In a multiple regression model, the values of the error term are assumed to be what?

In a multiple regression model, one of the key assumptions is that the values of the error term are independent of each other. This means that the error associated with one observation does not influence or predict the error associated with another observation. This independence is crucial because it allows for the proper estimation of regression coefficients and ensures that the statistical tests applied to these coefficients are valid. If the errors were dependent, it could lead to biased estimates and incorrect conclusions about the relationships being studied.

While other aspects of the error term, such as normal distribution and constant variance (homoscedasticity), are also important assumptions in regression analysis, the independence of errors is foundational for many of the inferential statistics that follow from the model. This independence assumption ensures that the model's residuals (error terms) provide a valid basis for assessing model fit and making predictions.