An elections officer wants to model voter turnout (y)in a precinct as a function of the type of precinct. Consider the model relating mean voter turnout, $E ( y )$, to precinct type:
$$\begin{array} { l l }
E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } , \text { where } & x _ { 1 } = 1 \text { if urban, } 0 \text { if not } \
& x _ { 2 } = 1 \text { if suburban, } 0 \text { if not } \
& \text { (Base level } = \text { rural) }
\end{array}$$
Interpret the value of $\beta _ { 2 }$.
A) the difference between the mean voter turnout for suburban and rural precincts
B) the difference between the mean voter turnout for suburban and urban precincts
C) the mean voter turnout for suburban precincts
D) the rate of increase in voter turnout $( y )$ for suburban precincts, i.e., the slope of the $y - x _ { 2 }$ line

Question

An elections officer wants to model voter turnout (y)in a precinct as a function of the type of precinct. Consider the model relating mean voter turnout, $E ( y )$, to precinct type:
$$\begin{array} { l l } 
E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } , \text { where } & x _ { 1 } = 1 \text { if urban, } 0 \text { if not } \
& x _ { 2 } = 1 \text { if suburban, } 0 \text { if not } \
& \text { (Base level } = \text { rural) }
\end{array}$$
Interpret the value of $\beta _ { 2 }$.
A) the difference between the mean voter turnout for suburban and rural precincts
B) the difference between the mean voter turnout for suburban and urban precincts
C) the mean voter turnout for suburban precincts
D) the rate of increase in voter turnout $( y )$ for suburban precincts, i.e., the slope of the $y - x _ { 2 }$ line

Quizplus · Accepted Answer

The value of $\beta_2$ represents the difference in mean voter turnout between suburban precincts (where $x_2 = 1$) and the base level, which is rural precincts (where both $x_1 = 0$ and $x_2 = 0$). This is because when $x_2 = 1$ (suburban), the model adjusts the mean voter turnout by $\beta_2$ compared to the base level (rural), where $x_2 = 0$.

An Elections Officer Wants to Model Voter Turnout (Y)in a Precinct