Linear regression is a statistical method used to model the relationship between a dependent variable (target) and one or more independent variables (features). The main idea is to find the best-fitting straight line (or hyperplane in higher dimensions) that predicts the target variable based on the input features.
The linear regression model can be expressed mathematically as:
y = w_0 + w_1x_1 + w_2x_2 + ... + w_nx_n + \epsilon
Where:
- ( y ) is the predicted value (dependent variable).
- ( w_0 ) is the intercept.
- ( w_1, w_2, ..., w_n ) are the coefficients (weights) for each feature.
- ( x_1, x_2, ..., x_n ) are the independent variables (features).
- ( \epsilon ) is the error term.
The goal of linear regression is to minimize the difference between the observed values and the predicted values, typically using the method of Ordinary Least Squares (OLS), which minimizes the sum of the squared differences between the observed and predicted values.
