One assumption about the error term ɛ in regression analysis is that its mean or expected value is what?

In regression analysis, one of the fundamental assumptions about the error term (often denoted as ɛ) is that its mean or expected value is zero. This assumption implies that the model does not systematically overestimate or underestimate the dependent variable. If the mean of the error term was not zero, it would indicate that there is some bias in the predictions made by the regression model, leading to systematic errors in the estimation of the dependent variable.

When the expected value of the error term is zero, it allows for the interpretation that the model's predictions are accurate on average, meaning that any individual prediction may be higher or lower than the actual value, but these deviations will balance out to zero across many observations. This condition is critical for ensuring the validity of statistical inferences made from the regression analysis, such as hypothesis testing and the accuracy of confidence intervals.

In summary, the assumption that the expected value of the error term is zero is essential for producing unbiased estimates in regression analysis, thereby supporting the overall reliability and interpretability of the model.