences | (2023)

Supervised machine learning is a widely used machine learning technique that predicts future outcomes or events. Use labeled datasets to learn and make accurate predictions. Supervised learning falls into two categories, namely regression and classification.

Regression is a model that predicts continuous (numerical) values, while classification primarily orders the data. Regression is performed using a linear regression algorithm and classification is obtained using logistic regression. This article highlights the key differences between linear and logistic regression.

### Index

• Linear Regression vs. Logistic Regression
• Understand the 13 key differences between linear and logistic regression

## Linear Regression vs. Logistic Regression

Supervised machine learning is a widely used machine learning technique that predicts future outcomes or events. Use labeled datasets to learn and make accurate predictions. Supervised learning falls into two categories, namely regression and classification.

Regression is a model that predicts continuous (numerical) values, while classification primarily orders the data. Regression is performed using a linear regression algorithm and classification is obtained using logistic regression..

### lineare Regression

A linear regression algorithm defines a linear relationship between independent and dependent variables. It uses a linear equation to identify the line of best fit (straight line) for a problem, allowing visualization and prediction of the dependent variable output.

For example, linear regression can predict how a person's obesity is linearly related to work-life imbalance.

lineare RegressionIt is divided into simple and multiple linear regression, which uses one or two or more independent variables to predict the outcome.

### logistic regression

The logistic regression score ranges from 0 to 1 because the algorithm is designed to predict a binary outcome for an event based on past observations in a dataset. It uses independent variables to predict the occurrence or failure of certain events.

For example, logistic regression predicts whether a patient has stage 2 (0) or stage 3 (1) cancer.

See more:What is artificial intelligence (AI) as a service? Definition, architecture and trends

## Understand the 13 key differences between linear and logistic regression

Linear and logistic regression are commonly used to perform data science tasks. However, each model addresses specific problems. Unlike the linear model, logistic regression uses a complex equation model that makes it difficult to understand and interpret. In addition to the equation model, linear and logistic regression differ significantly.

(Video) Linear Regression vs Logistic Regression | Data Science Training | Edureka

Let's understand the main differences between linear and logistic regression models.

### 1. Variable and Output Type

A linear regression model depends on acontinuous dependent variable🇧🇷 This implies that the dependent variable takes on numeric values ​​instead of being categorized or grouped.In contrast, logistic regression models are based on binary dependent variables.The dependent variable (or response) can only have two values: 0 or 1.

Also, the linear regression output has a continuous value (provides a range of values).For example,

• Roof length (25in, 19in, 5ft)
• Height (5ft 8in, 6ft 2in, 5ft 10in)
• Exhaust speed (26,000 mph, 21,500 mph, 29,500 mph)

On the other hand, the logistic regression model is revealed by probabilities.For example,

• 84.3% chance of losing a tennis match
• 23.1% probability of passing legislation in Congress
• 65.1% chance of imposing a curfew during a COVID-19 outbreak

In addition, the linear regression observes aNormal or Gaussian distribution, and the logistic regression shows abinomial distribution.

### 2. Relationship between variables

Understanding the relationship between the variables is critical to deciding what type of regression model to use for different purposes.

Linear regression describes a linear relationship between variables by drawing a straight line on a graph. It allows practitioners to review these linear relationships and track their movements over time. In contrast, logistic regression is known for examining and examining the probability of an event occurring. Since this is not a linear structure of a variable relationship, there is no need to track logistic regression using linear structures.

### 3. Mathematical Equation

The linear relationship between variables (i.e. predictor and response) for linear regression models can be interpreted by the following equation:

and = a0+ identical1X1+ identical2X2+ … + identicalUEXUE

Here,

• y denotes response variable
• XUEdenotes IºVariable predictors
• aUEdenote the average effect on y as xUEincreases by one (all predictors remain fixed)

Similarly, logistic regression predicts probability or observation events using the following equation:

y(x) = z(a0 + a1x1 + a2x2 + … + then)/ (1 + mi(a0 + a1x1 + a2x2 + … + then))

### 4. Equation fitting methods

A linear regression model uses a 'ordinary least squares' to determine the most appropriate regression equation. Depending on the method, the regression coefficients should be chosen to reduce the sum of the squared distances of each response to the fitted value.

(Video) Linear Regression vs Logistic Regression Explained

In contrast, logistic regression uses the 'Maximum Likelihood Estimate’, where the regression coefficients are chosen to maximize the probability of y for a given x (probability).In the context of ML, the system performs multiple iterations until the maximum likelihood estimates are reached.

### 5. Types of Forecasts

A linear regression model estimates an output "y" (true value) by considering the sum of the values ​​of all input features (variables). output (y) = z + p1X1+ page2X2+ page3X3+……..+SNorteXNorte

The model determines the values ​​for the coefficients z, p1, p2, p3….SideNorteand then fits the training data to predict the actual value (y) output with minimal error.

