Consider the model described by the equation $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \beta _ { 3 } x ^ { 3 }$$ .Which term provides a nonlinear component to the model enabling the line to reverse the direction of curvature?
A)$\beta _ { 0 }$
B)$\beta _ { 1 } x$
C)$\beta _ { 2 } x ^ { 2 }$
D)$\beta _ { 3 } x ^ { 3 }$

Question

Quizplus · Accepted Answer

The term $\beta _{3}x^3$ provides a nonlinear component to the model that can cause the line to reverse the direction of curvature because it is an odd-degree term. As x values become more negative, the term $\beta_{3}x^3$ becomes more negative, pulling the curve downward. Conversely, as x values become more positive, the term $\beta_{3}x^3$ becomes more positive, pushing the curve upward. This can cause the curvature of the line to reverse direction, creating an "S" shape. None of the other terms provide this type of nonlinearity.

Consider the Model Described by the Equation E(y)=β0+β1x+β2x2+β3x3E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \beta _ { 3 } x ^ { 3 }E(y)=β0​+β1​x+β2​x2+β3​x3

Consider the Model Described by the Equation $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \beta _ { 3 } x ^ { 3 }$