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

Multiple Choice

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 $\hat { y }$ and $x _ { 1 }$ .

A) The relationship between $\hat { y }$ and $x _ { 1 }$ is linear with negative slope.
B) The relationship between $y$ and $x _ { 1 }$ is quadratic with upward concavity.
C) The relationship between $\hat { y }$ and $x _ { 1 }$ is linear with positive slope.
D) The relationship between $\hat { y }$ and $x _ { 1 }$ is quadratic with downward concavity.