Which of the following statements is (are) true with respect to the standard error of estimates?

I. In essence, the standard error of estimate gives an indication as to how imperfect the regression model is.
II. If the dependent variables are normally distributed, it can be concluded that 68% of all possible future observations will lie within one standard error of estimate of the regression line.
III. The standard error of estimate may be used to compute confidence intervals around historical data and projected data.
IV. The standard error associated with a predicted value for the dependent variable will always be greater than the standard error of estimate.

Correct Answer: I and IV

II is incorrect because if the dependent variables are normally distributed, it can be concluded that 68% of all "historical observations" will lie within one standard error of estimate of the regression line. Consequently, (III) is incorrect as well.

IV is correct because when predicting values for the dependent variable, there are other sources of error in addition to the standard error of estimate. Namely, the regression equation itself is a composite of variables. Hence, the errors associated with the regression coefficient can cause greater dispersion between the predicted values for the dependent variable and its actual outcome.