Linear Regression

Definition

Linear regression is a classical statistical tool that models relationship between a dependent variable or regress and Y, explanatory variable or regressor X = {x₁, … , x_I} and a random term ε by fitting a linear function,

$$ Y={\alpha}_{+}{\alpha}_1{x}_1+{\alpha}_2{x}_2+\dots +{\alpha}_I{x}_I+\varepsilon $$

where α₀ is the constant term, the α_is are the respective parameters of independent variable, and I is the number of parameters to be estimated in the linear regression.

Key Points

Linear regression analysis is an important component for several tasks such as clustering, time series analysis, and information retrieval. For instance, it is a very powerful forecasting method for time series data. It helps identify the long-term movement of a certain data set based on given information and explore the dependent variable as function of time.

To solve the linear regression problem, there are various kinds of approaches available to determine suitable regression coefficients [