Linear regression and logistic regression are both techniques used in statistical modeling and machine learning, but they serve different purposes and are applied to different types of problems. Here are the key differences between linear and logistic regression:
Linear Regression:
Type of Output:
Linear Regression: Predicts a continuous output variable. The output can take any real value within a range.
Use Cases:
Linear Regression: Commonly used for predicting values such as house prices, temperature, sales amounts, or any other continuous variable.
Equation:
Linear Regression: The equation of a linear regression model is a linear combination of the input features, each multiplied by a weight, and summed up.
Output Interpretation:
Linear Regression: The output is interpretable as the predicted value for the target variable.
Assumption:
Linear Regression: Assumes a linear relationship between the input features and the output variable.
Activation Function:
Linear Regression: Does not use an activation function. The output is a direct linear combination of the input features.
Logistic Regression:
Type of Output:
Logistic Regression: Predicts the probability of an event occurring, and the output is a probability between 0 and 1.
Use Cases:
Logistic Regression: Commonly used for binary classification problems, where the target variable has two classes (e.g., spam or not spam, fraud or not fraud).
Equation:
Logistic Regression: Applies the logistic function (sigmoid function) to the linear combination of input features, transforming the output into a probability.
Output Interpretation:
Logistic Regression: The output represents the probability of the event occurring. A threshold (commonly 0.5) is used to classify the instance into one of the two classes.
Assumption:
Logistic Regression: Assumes a linear relationship between the log-odds of the probability and the input features.
Activation Function:
Logistic Regression: Uses the sigmoid activation function to squash the output into the range (0, 1), representing probabilities.
Summary:
Linear Regression: Used for predicting continuous numerical values. The output is a direct linear combination of input features.
Logistic Regression: Used for binary classification problems. The output is a probability between 0 and 1, transformed using the logistic function (sigmoid function).
In both cases, the models are trained by adjusting weights to minimize the difference between predicted and actual outcomes, but the nature of the outcomes and the mathematical formulation of the models distinguish linear and logistic regression.