Linear regression

Linear regression is a statistical analysis technique used to understand the relationship between two variables. It is a fundamental tool in statistics, machine learning, and data science.

Overview

Linear regression models the relationship between two variables by fitting a linear equation to observed data. The steps to perform linear regression are:

1. Collect and prepare data
2. Choose the type of regression to use
3. Create the model
4. Check the model fit
5. Make predictions

Types of Linear Regression

There are two types of linear regression:

1. Simple linear regression: One independent variable and one dependent variable
2. Multiple linear regression: More than one independent variable and one dependent variable

Assumptions of Linear Regression

Linear regression makes several assumptions:

1. Linearity: The relationship between the independent and dependent variable is linear.
2. Independence: The observations are independent of each other.
3. Homoscedasticity: The variance of the errors is constant across all levels of the independent variables.
4. Normality: The errors of the prediction will follow a normal distribution.

Applications of Linear Regression

Linear regression is used in various fields including:

1. Economics: To understand the economic factors affecting business
2. Finance: To predict stock prices
3. Healthcare: To predict disease trends
4. Machine Learning: As a prediction algorithm

See Also

• Regression analysis
• Correlation coefficient
• Ordinary least squares

• Linear least squares example
  Linear least squares example
• Polynomial regression example
  Polynomial regression example
• Heteroscedasticity in linear regression
  Heteroscedasticity in linear regression
• Independence of errors assumption for linear regressions
  Independence of errors assumption for linear regressions
• Anscombe's quartet example
  Anscombe's quartet example
• Linear regression
  Linear regression
• Galton's correlation diagram 1875
  Galton's correlation diagram 1875
• Thiel-Sen estimator
  Thiel-Sen estimator