The shape of the model described by the equation $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$ could be:
A) parabolic resembling an upright"U".
B) parabolic resembling an upside-down"U".
C) a straight line with an intercept $\beta _ { 0 }$ and slope $\beta _ { 2 } / \beta _ { 1 }$ .
D) a straight line with an intercept $\beta _ { 0 }$ and slope $\beta _ { 1 } / \beta _ { 2 } .$.
E) Both A and B.

Question

Quizplus · Accepted Answer

The equation $E(y) = \beta_0 + \beta_1x + \beta_2x^2$ represents a quadratic equation, which graphically is a parabola. Depending on the sign and magnitude of $\beta_2$, the parabola can open upwards (resembling an upright "U") or downwards (resembling an upside-down "U"). Choices A and B are both possible shapes for this model, making E the correct answer.

The Shape of the Model Described by the Equation E(y)=β0+β1x+β2x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }E(y)=β0​+β1​x+β2​x2

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