The Following Estimated Regression Equation Has Been Proposed to Predict $\hat { y } = 18 - 2 x _ { 1 } + 7 x _ { 2 } + 15 x _ { 3 }$

question 43

Essay

The following estimated regression equation has been proposed to predict sales at a fast food outlet.
​ $\hat { y } = 18 - 2 x _ { 1 } + 7 x _ { 2 } + 15 x _ { 3 }$
where
$x _ { 1 } =$ the number of competitors within 1 mile
$x _ { 2 } =$ the population within 1 mile (in $\left. 1000 \mathrm {~s} \right)$
$x _ { 3 } = 1$ if drive-up windows are present; 0 otherwise
$\widehat { y } =$ estimated sales $($ in $\$ 1000 \mathrm {~s} )$
a.
What is the interpretation of 15 (the coefficient of x₃) in the regression equation?
b.
Predict sales for an outlet with 2 competitors, a population of 10,000 within one mile, and one drive-up window (give the answer in dollars).
c.
Predict sales for an outlet with 2 competitors, a population of 10,000 within one mile, and no drive-up window (give the answer in dollars).

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