Regression 2. Linear Regression - An Overview

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 Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. 

Goal

The goal is to find a linear equation that best predicts the dependent variable from the independent variables. 

Types of Linear Regression

There are two main types of linear regression:

1. Simple Linear Regression: 

This involves two variables - one independent variable (predictor) and one dependent variable (response). The relationship between these variables is modeled with a straight line (linear). The equation for simple linear regression is:


2. Multiple Linear Regression: 

This extends simple linear regression by using more than one independent variable to predict the dependent variable. The equation is:


Key Concepts in Linear Regression:

Fit of the Model: 

The process of "fitting" a linear regression model involves estimating the coefficients w_i based on the available data. This is typically done using a method called least squares, which minimizes the sum of the squared differences between observed values and model-predicted values.

Interpretation: 

The coefficients in the linear regression equation represent the expected change in the dependent variable for a one-unit change in an independent variable, holding all other variables constant (in the case of multiple regression).

Assumptions: 

Linear regression has several key assumptions, including linearity, independence, homoscedasticity (constant variance of errors), and normality of error terms.

Use Cases: 

Linear regression is widely used in various fields for predictive modeling, trend analysis, and causal inference. It's particularly useful when the relationships between variables are expected to be approximately linear.

Limitations: 

Linear regression is not suitable for modeling complex relationships that are not linear in nature. It also doesn’t handle overfitting well and is sensitive to outliers.

Linear regression is a fundamental technique in statistics and machine learning, providing a simple yet powerful tool for understanding and predicting relationships between variables.

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