3.5 An Estimator of σ^2

Question 1

Estimation of σ^2 and σ for the Straight-Line (First-Order) Model

Answer 1

Question 2

Interpretation of s, the Estimated Standard Deviation of ε

Answer 2

Question 3

Def coefficient of variation

Answer 3

The value of CV for the advertising–sales example, highlighted on Figure 7, is CV = 30.3. This implies that the value of s for the least squares line is 30% of the value of the sample mean sales revenue, y¯. As a rule of thumb, most regression analysts desire regression models with CV values of 10% or smaller (i.e., models with a value of s that is only 10% of the mean of the dependent variable). Models with this characteristic usually lead to more precise predictions. The value of s for the advertising–sales regression is probably too large to consider using the least squares line in practice