Which method predicts the probability of an event based on independent variables and is commonly used for binary classification?

Which method predicts the probability of an event based on independent variables and is commonly used for binary classification?

• A. Linear Regression
• B. K-Means Clustering
• C. Logistic Regression
• D. Support Vector Machines

Answer: (C)

This question is about modeling the probability of a binary event using a method that yields probability estimates based on several input features. The best fit is logistic regression. It takes a linear combination of the predictors, z = β0 + β1X1 + β2X2 + ... , and maps it through a sigmoid function to produce a probability: P(Y=1|X) = 1 / (1 + exp(-z)). The coefficients are typically estimated by maximum likelihood, which aligns the model’s predicted probabilities with the observed outcomes. Logistic regression is ideal for binary classification because its output is always between 0 and 1, making it easy to interpret as a probability. It works with multiple predictors (continuous or categorical, once encoded), and the coefficients tell you how each predictor changes the odds of the event. You can then choose a decision threshold (commonly 0.5, but adjustable) to assign class labels. In contrast, linear regression predicts a continuous outcome and can give values outside the 0–1 range, which isn’t meaningful for probability. K-means clustering is an unsupervised method for grouping data, not for predicting event probabilities. Support vector machines focus on creating a decision boundary; while probabilistic outputs can be obtained with additional calibration, SVMs aren’t inherently modeling probabilities in the straightforward way logistic regression does.

This question is about modeling the probability of a binary event using a method that yields probability estimates based on several input features. The best fit is logistic regression. It takes a linear combination of the predictors, z = β0 + β1X1 + β2X2 + ... , and maps it through a sigmoid function to produce a probability: P(Y=1|X) = 1 / (1 + exp(-z)). The coefficients are typically estimated by maximum likelihood, which aligns the model’s predicted probabilities with the observed outcomes.

Logistic regression is ideal for binary classification because its output is always between 0 and 1, making it easy to interpret as a probability. It works with multiple predictors (continuous or categorical, once encoded), and the coefficients tell you how each predictor changes the odds of the event. You can then choose a decision threshold (commonly 0.5, but adjustable) to assign class labels.

In contrast, linear regression predicts a continuous outcome and can give values outside the 0–1 range, which isn’t meaningful for probability. K-means clustering is an unsupervised method for grouping data, not for predicting event probabilities. Support vector machines focus on creating a decision boundary; while probabilistic outputs can be obtained with additional calibration, SVMs aren’t inherently modeling probabilities in the straightforward way logistic regression does.