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

question 68

Short Answer

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

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

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Definitions:

Marginal Tax Rate

The tax rate that applies to each additional dollar of income, indicating how much of the next dollar earned will be taken in taxes.

Average Tax Rate

Average Tax Rate is the proportion of the total income paid as taxes, calculated by dividing the total taxes by the total taxable income.

Total Taxes

The combined amount of all the taxes imposed by a government on an individual or business, including income tax, property tax, sales tax, etc.

Average Tax Rate

The proportion of total income that is paid in taxes, calculated by dividing the total tax paid by the total income.