Linear and Logistic Regression

Linear regression and logistic regression are two of the most fundamental algorithms in machine learning. Despite the shared name, they solve different tasks: linear regression predicts continuous values (regression), while logistic regression predicts discrete categories (classification).

---

Linear Regression

Linear regression models the relationship between one or more input features and a continuous target variable by fitting a straight line (or hyperplane in multiple dimensions) through the data.

Simple Linear Regression

With one feature, the model is:

y = w * x + b

Where:

• y is the predicted value
• x is the input feature
• w (weight/slope) is the coefficient
• b (bias/intercept) is the y-intercept

Multiple Linear Regression

With multiple features, the model becomes:

y = w1 * x1 + w2 * x2 + ... + wn * xn + b

How Linear Regression Learns

Linear regression finds the line of best fit by minimising the sum of squared residuals (Ordinary Least Squares — OLS).