On the other hand oneLogistisches Regressionsmodellconsiders the sum of the values ​​of the input variables and applies a logistic function orSigmoidfunktionabout the result The non-linear function produces a binary output in the form of 0 or 1 (or even "true or false"). y = Logistic (z + p1X1+ page2X2+ page3X3+……..+SNorteXNorte)
y=1/1+e^[−( z + p1X1+ page2X2+ page3X3+……..+SNorteXNorte)]

### 6. Graphic representation: curve

Linear regression is represented by a straight line, also known asRegressionslinie🇧🇷 This row shows the predicted 'y' score for each 'x' value. The distance between the data points in the regression line diagram also reveals errors in the model. Linear regression graph

On the other hand, logistic regression shows aS-shaped curve🇧🇷 Here, changing the regression coefficients affects the direction of the curve and its slope. From this it can be concluded that a positive slope leads to an S-shaped curve and a negative slope leads to a Z-shaped curve. (Video) Linear Regression vs Logistic Regression | Learn Data Science | Great learning

Logistic regression graph

### 7. Correlation between independent variables

A linear regression test model effectively determines correlations between multiple variables.A simple linear regression tends to define the correlation between the dependent and independent variables.You can also use multiple linear regression to identify one or more possible correlations between variables. The phenomenon of correlation is very similar to the cause and effect relationship.

On the other hand, in logistic regression, the independent variables do not share any correlation. Here the independent variables are all independent and there are no dependent variables for the occurrence of a correlation.

### 8. Weight of next observations

Linear regression uses the root mean square error (RMSE) to calculate the closest weight value for the data points (or observations) distributed across the regression line. On the other hand, logistic regression uses a precision method to predict the next weight value. The RSME method effectively assesses the accuracy of the linear model and helps determine the prediction errors indicated by the logistic model.

### 9. Activation Features

Regression models in machine learning use different onesactivation functionsmark aArtificial Intelligence Networkto activate a specific neuron. A linear regression model does not need such an activation function. However, when transforming a linear model into a logistic model, an activation function becomes essential.

In logistic regression, the sigmoid function is used as an activation function that transforms the result into a categorical value. The role activates the AI ​​system or network when certain parameters or criteria are met.

### 10. Interpretability

The linear and logistic probability models are given by the following equations:

p = eins0+ identical1X1+ identical2X2+ … + identicalUEXUE———(1) [Linear Model]

ln[p/(1-p)] = b0+b1X1+b2X2+ … + SecondskXk—— (2) [Logistikmodell]

Where p = probability.

From equations 1 and 2 it can be said that the probability (p) is considered as a linear function of the regressors for the linear model. Whereas for the logistic model, the log p/(1-p) probabilities are considered as a linear function of the regressors.

Considering the previous equations, it can be said that the linear model is more interpretable than the logistic model. For example, consider a1than 0.07 in Equation 1. This implies that a single unit in x increases1increases the probability of y by 7 percentage points.

Now consider equation 2 of the logistic model. Let's consider b10.07, this implies a 0.07 increase in the log odds of y for a single unit increase in x1🇧🇷 This makes the interpretation of the general scenario complex.

(Video) Linear Regression Vs Logistic Regression - Machine Learning | Code Fantasy

### 11. Golden Rule

In situations where you are modeling extreme probabilities (probability closest to 0 or 1), you may prefer logistic regression. However, if the probabilities are somewhere in the middle, say between 0.30 and 0.70, you can opt for linear regression. Although linear and logistic regression work equally well in this case, linear regression is easier to interpret than the logistic model.

Consider a use case where you model the likelihood of a search. Almost all modeled probabilities will necessarily fall between 0.25 and 0.75.A linear probability model may be appropriate here due to its ease of interpretation.

On the other hand, if you model the probability of whether or not an ATM transaction is fraudulent, the modeled probabilities range from 0.000003 to 0.25. This use case is designed for the logistic model and the linear model doesn't work well here.

### 12. Computing Speed

Linear and logistic models work with different computing speeds. Logistic regression uses an iterative maximum likelihood process to fit the model, slowing it down from the start. This computational speed slowdown may not be apparent when using a small data set or fitting a simple model. However, the situation gets worse when a larger data set comes into play or when a complex model is fitted.

In contrast, the linear probability model is faster than the logistic model because it cannot be predicted iteratively using the "ordinary least squares" method.

### 13. Applications

Both regression models are used in a variety of applications. In particular, linear regression has applications in data science, economics, finance, and marketing.

• business ideas: Companies use linear regression for developmentbusiness ideasto help them streamline and optimize their operations in line with market trends. The various parameters tracked using linear regression include evaluating trends, determining consumer bias or behavior, making sales forecasts, and estimating profit or loss margins. In a way, these linear models drive the overall performance of the organization.
• market analysis: Companies conduct a thorough analysis of the market using linear regression models. Various marketing strategies are evaluated as companies focus on the factors that affect the overall sale of a product or service such as: B. price, design, marketing campaigns and promotions.
• Financial risk assessment: Linear regression is commonly used by analysts in the finance vertical. It is used for return forecasting, portfolio management and asset valuation. These models play a crucial role in determining the relationship between the estimated returns on the assets and the associated market risk.

