It Is Desired to Build a Regression Model to Predict $\mathrm { y } =$

It is desired to build a regression model to predict $\mathrm { y } =$ the sales price of a single family home, based on the $x _ { 1 } =$ size of the house and $x _ { 2 } =$ the neighborhood the home is located in. The goal is to compare the prices of homes that are located in two different neighborhoods. The following complete 2nd-order model is proposed: $\mathrm { E } ( \mathrm { y } ) = \beta _ { 0 } + \beta _ { 1 } \mathrm { x } _ { 1 } + \beta _ { 2 } \mathrm { x } _ { 1 } ^ { 2 } + \beta _ { 3 } \mathrm { x } _ { 2 } + \beta _ { 4 } \mathrm { x } _ { 1 } \mathrm { x } _ { 2 } + \beta _ { 5 } \mathrm { x } _ { 1 } ^ { 2 } \mathrm { x } _ { 2 }$ .
What hypothesis should be tested to determine if the quadratic terms are necessary to predict the sales price of a home?

A) $\mathrm { H } _ { 0 } : \beta _ { 2 } = \beta _ { 5 } = 0$
B) $\mathrm { H } _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$
C) $\mathrm { H } _ { 0 } : \beta _ { 1 } = \beta _ { 3 } = \beta _ { 4 } = 0$
D) $\mathrm { H } _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = \beta _ { 5 } = 0$