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

Multiple Choice

It is desired to build a regression model to predict $\mathrm { y } =$ the sales price of a single family home, based on the neighborhood the home is located in. The goal is to compare the prices of homes that are located in four different neighborhoods. Which regression model should be built?

A) $\mathrm { E } ( \mathrm { y } ) = \beta _ { 0 } + \beta _ { 1 } \mathrm { x } _ { 1 }$ , where $\mathrm { x } _ { 1 }$ is a qualitative variable that describes the four neighborhoods.
B) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 }$ , where $x _ { 1 } - x _ { 3 }$ are qualitative variables that describe the four neighborhoods.
C) $\mathrm { E } ( \mathrm { y } ) = \beta _ { 0 } + \beta _ { 1 } \mathrm { x } _ { 1 } + \beta _ { 2 } \mathrm { x } _ { 2 } + \beta _ { 3 } \mathrm { x } _ { 3 } + \beta _ { 4 } \mathrm { x } _ { 4 }$ , where $\mathrm { x } _ { 1 } - \mathrm { x } _ { 4 }$ are qualitative variables that describe the four neighborhoods.
D) $\mathrm { E } ( \mathrm { y } ) = \beta _ { 0 } + \beta _ { 1 } \mathrm { x } _ { 1 } + \beta _ { 2 } \mathrm { x } _ { 1 } ^ { 2 }$ , where $\mathrm { x } _ { 1 }$ is a qualitative variable that describes the four neighborhoods.