Likewise, logistic regression has the following applications:

• medicine: Logistic regression can be used by physicians who wish to examine the effect of vigorous jogging and running on the likelihood of knee injury in an athlete. The response variable in this case is equal to "knee injury" and gives two possible outcomes:
1. A serious knee injury.
2. A minor knee injury.

The model output will rationalize how intense jogging and running can affect an athlete's likelihood of knee injury.

• credit-worthiness: Automated credit scoring can be achieved through developmentprediction modelswith logistic regression. Various parameters such as account status, credit history, marital status, gender and others are taken into account when calculating credit scores. As the number of variables considered increases, logistic models tend to provide accurate predictions in most cases.
• Customer Behavior Tracking: The logistic regression is aMachine Learning Modelthat tracks customer behavior across online platforms, social networking services and even video game services.These models are fast, self-learning and easy to interpret. This makes them ideal for automating functions and enhancing the overall end-user experience.
• hotel reservations: Many hotel booking websites and apps use logistic regression to predict traveler behavior, interests, and intentions. This data is used to recommend future vacation destinations and accommodation options to travelers. The models are based on historical user data showing how users interact with your websites. This increases the chances that users will finalize a particular hotel for the upcoming holiday season.
• text editing: Logistic regression models are used by various text editing tools that identify and correct errors of various kinds, such as B. Grammar errors, syntax errors, typos and even structural errors in sentences. It is also possible to train these models to identify and flag offensive words, morally insensitive words, and others based on user choices and available software features.

See more:Top 10 AI Companies in 2022

### To learn

Regression analysis identifies trends in data by revealing a relationship between a set of dependent and independent variables.It is a crucial machine learning and statistical analysis tool that predicts outcomes, predicts data, and determines dependencies between variables.

Both linear and logistic regression represent the two types of the same regression analysis, where linear regression predicts a continuous outcome while logistic regression produces a discrete value. In simple terms, regression is done by linear regression while classification is done by logistic regression.

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## FAQs

### What is the difference between multiple linear and logistic regression? ›

The relation between Linear and Logistic Regression is the fact that they use labeled datasets to make predictions. However, the main difference between them is how they are being used. Linear Regression is used to solve Regression problems whereas Logistic Regression is used to solve Classification problems.

What is the main difference between linear regression and logistic regression Mcq? ›

Linear Regression is mostly used for evaluating regression problems. Logistic regression is mostly preferred to solve classification problems.

What 3 things tell us that linear regression is appropriate for the data? ›

Three major uses for regression analysis are (1) determining the strength of predictors, (2) forecasting an effect, and (3) trend forecasting.

How is logistic regression different from linear regression cost function? ›

The cost functions of linear and logistic regressions are different. The linear regression cost function is the sum of the squared errors, while the logistic regression cost function is the negative log-likelihood.

Is there a difference between linear regression and logistic regression? ›

Linear regression is used for predicting the continuous dependent variable using a given set of independent features whereas Logistic Regression is used to predict the categorical. Linear regression is used to solve regression problems whereas logistic regression is used to solve classification problems.

What is the major similarity between linear and logistic regression models? ›

Similarities between Linear Regression & Logistic Regression

There are very few similarities between the two regression models. Both are supervised machine learning algorithms. Both the regression model uses the linear equation for prediction.

What are the similarities and differences between linear regression and logistic regression? ›

Linear regression is used to predict the continuous dependent variable using a given set of independent variables. Logistic Regression is used to predict the categorical dependent variable using a given set of independent variables. Linear Regression is used for solving Regression problem.

Which of the following correctly describes a difference between linear and logistic regression? ›

The main difference between logistic and linear regression is that logistic regression provides a constant output, while linear regression provides a continuous output. In logistic regression, the outcome, or dependent variable, has only two possible values.

What are the 3 types of logistic regression? ›

There are three main types of logistic regression: binary, multinomial and ordinal.

Is multiple regression and multiple linear regression the same? ›

Multiple linear regression (MLR), also known simply as multiple regression, is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. Multiple regression is an extension of linear (OLS) regression that uses just one explanatory variable.

### What are the three types of multiple regression? ›

There are several types of multiple regression analyses (e.g. standard, hierarchical, setwise, stepwise) only two of which will be presented here (standard and stepwise).

Why do we use multiple logistic regression? ›

The goal of a multiple logistic regression is to find an equation that best predicts the probability of a value of the Y variable as a function of the X variables. You can then measure the independent variables on a new individual and estimate the probability of it having a particular value of the dependent variable.

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Last Updated: 08/09/2023

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