Error Term Assumptions in Multiple Regression

In multiple regression analysis, certain assumptions must be met for the model to yield valid results. One of the key assumptions relates to the error terms in the regression model. Consider a multiple regression model represented as follows:

$$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + ... + \beta_nX_n + \epsilon$$

where:

• $$Y$$ is the dependent variable,
• $$X_1, X_2, ..., X_n$$ are the independent variables,
• $$\beta_0, \beta_1, \beta_2, ..., \beta_n$$ are the coefficients, and
• $$\epsilon$$ is the error term.

Which of the following assumptions must hold true regarding the error term $$\epsilon$$ in multiple regression analysis?