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# Linear Regression vs Logistic Regression

## What is Linear Regression?

Linear regression is used to find the relationship between two variables, where one variable (the dependent variable) can be predicted based on the other variable (the independent/target variable) through a linear equation. In simple terms, it's like drawing a straight line through a set of points to understand the trend or pattern in the data.

## What is Logistic Regression?

Logistic regression is used to model the probability of a binary outcome (e.g., success/failure, yes/no) based on one or more predictor variables. It's called "logistic" because it's an extension of linear regression but applied to predict probabilities between 0 and 1, which are then transformed using a logistic function to make predictions about the likelihood of a particular outcome. It's commonly used in situations where the outcome variable is categorical.

## Difference between Linear Regression and Logistic Regression

Both linear regression and logistic regression are types of regression analysis, which means they are used to analyze the relationship between one or more independent variables and a dependent variable. Both types of models can be used for prediction tasks. Linear regression predicts a continuous outcome variable, while logistic regression predicts the probability of a binary outcome.

Despite these similarities, linear regression and logistic regression are used in different scenarios due to the nature of the dependent variable (continuous for linear regression, categorical for logistic regression).

The below image represents the graphical differences between Linear and Logistic Regression:

Image Source: www.ejable.com

The following table summarizes the comparison of linear and logistic regression.

 Linear Regression Logistic Regression Type of supervised learning Linear regression is primarily used for solving Regression tasks and predict a continuous outcome variable such as price and age. Logistic regression is primarily used for solving classification tasks and predict the probability of an instance belonging to a particular class in binary classification such as 0 or 1, True or False. Outcome Variable Continuous and numeric. Binary or categorical. Variable relationship In Linear regression, the relationship between the dependent and independent variables must be linear. The relationship between the dependent and independent variables DOES NOT need to be linear. Purpose The purpose of Linear Regression is to find the best-fitted line. The purpose of the Logistic regression is one step ahead and fit the line values to the sigmoid curve. Use Cases Examples: Predicting house prices, stock prices, temperature, etc. Examples: Spam detection, disease diagnosis, customer churn prediction. Assumptions Assumes a linear relationship, normal distribution of errors, and homoscedasticity. Assumes a log-odds linear relationship, absence of multicollinearity, and independence of errors. Evaluation Metrics Mean Squared Error (MSE), R-squared. Accuracy, precision, recall, F1 score, ROC-AUC Best suited for Tasks requiring a predicted continuous dependent variable from a scale. Tasks requiring a predicted likelihood of a categorical dependent variable occurring from a fixed set of categories.

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