Linear regression is a statistical method used to understand the relationship between variables and make predictions. It has assumptions about linearity, independence, homoscedasticity, normality of residuals, no multicollinearity, and no influential outliers. It is popular due to its simplicity, interpretability, and usefulness for modeling continuous outcomes. The algorithm involves calculating coefficients using mathematical equations and can be extended to multiple dimensions using matrix notation. Regularization techniques like L1 and L2 can be used to prevent overfitting. R2 score is a metric used to assess the model's fit to the data.
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