Consider the second-order model $$\hat { y } = - 3.24 + 1.12 x _ { 1 } + 2.57 x _ { 2 } - 3.22 x _ { 1 } x _ { 2 } + 5.78 x _ { 1 } ^ { 2 } = 4.69 x _ { 2 } ^ { 2 }$$
If $x _ { 2 }$ is held fixed at $x _ { 2 } = 3$, describe the relationship between $y$ and $x _ { 1 }$.
A) The relationship between $y$ and $x _ { 1 }$ is quadratic with downward concavity.
B) The relationship between $y$ and $x _ { 1 }$ is linear with negative slope.
C) The relationship between $y$ and $x _ { 1 }$ is quadratic with upward concavity.
D) The relationship between $y$ and $x _ { 1 }$ is linear with positive slope.

Question

Quizplus · Accepted Answer

The presence of $x_1^2$ with a positive coefficient (5.78) in the equation indicates a quadratic relationship between $y$ and $x_1$, with upward concavity since the coefficient of $x_1^2$ is positive.

Consider the Second-Order Model y^=−3.24+1.12x1+2.57x2−3.22x1x2+5.78x12=4.69x22\hat { y } = - 3.24 + 1.12 x _ { 1 } + 2.57 x _ { 2 } - 3.22 x _ { 1 } x _ { 2 } + 5.78 x _ { 1 } ^ { 2 } = 4.69 x _ { 2 } ^ { 2 }y^​=−3.24+1.12x1​+2.57x2​−3.22x1​x2​+5.78x12​=4.69x22​

Consider the Second-Order Model $\hat { y } = - 3.24 + 1.12 x _ { 1 } + 2.57 x _ { 2 } - 3.22 x _ { 1 } x _ { 2 } + 5.78 x _ { 1 } ^ { 2 } = 4.69 x _ { 2 } ^ { 2 }$