What is the Difference Between Linear and Logistic Regression?

Linear and logistic regression are both statistical methods used for modeling relationships between variables, but they serve different purposes and have distinct characteristics. Here are the key differences between linear and logistic regression:

1. Outcome Type:

• Linear regression is used with continuous outcome variables, which have numeric values (e.g., height, temperature).
• Logistic regression is used with categorical outcome variables, which have non-numeric values (e.g., binary outcomes like "yes" or "no").

1. Mathematical Equations:

• Linear regression models use a linear equation to represent the relationship between the dependent variable and independent variables: $$y = a0 + a1x1 + a2x2 + … + aix_i$$.
• Logistic regression models use a series of mathematical transformations and a logistic function to estimate the probability of a categorical outcome.

1. Interpretation:

• Linear regression predictions can be directly interpreted as the expected value of the dependent variable given the independent variables.
• Logistic regression predictions require an additional step to convert the predicted probabilities into class labels (e.g., using a threshold). This makes the interpretation of logistic regression results slightly more complex.

In summary, linear regression is used to model the relationship between continuous variables, while logistic regression is used to model the relationship between independent variables and binary or categorical outcomes. The mathematical equations used in these models are different, as are the interpretations of their predictions.

Comparative Table: Linear vs Logistic Regression

Here is a table outlining the key differences between linear and logistic regression:

In summary:

• Linear regression is used for predicting continuous outcomes based on predictor variables, while logistic regression is used for predicting binary outcomes based on predictor variables.
• Linear regression models rely on a continuous dependent variable, whereas logistic regression models rely on binary dependent variables.
• The mathematical equation for linear regression involves the summation of the product of the intercept and the independent variables, while the equation for logistic regression is a sigmoid function that maps the input values onto a categorical variable depending on their position.
• Linear regression uses the ordinary least squares method to minimize errors, while logistic regression uses maximum likelihood estimation.