planetdestroyyer / linear-regression-from-scratch-using-python-

Linear regression is a statistical method used for modeling the relationship between a dependent variable (target) and one or more independent variables (features).

Linear regression is a statistical method used for modeling the relationship between a dependent variable (target) and one or more independent variables (features). It assumes that the relationship between the variables is linear, meaning that a change in one independent variable is associated with a constant change in the dependent variable, holding all other variables constant.

The linear regression model is represented by the equation:

[ Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + ... + \beta_n*X_n + \epsilon ]

Where:

• ( Y ) is the dependent variable (target),
• ( X_1, X_2, ..., X_n ) are the independent variables (features),
• ( \beta_0, \beta_1, \beta_2, ..., \beta_n ) are the coefficients (parameters) representing the relationship between the independent variables and the dependent variable,
• ( \epsilon ) is the error term representing the difference between the observed and predicted values.

The goal of linear regression is to estimate the coefficients ( \beta_0, \beta_1, \beta_2, ..., \beta_n ) that minimize the sum of squared residuals (the vertical distance between the observed and predicted values) and provide the best fit line to the data.

Linear regression can be extended to handle multiple independent variables (multivariate linear regression) and can also be adapted for tasks such as polynomial regression, where the relationship between the variables is not strictly linear.

Linear regression is widely used in various fields, including economics, finance, social sciences, and engineering, for tasks such as prediction, forecasting, and understanding the relationship between variables.