In regression analysis, what is the expected value of the error term ε?

In regression analysis, the expected value of the error term, denoted as ε, is fundamentally understood to be zero. This stems from the assumption that errors are random deviations from the true regression line.

When a regression model is fitted to data, it aims to minimize the discrepancies between the observed values and the values predicted by the model. The errors represent the difference between these observed values and the values estimated by the regression equation. A key assumption in linear regression is that these errors average out to zero—meaning that, on average, the errors do not systematically underpredict or overpredict the dependent variable. This assumption is necessary for the validity of statistical inferences made from the regression output, such as hypothesis testing about the coefficients.

If the expected value of the error was something other than zero, it would imply that there might be systematic bias in the predictions, which contradicts the purpose of regression analysis aiming for an unbiased estimate of relationships. Therefore, the correct answer is that the expected value of the error term ε is zero.