The primary usage of the linear regression model is to quantify the relationship between the dependent variable Y (also known as the response variable) and the independent variable/s X (also known as the predictor, driver, or regressor variables) in a linear manner. In other words, the model expresses the dependent variable as a linear combination of the independent variables. A linear relationship between the dependent and independent variables can be generalized by the following equations:
- In the case of a single independent variable, the equation is as follows:
- For n independent variables, the equation looks as follows:
The model variables for these equations are as follows:
- i represents the observations index, i = 1,..., N
- Yi represents the i observation of the dependent variable
- Xj,i represents the i value of the j independent variable, where...