What is one of the assumptions about the error term ε in regression analysis concerning its values?

In regression analysis, one of the key assumptions concerning the error term ε is that they are independent. This means that the errors associated with different observations are not correlated with one another. Independence of the error terms is crucial because if the errors are correlated, it can lead to biased estimates of the regression coefficients and incorrect conclusions about the relationships between the variables.

The assumption of independence helps ensure that the estimates of the regression parameters are efficient and the statistical tests based on these estimates are valid. If the errors are independent, it indicates that each observation provides unique information about the relationship we are studying, allowing for more reliable inferences.

In contrast, other options suggest various characteristics of the error terms that are not assumptions typically required in regression analysis. For instance, while normality of the errors can be an assumption for certain types of statistical testing, it is not a required condition for all regression models. Similarly, having all values being positive or dependent would contradict the goal of regression modeling, where errors can be positive or negative and should not exhibit dependence across observations.