At its heart, Linear Regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It is the ultimate gateway into supervised machine learning.
1The Geometry of Prediction
If you recall high school algebra, the equation of a line is y = mx + b. In machine learning, we express this as y = wX + b, where 'w' is the weight (slope) and 'b' is the bias (intercept). The goal of the algorithm is to find the values of 'w' and 'b' that result in the smallest possible error across all training examples.
2Ordinary Least Squares (OLS)
How does the model find the *best* line? It uses a technique called Ordinary Least Squares. It calculates the 'residual' (the gap between a real data point and the model's line) for every example, squares them to penalize large errors, and then minimizes the total sum of these squares.
3Implementation Workflow
Using Scikit-Learn, the process is streamlined into three steps:
1. Instantiate: model = LinearRegression()
2. Fit: model.fit(X, y) where X is a 2D matrix of features.
3. Predict: model.predict(X_new) to get your numerical outcome.
