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.

Question

Quizplus · Accepted Answer

To compare the prices of homes in four different neighborhoods using a regression model, one would typically use dummy variables to represent the qualitative neighborhood variable. Since there are four neighborhoods, three dummy variables ($x_1, x_2, x_3$) are needed to encode the neighborhoods, with the fourth neighborhood being represented by the absence of these three (all zeros). This is why option B is correct, as it correctly sets up a model with three dummy variables for the four neighborhoods.

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

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