Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. The goal of linear regression is to find the best-fitting line (or hyperplane in multiple dimensions) that summarizes the relationship between the dependent variable and the independent variables.
Linear regression models are used in a wide range of applications, from simple linear models with one independent variable to complex models with multiple independent variables and interaction effects.
The basic equation for a simple linear regression model with one independent variable is:
y = β_0 + β_1 * x
where y is the dependent variable, x is the independent variable, β_0 is the intercept, and β_1 is the slope of the line. The values of β_0 and β_1 are estimated from the data using methods such as ordinary least squares (OLS), and are used to make predictions about the dependent variable based on the independent variable.
In multiple linear regression, the basic equation is extended to include multiple independent variables:
y = β_0 + β_1 * x_1 + β_2 * x_2 + ... + β_p * x_p
where x_1, x_2, ..., x_p are the independent variables and β_1, β_2, ..., β_p are the corresponding coefficients.
Linear regression is a powerful and widely used tool in many fields, including economics, finance, marketing, engineering, and many others, as it provides a simple and effective way to model relationships between variables and make predictions based on those relationships.