Determine which of the following statements is NOT true about the equation

[[math]] Y = \beta_0 + \beta_1X + \epsilon [[/math]]

• [math]\beta_0[/math] is the expected value of [math]Y[/math] .
• [math]\beta_1 [/math] is the average increase in [math]Y[/math] associated with a one-unit increase in [math]X[/math].
• The error term, [math]\epsilon[/math] , is typically assumed to be independent of [math]X[/math].
• The equation defines the population regression line.
• The method of least squares is commonly used to estimate the coefficients [math]\beta_0[/math] and [math]\beta_1[/math].

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: A

(A) is false. [math]\beta_0[/math] is the expected value of Y when X = 0. The other four statements are true (see Page 63 of James, et al.)

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.