What is the difference between a residual and an independent variable in a multiple linear regression? I’ve provided an example below. I understand the concepts of the independent and dependent variable, but I realized that was using the concept of an independent variable and a residual interchangeably. Thanks!
Yi = b0 + b1X1i + b2X2i + E
The Xs are the independent variables, and E (properly, εi) is the residual.
Errors and residuals aren’t technically the same, but I’ll use them interchangeably for simplicity.
The residuals are the “left over” portion of Y that the function of independent variables aren’t able to explain. Think of Y as comprising two parts one of which is “explainable” by the betas and X’s and the other of which is unexplainable and represented by the errors that follow a specified distribution.
Thank you!!